treqna base manual ed

Treqna Base Manual

First Edition 1 © All Rights Reserved TreQna 2005

treqna.com

Treqna Base Manual


DEFINEStep D1 – Map Project Page 4 Step D2 – Approve Project Page 36

MEASUREStep M1 – CTQ Characteristics & Standards Page 45Step M2 – Measurement System Analysis Page 82Step M3 – Data Collection Plan Page 116

ANALYZEStep A1 – Baseline Process Page 145Step A2 – Performance Objective Page 191Step A3 – Identify drivers of Variation Page 197

IMPROVEImprove Step I1 – Screen for Vital Xs 93Improve Step I2 – Study Interaction between Xs Page 298Improve Step I3 – Define Improved Process Page 303

CONTROLControl Step C1 – MSA on Xs Page 317Control Step C2 – Improved Process Capability Page 319Control Step C3 – Establish Control Plan Page 321

C ontents

Treqna Base Manual


DEFINE

MEASURE

ANALYZE

IMPROVE

CONTROL

Map project

CTQ Characteristics and standards

Measurement System Analysis

Baseline process

Screen for vital X’s

Defined Improve Process

MSA on X’s

Approve project

Data collection

Performance objective

Identify drivers of variation

Study interaction between X’s

Improved Process capability

Establish control plan

Treqna Base Manual


Define Phase

DEFINE MEASURE ANALYZE IMPROVE CONTROL

Tools

Deliverables

Step

Step D.2Step D.1

CBAFMEA

Survey,Focus Group,Interview,Charter,COPIS

Project feasibilityProject CharterCOPIS

Approve projectMap project

Treqna Base Manual


Topics

About Projects

Customer, CTQs and VOC

COPIS

Project Charter

Treqna Base Manual


Characteristics of a good project

Should have clearly defined scope

Should have significant impact on customer

Should be in line with business objectives

Should have synergy with other projects (must not conflict)

Should be focused on key CTQ

Should generate bottom-line hard dollar benefits, Cost Avoidance or Productivity

increase

Treqna Base Manual


Sources for project ideas ?

Project topics usually surface as issues in a product or process. The project ideas

may also come from:

Customer dashboards

Customer Surveys

Other related projects

Internal issues

The tools which can be used to identify project ideas:

Brainstorming

QFD

Root cause analysis

Treqna Base Manual


Topics

About Projects

Customer, CTQs and VoC

COPIS

Project Charter

Treqna Base Manual


Who is the customer? Internal Customer or External Customer ?

Identifying the Customer

CustomerOutput Input

Supplier

Process

Customer receives the output of a process

Internal customer: E.g. Marketing person for manufacturing company is an

internal customer.

External customer: E.g. Buyer of the product or services

Treqna Base Manual


Critical to Quality (CTQ)

Customer to CTQ

External Customer Internal Customer

Customer driven CTQ’s Process driven CTQ’s

Identify Customer Capture customer requirement Derive and Define CTQ’s

CTQ’s from any process are translated from customer requirements

What is a CTQ?A CTQ (Critical to Quality) also known as a KPI (Key Process Indicator) is a metric that measure

some aspect of a product or process which is critical to the customer. The customer defines acceptable levels for CTQs using specification limits.

Treqna Base Manual


Voice of the Customer (VoC)

The "voice of the customer" is a process which is used to capture the

requirements/feedback from the customer (internal or external). It helps us

understand the customers expectations.

The voice of the customer can be captured in a variety of ways:

Direct discussion or interviews

Surveys

Focus groups

Complaints

Others ways like, Customer specifications, Observation, Field reports etc.

Treqna Base Manual


VOC Tools Evaluation

SurveyAdvantages:

Low administration cost

Relatively faster results in case of telephone

survey

Excellent approach to reach larger end customer

base

Least trained resources required to execute

Disadvantages:

Low response rate with Mail surveys

Unclear understanding by customer

Incomplete responses to mail surveys

Potential risk of biased response due to interviewer influence

Focus Groups

Advantages:

Help gather qualitative and in depth information

Excellent for understanding and getting CTQ

definitions

Not prone to understanding and interpretation

gaps

Disadvantages:

Bias due to limited participants

Limited data due to qualitative focus

Can have a lot of anecdotal information

Treqna Base Manual


Interviews

Advantages:

Complex questions can be asked and a wide

range of information gathered

Both qualitative and quantitative data can be

collected

Better communication and interpretation

Disadvantages:

Higher cost alternate

Time consuming

Requires trained, experienced resources to execute

Customer Complaints

Advantages:

Specific feedback

Provides opportunity to respond appropriately to

dissatisfied customer

Disadvantages:

Sample size issue

Situation specific, might be anecdotal

Prone to small sample bias

VOC Tools Evaluation

Treqna Base Manual


Survey Development

Objectives

Why is the survey needed?

Who will use the survey results?

What specific information is required with the help of this survey?

Who needs to be surveyed?

Logistics

How much time is available to administer the survey?

Who will conduct the survey?

What is the medium to conduct the survey?

What are the financial resources available to conduct the survey?

Design

Draft questions and validate against objectives.

Devise measurement scale.

Design report out structure

Administration

Determine sample size and sampling strategy

Pilot survey on selected group (ensure the methodology)

Designing survey question: Survey results will be meaningless unless you ask the right questions. The question must contain enough specifics so the respondent can give a meaningful answer.

Types of questions:•open questions: Open questions allow the customer to respond to a question in his or her own words.•closed questions. Closed questions offer the customer a choice of specific responses from which to select. Multiple choice, rating scale and yes/no questions are examples of closed questions.

Bias from Design of Questions: The questions you ask your customers must be properly worded in order to achieve good end results. Avoid the following:•Leading questions-They inject interviewer bias.•Compound questions-They may generate a partial or no response.•Judging questions-They can lead to guarded or partial responses.Ambiguous or vague questions-They produce meaningless responses•Acronyms and jargon-These may be unknown to the respondent.Double negatives-They may create misunderstanding.•Long surveys-They discourage respondent participation.

Other sources of bias in survey:Question sequenceSample BiasNo-response biasUnclear questions

Interviewer / facilitator induced bias

Treqna Base Manual


Understanding Customer Needs

Real vs. Stated Needs: Use questions like “Why do you want…?” until you understand the need

Perceived Needs: The same product or service may be perceived differently by customers

Intended vs. Actual Usage: Be careful of how customers say they will use a product/service versus how they actually use it.

Internal Customers: Internal customers have needs associated with job security, prestige, etc.

Effectiveness vs. Efficiency Needs: The external customer will generally express effectiveness needs–those relating to the value they receive from the product or service. The internal customer, however, will generally express efficiency needs, those relating to the amount of resources allocated or consumed in meeting customer needs.

Treqna Base Manual


Topics

About Projects


COPIS

Project Charter

Treqna Base Manual


COPIS

Puts process and customer in perspective

Depicts process flow

Highlights process boundaries and interdependencies

COPIS maps customer and process interaction by defining customer requirements and steps taken to deliver the desired output

CCustomer

OOutput

PProcess

IInput

SSupplier

Thought Process

Process Flow

COPIS and SIPOC are used interchangeably.

Treqna Base Manual


COPIS - Components

Customer: Recipient of the process output.

Output: Anything produced for the customer (internal or external). Outcome of the process.

Process: Group of activities required to transform inputs in to customer desired output

Input: Material or knowledge required to produce the desired output

Supplier: Source that supplies the input

Metric: A measure of compliance with customer expectation or established standard

CCustomer

OOutput

PProcess

IInput

SSupplier

Treqna Base Manual


Step3: Identify process steps

Step2: Identify customer requirements

Step1: Identify Customers, Outputs, Inputs, Suppliers and Process Name

COPIS - Components

CCustomer

OOutput

PProcess

IInput

SSupplier

Treqna Base Manual


Topics

About Projects


COPIS

Project Charter

Treqna Base Manual


Project Charter

Project charter is a written roadmap that defines key questions or issues to be addressed by the project. It defines the project's purpose and its intended outcomes.

The critical elements of a project charter are:

Business Case

Problem and Goal Statement

Project Scope and Boundaries

Project Team

Project Timelines

Communication Plan

Treqna Base Manual


Critical Elements Of A Charter

Business Case: The need to do the project

Problem and Goal Statement: Project problem and improvement goal in distinct and measurable terms

Project Team: Who will be involved in the project and what role will he or she play?

Project Scope: Area of influence and resources for the project

Project Timelines: Project plan and key milestones

Communication Plan: Communication strategy through the project

Treqna Base Manual


The Business Case

Project Business Case has three critical elements:

It tells us why is the project worth doing

It tells us why is it important to do it now

It tells us the consequences of both, NOT doing the project and delaying it

Business case also talks about:

Brief introduction to the process/business where project is undertaken

How does the project help in achieving business goals.

Treqna Base Manual


The Problem Statement

The problem statement:

Represents the problem in measurable (quantifiable) terms. For instance, yield, defect rate, ppm, sigma etc.

Measures the problem against a target (if one exists)

Questions that a problem statement must answer

What is the problem?

Where is the problem?

What is the magnitude of the problem?

Over what period has the problem been recorded?

What is the impact of the problem?

Treqna Base Manual


The Problem Statement Examples

Problem Statement: “Our customers are not happy with the delay in monthly credit card account statement mailing”

Poorly defined problem statement – generic in nature. It does not highlight the magnitude or the impact of the issue at hand.

Problem Statement: “In the last 3 months 26% of the monthly credit card account statement were delayed by 10 or more days, due to which business had to waive off $280,000 in late fee charges.”

Well defined problem statement – specific and direct. Clearly brings out the magnitude of the problem and its consequences to the business.

Treqna Base Manual


Things To Watch Out For

Potential Pitfalls:

Anecdotal: The problem statement is based on assumption (guess) or based on insufficient data?

Leading: Problem statement giving hint to a prejudged root cause? (implied solution, this might happen in business case also)

Immeasurable: Challenges in collecting data or data can not be collected (Insight into a problem is limited by measurability of a problem)

Scope: Problem statement too narrowly or broadly defined

Treqna Base Manual


The Goal Statement

A Goal Statement defines the improvement objective that a project team sets out to

achieve. It must

Be time bound

NOT suggest or assume a solution

Have a specific, measurable target

The goal statement would usually start with the verb, e.g. reduce, increase, eliminate etc.

Treqna Base Manual


Goal Statement: “We intend to reduce the no. of delayed credit card statements.”

Poorly defined goal statement – generic in nature. The target and time frame to achieve

it have not been defined.

Goal Statement: “Reduce the percentage of delayed monthly credit card account

statement from 26% to 2% by 26th Nov 2004.”

Well defined goal statement – is specific, measurable and time bound.

The Goal Statement Example

Treqna Base Manual


Project Scope and Boundaries

Project Scope and Boundaries provide clear demarcation between what the project team

can and cannot influence.

While defining the scope of a project, you must identify

Processes under study

Resources available to the project team

Constraints, if any, on the project team

You must also define boundaries (start and stop points) for each process under study to

avoid ambiguity

Treqna Base Manual


Steps in Scoping a Project

Identify customer expectations – Who is the customer? What is the output? What does the customer expect from the output?

Translate customer expectations to process CTQs – which process CTQs best represent customer want

Map process – detail the process(es) under study to identify areas of specific focus

Identify resources – what are the resources available to the project team

Understand constraints – what are the other CTQs or parameter that can be influenced by the process but need to remain as is

Treqna Base Manual


Timelines & Project Plans

Establishing critical milestones helps ensure focus through the life of the project, timelines should be aggressive, yet realistic

Project Plan: An activity by activity plan to help meet project timelines.

Identifies order of execution for critical tasks

Identifies interdependencies, if any, between tasks

Gives an estimate of time requirement

Helps identify potential roadblocks and plan contingency measures

Treqna Base Manual


Communication Plan

Communication plan:

To prevent sudden surprises: Keep all stakeholders informed about project status

To ensure that timely communication of vital information to those who need it

To help efficient management of information logistics

Good communication plan would address the following:

Who would communicate? (Project Owner)

What to communicate? (Project Status, schedule, plan, challenges, successes, failures)

When and how frequently? (Tollgates, weekly, monthly…)

Reason for communication? (importance)

Recipients of communication? (Project Manager, Process Owner, Champion/Sponsor, Process Team, Cross-functional Teams, Process Teams etc..)

Other things to be covered in the plan include the choice of media, information residence,

information source and comments regarding details of information

Treqna Base Manual


Team Roles

Roles which should be defined in the Project Charter:

Project Manager – GB/BB or MBB

Mentor - BB or MBB

Project Champion

Project Sponsor

Project team members

While defining roles:

The project champion and the sponsor might be the same person

Team members are usually from the process or related to the product for which the project is undertaken. Involvement of support staff is also common.

It is not unusual to have team members specific to a particular activity or phase

Green belt - An employee of an organization who has been trained on Six Sigma and executes projects as a part of his/her full time job. Green belts are usually supervised or mentored by a Black belt.Black belt – An employee of an organization who has been trained on Six Sigma and executes/mentors projects. Black belts are Six Sigma specialists and mentor Green Belts, Black belts are usually mentored by Master Black BeltsMaster Black Belt – Master Black Belts are Six Sigma Quality experts that are responsible for the strategic deployment of Six Sigma resources within an organization. Master Black Belt main responsibilities include training and mentoring BBs and GBs; selection, execution and support of Six Sigma projects.Black belts usually report into a Master Black Belt.Champion – A member from the leadership team who reviews the progress of projects that he/she champions. The champion is also responsible for supporting the project and help it overcome any challengesSponsor – Usually the process owner of the process on which a project is being done, he/she provides the necessary resources for execution of the project

Treqna Base Manual


Potential Pitfalls

Common mistakes made while selecting a project team

Time commitment from team members is not clearly defined

Incorrect mix – lack of influence (hierarchy), knowledge (subject matter expertise) or competence (statistical or technical skills)

Champion’s role is not clearly defined

Treqna Base Manual


Topics covered

About Projects– Characteristics of a good project– Sources for project ideas

Customer, CTQs and VoC– Internal or External Customer– Critical to Quality Metrics– Voice of the Customer – VoC tools

COPIS

Project Charter– Business Case– Problem and Goal Statement– Project Scope and Boundaries– Project Team– Project Timelines– Communication Plan

Treqna Base Manual


Define Phase


Tools

Deliverables

Step

Step D.2Step D.1

CBAFMEA

Survey, Focus Group, Interview, Charter, COPIS

Project feasibilityProject CharterCOPIS

Approve projectMap project

Treqna Base Manual


Topics

Project Risks

Cost Benefit Analysis

Project Go/No Go decision

Treqna Base Manual


Project Risks

Brainstorm to identify potential risks associated with each phase of the project – risks that restrict its execution or cause it to fail

Assess the likelihood of the risk to occur

Evaluate risks associated with external factors influencing the process or product under study

Identify contingency measures to mitigate identified risks.

Evaluate project feasibility under light of associated risks and contingency plans

Treqna Base Manual


Topics

Project Risks



Treqna Base Manual



Identify costs associated with the project

Would new technology or changes to existing technology be required?

Is there some new infrastructure that would be required?

Translate improvement target, if possible, in to quantifiable dollar benefit

Would the raw material costs come down?

Would the no. of people required to do the job reduce?

Understand business budget constraints

Are there any budget constraints?

Are there other projects with equal or high priority?

A Cost Benefits Analysis (CBA) is a calculation which is done in order to evaluate the costs that a project/change may incur and if it will have generate enough benefits to justify the costs.

Treqna Base Manual


Topics

Project Risks



Treqna Base Manual


Project Go/ No-go

Evaluate the following before undertaking a project

Potential risks associated with the project, the contingency plans to mitigate those risks and the residual exposure to such risks

The champion’s commitment to mitigate risks and drive contingency measures, if any require his influence

Financial commitment for the completion of the project (allocate budget)

Treqna Base Manual


Topics Covered

Project Risks

– Identify and plan for risks that may delay the project


– Evaluate costs associated with the project, its benefits and its importance from the business stand point


– Contract the champion’s commitment to ensure the success of the project

Treqna Base Manual


DEFINE

MEASURE

ANALYZE

IMPROVE

CONTROL

Map project



Baseline process



MSA on X’s

Approve project

Data collection






Treqna Base Manual


Measure Phase

Continuous Gage R&R, Short Form Gage,

Test/ Retest Study,Attribute Gage R&R

Identify gage error

Measurement system analysis

Step M.2

Tools

Deliverables

Step

Step M.3Step M.1

Process Map, QFD,FMEA,Pareto

Sampling StrategySegmentation factors

Identify project Y metricEstablish performance standards

Data collectionCTQ characteristics and standards


Treqna Base Manual


Topics

Selecting CTQ Characteristics

Process mapping

CTQ Drill down tree

QFD

FMEA

Performance Standards

Treqna Base Manual


Process mapping

Process Mapping:

Is a graphical representation of activities, steps, information, resources and their interactions.

Process Map is also called a flowchart.

Process Mapping is a first step in understanding how and why a process behaves the way it does.

Treqna Base Manual


A process is a series of logical steps that transform inputs (raw materials) in to customer defined outputs.

A process may be largely affected by one or more of the following factors:

personnel who operate the processes;

materials which are used as inputs (including information);

machines or equipment being used in the process (in process execution or monitoring / measurement;

methods (including criteria and various documentations used along the process);

work environment

Understanding a process

CustomerOutput Input

Supplier

Process

Treqna Base Manual


------------------- Process Boundary --------------------

Process Controls

Metrics and Measurements

Process Boundary defines the process limit. It helps understand the scope of the process and its constraints.

Process controls help ensure the process is consistent in behavior

Metrics and Measurements are the means to measure conformance with requirements placed by customers on outputs and processes on inputs.

Components of a process

Treqna Base Manual


Why map a process?

Mapping a process has many uses:

Compare actual vs. assumed (designed) flow

Identify redundant, duplicate or non value add steps

Identify data collection points in the process

Study interaction and interdependencies between different departments (highlight hand off points)

Treqna Base Manual


How to map a process?

To map a process:

Understand the process boundaries and scope

Observe the process and identify its steps

Arrange the process steps in the order that they are followed

Identify the outputs, the customers, and their key requirements

Identify the inputs, the suppliers, and the process’s key requirements

Treqna Base Manual


Frequently used symbols

Process step Decision box

Process Start / End

Off page connector

Document Multi-document

Process steps connector

Input to a process

Treqna Base Manual


Types of process maps

Alternate path process map: used for complex and/or large process. Alternate paths replace decision boxes in the map. The percentage depiction of alternate paths makes this map more informative. 80%

20%

Human Resource

Operations

Finance

Three frequently used process maps are:Basic Process map: used when the process is small and simple

Cross functional process map: used when the process has many handoffs between different departments. It is also known as deployment map.

Treqna Base Manual


Topics


Process mapping

CTQ Drill down tree

QFD

FMEA


Treqna Base Manual


CTQ Drill down Tree

E.g. Ticket Counter at Movie theatre. From customer VOC to project metric

Better Billing Process

Good Customer Service

Timely Process

Curt and Polite Accurate BillingKnowledgeable Less queue time

Big Y

A CTQ drill down tree tool assists in choosing a project metric. It shows linkage between the project metric and the company goals. Once established it can be used in projects to help finalize relevant project metrics.

A ‘Y’ is a dependent output variable. The higher the ‘Y’ in a hierarchy of ‘Y’ the bigger it is considered to be. A ‘X’ is an independent variable that effects the ‘Y’.

Treqna Base Manual


Topics


Process mapping

CTQ Drill down tree

QFD

FMEA


Treqna Base Manual


Quality Function Deployment

Quality Function Deployment (QFD) is a structured approach to defining customer needs or requirements and translating them into specific plans to produce products to meet those needs.

It helps to understand:

What customer wants when the customer requirement is not explicit or is indirect.

How important it is to the customer

What the customer does not want

Treqna Base Manual


QFD -Objectives

Understand Quality Function Deployment (QFD) as a tool.

Describe the steps of QFD.

Analyze output from QFD.

Treqna Base Manual


Definition of QFD

QFD is a methodology and tool to identify and translate customer needs and wants into measurable features and requirements – converting the “what’s” in to “how’s”

QFD links the needs of the customer (end user) with design, development, manufacturing, and service functions.

Used to identify Critical to Quality Characteristics (CTQ’s)

QFD is also known as the “House of Quality”

Treqna Base Manual


18

9

Ingredient cost

48

3

9

Temperature (cold)

423936

93Good service

32Should be reasonably priced

94Should taste good

934Quenches thirst

Quantity

Time to prepare

Ingredient mix

Customer Needs

Customer’s importance rating

Customer’s Expectations

Measures that capture customers requirement

Impact a CTQ has on the customer’s expectations

Overall CTQ impact on customer needs

QFD Matrix

××

×Correlation between measures

Strong Positive Strong Negative Positive Negative×× ×

Elements of QFD matrix:Rows: The rows of the QFD matrix represent the customer needs (VOC) Columns: The columns of the QFD matrix represent the CTQs that measure the customer’s need.The cross section matrix cells are filled with values 1,3 and 9 depending on the correlation between the customer needs and the CTQs. 1 represents low correlation, 3 medium correlation, and 9 high correlation. The cell is left blank where no correlation exists.The column next to needs contains the relative importance given to needs by customer. The roof of the house is used to depict correlation between various measuresWhen the matrix is complete, to prioritize the CTQs or requirement:

Multiply the strength of each relationship (1 for weak, 3 for moderate and 9 for strong) by the priority number (1 to 5) for each corresponding customer expectation. Add the results and enter the sum for each requirement at the bottom of the matrix. This is the output of the QFD exercise.

It is not necessary to complete every cell of the QFD matrix. Typically, a QFD matrix would have 30-50% of the cells filled.Caution: An empty row indicates that the need is not captured by any measure. An empty column indicates that the measure does not fulfill any need and is redundant.

Treqna Base Manual


Analyzing the QFD matrix

Look for blank rows and columns-

blank row means that we don’t have any measure to satisfy customer requirement and

a blank column means that we have a measure that does cater to any customer requirement.

Identify processes/measures which have high impact on customer CTQ’s

Resolve negative correlations between measures/ processes

QFD can be used in iteration to translate customer needs to process CTQs.

For instance - customer needs can be translated to functional requirements using a QFD. A second level of QFD drill down can translate these requirements to product characteristics. A third level QFD can then translate the characteristics to process output measures.

Treqna Base Manual


Topics


Process mapping

CTQ Drill down tree

QFD

FMEA


Treqna Base Manual


FMEA - Objectives

Understanding what an FMEA does

Types of FMEAs

When to use

Learn steps involved in making of FMEA

Treqna Base Manual


Failure Modes and Effects Analysis

FMEA is a structured tool to:

Identify failure modes for a process

Estimate its effect and the risk associated with it

Identify and prioritize probable causes of failure

Evaluate and develop control plan to contain the risk

Treqna Base Manual


Types of FMEAs

System FMEA: Used to analyze potential failure modes in systems during the design or concept stage.

Design FMEA: Used to analyze potential failure modes in products before they are released to production.

Process FMEA: Used to analyze assembly line, manufacturing, transactional or other such processes.

Treqna Base Manual


When is FMEA useful?

Evaluate and control potential risk associated with product, systems in there design phase

Evaluate potential risk when existing systems, processes or products are changed

Proactive tool to evaluate and contain risk associated with any process or change in the process.

FMEA can be used at different phases for different purpose.Measure – CTQ’s identificationImprove – Risk analysis on solutionControl – To develop process control plan

Treqna Base Manual


Preparing a FMEA

Identify process and map the process.

Identify input and output of the process

Understand the effect of inputs (process variables) on output of the process

Rank inputs according to importance

List ways in which inputs can vary and the associated failure modes and effects on outputs

Assign severity, occurrence and detection to each of the items and calculate risk priority number

Prioritize causes with high RPN and develop control plan to minimize risk

FMEA:•Is a team exercise•Living document and should be updated regularly to evaluate risk and make control plans

Treqna Base Manual


FMEA: Definition of terms

Failure Mode

Way in which a process can fail to meet expectation

Any fluctuation which can cause break down in process

Any fluctuation in process variable which can result in defect or non conformance

Potential Cause

A deficiency leading to a Failure Mode

Any source of variation in inputs or process variables

Potential Effect

The impact on customer if the failure mode in not contained or avoided

Customer could be internal or external. The impact could be on the business or employees also (which is internal customer)

Treqna Base Manual


Identifying causes

Causes can be identified using:

Brainstorming

Cause and effect diagram

Ask the question - “What can cause process to fail or what can cause a failure to impact the customer?”

Treqna Base Manual


Rating and RPN

Severity

How severe is the impact of failure mode on customer?

Occurrence

How frequent the cause leading to failure mode can occur?

Detection

What is the possibility of detecting the failure mode if it occurs?

Risk Priority Number

RPN signifies the amount of risk associated with failure mode

RPN = Severance * Occurrence * Detection

Treqna Base Manual


Rating Scale

Many scales are available for rating severity, occurrence and detection. For simplicity (recommended for GBs) one can use the following scale:

Low- e.g. not detectableHigh- e.g. almost assured failure

High- e.g. effecting customer

9

MediumMedium-Medium3

High- e.g.. always detectable

Low – e.g. remote likelihood

Low- e.g. Low or no effect customer

1

DetectionOccurrenceSeverityRating

Treqna Base Manual


Failure Modes and Effects analysis (FMEA)

Date Prepared By:

Process Step Potential failure mode

Potential failure effect

SEV.

Potential Causes

OCC

Current Controls

DET

RPN

RecommendationsSEV.

OCC

DET

RPN

How does it look?

List process steps or product parts

List Failure Modes for each process step

Rate the Severity of the Effect to the customer

Rate how often a particular cause or Failure Mode occurs

List the causes for each Failure ModeList the Effects of each

Failure Mode

Rate the detection based on current controls

Calculate RPN and give recommendations for reducing RPN. Calculate new RPN post implementation of actions

Treqna Base Manual


Topics


Process mapping

CTQ Drill down tree

QFD

FMEA


Treqna Base Manual


Performance Standard

A Performance Standard defines

The customer want

Clearly whether a process is performing well or not

E.g. loan approval within 24 hours, first call resolution

A Performance Standard translates the “Voice of Customer” a measurable metric.

Treqna Base Manual


Elements - CTQ performance standard

Performance Standard

CTQProject Y

CTQUnit of Measure

CTQ Target

Specification Limits

Defect Definition

An Example

Turn Around Time

Days

3 Days

Not greater than5 days

Each new accountApplication whichTakes more than

5 days

CTQ Definition

Time from application to new account opening

Treqna Base Manual


Operational Definition

A precise description that clarifies:

What the CTQ is

And how to measure it.

Why do we need to have operational definitions?

It removes ambiguity in understanding between team members

It clearly defines a “standard” way to measure a CTQ

Ensure that CTQ representation is correct and independent of different times and operators

Treqna Base Manual


Target, Specification limit and Defect

One can understand Target as “a reference point to shoot at”, however Specification Limits (SL) define the acceptable tolerance in deviation from target. Target and SL are defined using VOC.

E.g. VOC - “average time to process a loan should be 3 days but it should not exceed 7 days.”

Would translate into :

Target: 3 days

Upper SL: 7 days (situation where LSL is not required!)

Treqna Base Manual


Target

Specification Limit

Defect

Defect

Anything that results in customer dissatisfaction. Nonconformance to the CTQ.

Target, Specification limit and Defect

Treqna Base Manual


Definitions

Unit (U)The output of a process.

Opportunity (OP)A characteristic of the unit, always at least 1 or more.

Defect (D)Anything that results in a non-conformance with set quality standards

Note: All Opportunities should be independent of each other and must be of significance to the customer

Treqna Base Manual


Defects per UnitTotal Defects per Unit. If there is more than 1 opportunity per unit then the Defects

produced may be more than the number of units. A strict measure of quality.

Total OpportunitiesTotal number of units multiplied by opportunity per unit.

Defects per OpportunityTotal Defects divided by total opportunities.

Defects per Million OpportunitiesDefects per opportunity multiplied by a million.

Formulas

Treqna Base Manual


Topics Covered


Process mapping

CTQ Drill down tree

QFD

FMEA


Treqna Base Manual


Measure Phase



Identify gage error


Step M.2

Tools

Deliverables

Step

Step M.3Step M.1






Treqna Base Manual


Topics

Measurement System Analysis - Concepts

Types of MSA

Treqna Base Manual


Understand the terms: Precision , Accuracy, Resolution , Stability, Linearity, Repeatability, Reproducibility,

Evaluated the measurement system and established variation induced by it in process data.

Project team’s consensus on measurement system

And define calibration standards

Measurement System Analysis - Objectives

Treqna Base Manual


Measurement System & Process Variation

Process variation consists of the true variation of process and the variation due to measurement system.

Total Variation = True Process Variation + Measurement System Variation

In this step we try to reduce the variation induced by measurement system. If the measurement system is not studied and calibrated:

Analysis of data may give misleading results

The variation problem may get fixed by fixing measurement system and the project may not be required

One might disturb the process operations without realizing that the cause of variation is measurement system

A Gage study tells us:•Amount of measurement error•Source of measurement error

Once the measurement error is quantified using gage study the next step is to minimize to the level when it becomes acceptable. The gage study is repeated until the level of acceptance is achieved. Until the problem of measurement variation is fixed the data can not be used for analysis and project purpose.

Treqna Base Manual


Process Variation

Process True Variation producing parts different lengths for parts

Input OutputProcess

Variation Induced by measurement system

True Process Variation

Perceived total Variation

Because our knowledge about a problem is limited by the data available, it becomes critical to study variation induced by measurement system - the data is only as good as the measurement system that produces it.

Treqna Base Manual


Sources of Variation

Observed Process Variation

Actual Process Variation

Measurement Variation

Long Term Process Variation

Short Term Process Variation

Sample Variation Gage Variation

Operator Variation

(Repeatability)

Accuracy (Bias) Precision(Reproducibility) Stability Linearity`

Treqna Base Manual


Measurement Variation – Key concepts

Accuracy / Bias – Difference between the standard and observation.

Example - A weighing scale measuring greater than “0” in free state

Repeatability – Variation in measurements of the same unit measured by the same operator using the same equipment.

Example – Observed difference in the length of a pencil measured by the same operator using the same measuring scale

Reproducibility – Variation in measurements of the same unit measured by different operators using the same equipment.

Example – Observed difference in the length of a pencil measured by different operators using the same measuring scale.

Stability – Variation in measurement of the same unit measured by the same operator using the same equipment over time

Example – Observed difference in the length of a pencil measured by different operators using the same measuring scale on different days.

Linearity – Consistency of accuracy across the entire range of measurement system.

Example – Observed difference in the length of a pencil when measured using different ends of the same measuring scale.

Treqna Base Manual


Understanding Precision and Accuracy

Precision: The variation caused due to gage (noise) should be less than the process variation otherwise it will be difficult to detect process variation.

Accuracy: Minimal or no difference between an observed reading average and a standard.

Resolution: Resolution as defined is the smallest unit in which the gage can measure. Ideally the gage should be able to resolve the tolerance into approximately ten levels.

Treqna Base Manual


Understanding Precision and Accuracy

Precise and accurate

==

At target and precise

Accurate but not precise

At target but not precise

Precise but not accurate

Target Precise but away from target

Treqna Base Manual


Measurement System Variability

Method

Material

Measurement

Machine

Environment

People

Fishbone may be used as a tool to identify Sources of variation in the measurement system

Some other terms associated with gage:Repeatability– Variation when one operator repeatedly measures the same unit with the same measuring equipment.

Reproducibility–Variation when two or more people measure the same unit with the same measuring equipment.

Stability–Variation obtained when the same person measures the same unit with the same equipment over a large gap of time.

Linearity–The consistency of the accuracy of gage across the entire range of the measurement system.

Treqna Base Manual


Topics

Measurement System Analysis - Concepts

Types of MSA

Treqna Base Manual


Types of MSA

Attribute Gage: Done when discrete data is involved

Gage ANOVA: with continuous data and the most exhaustive gage study. Requires resource commitment and time. Continuous data can also be run through short form gage and test-retest.

Destructive Gage: Done when the event is destructive in nature and can not be repeated.

Treqna Base Manual


Improving the Measurement System

NOT Precise and NOT Accurate


Precise but NOT Accurate


Precise and Accurate


Treqna Base Manual


Attribute GAGE

Checks gage for:

Repeatability

Reproducibility

Accuracy

Treqna Base Manual


Attribute Gage standards

Ideally an attribute gage is treated as adequate if:

Repeatability: 90% of repeated measures by an operator match

Reproducibility: 90% of repeated measures across all operators match

Accuracy: 90% of all individual measures by across all operators match with the standard

Treqna Base Manual


Attribute Gage standards

Repeatability test is more sensitive if there are greater no. of repeated measurements of the same unit. For instance, it is better to measure 10 units 9 times, than to measure 30 units 3 times.

Reproducibility test is more sensitive if the same unit is measured by more operators. For instance, it is better to have 10 units measured by 9 operators than to have 30 units measured by 3 operators.

Accuracy is calculated by taking each measurement as a data point. Therefore, whether we have 30 units measured 3 times by 3 operators or 10 units measured 3 times by 9 operators or 10 units measured 9 times by 3 operators, there are 270 data points to calculate accuracy.

Treqna Base Manual


Sample Size for the Attribute Gage

Consider the desired resolution to determine the sample size

Greater the desired resolution, higher is the sample size requirement.

If the desired resolution is 0.5%, will a sample size of 100 be enough?

A desired resolution of 0.5% means that the gage needs to distinguish a difference of half percentage point. If the sample size is hundred, the gage is good to distinguish a difference of one percentage point only (1/100), which may not solve the purpose.

Treqna Base Manual


Attribute gage sheet

Repeatability: % times each operator matches on all three measures for the same unit. Total 90 opportunity exist in the example.

Accuracy % times each individual measure matches with the standard. Since there are total 270 measures, there are 270 opportunities

Reproducibility: % times all operators match on all repeated measures for the same unit. Total 30 opportunities exist in the example

TRUE First Operator Second Operator Third Operator

Sample Answer Trial1 Trial2 Trial3 Trial1 Trial2 Trial3 Trial1 Trial2 Trial3

1 N N N N N N N Y N N2 Y Y Y Y Y Y Y Y Y Y3 Y Y Y N Y Y Y Y Y Y4 N N N N Y Y Y N N N5 N N N N N N N N N N6 Y Y Y Y Y Y Y Y Y N7 Y N Y N Y N Y Y Y Y8 N N N N Y N Y N N N9 N N N N N N N N N N

10 N N N N N N N Y N Y11 Y Y Y Y Y Y Y Y Y Y12 Y N N N Y Y Y Y Y Y13 Y Y Y Y Y Y Y Y Y Y14 N N N N N N N N N N15 N N N N N N N Y Y Y16 N N N N N N N N N N17 Y Y Y Y Y Y Y Y Y Y18 N N N N N N N N N N19 Y Y Y Y Y Y Y Y Y Y20 Y N N N Y Y Y Y Y Y21 Y Y Y Y Y Y Y Y Y Y22 N N N N Y Y Y N N N23 N N N N Y Y Y N N N24 N N N N N N N Y Y Y25 N N N N N N N N N N26 Y Y Y Y Y Y Y Y Y Y27 N N N N N N N N N N28 N N N N N N N N N N29 N N N N N N N N N N30 Y N Y N Y Y Y Y Y Y

Treqna Base Manual


Test Re-test study

When to use it?

To check for precision of gage or measurement system. Test re-test is used when same operator does the measurements. It is good practice to use it before opting for complex gage ANOVA.

Remember that if a gage is good on precision, the problem of accuracy can be solved by calibration (correction).

Treqna Base Manual


Test Re-test standard

Precision: Ideally precision should be less than 10% of tolerance. Tolerance is defined by the customer. For example, +10 seconds of specifications would translate into tolerance of 20 seconds.

Accuracy: Can be only measured when one knows the standard value.

Treqna Base Manual


Test re-test gage

Let us take an example where we have readings for diameter of a ball. The tolerance given is 16 mm (+8mm) and the standard diameter of ball is 98mm .

104, 95, 101, 99, 95, 97, 96, 105, 101, 106, 94, 100, 98, 103, 98, 96, 100, 98, 95, 103

Treqna Base Manual


Test re-test gage

Make Run chart to find out if the data is stable

Observation

C1

2018161412108642

107.5

105.0

102.5

100.0

97.5

95.0

Number of runs about median:

0.17906

13Expected number of runs: 11.00000Longest run about median: 3Approx P-Value for Clustering: 0.82094Approx P-Value for Mixtures:

Number of runs up or down:

0.04762

16Expected number of runs: 13.00000Longest run up or down: 2Approx P-Value for Trends: 0.95238Approx P-Value for Oscillation:

Run Chart of C1

Treqna Base Manual


Test re-test gage

Run Descriptive test to calculate mean and standard deviation

Mean=99.2, S=3.6

S=3.6 > 10% of 16 = 1.6

The inaccuracy or bias can be calculated as 99.2-98=1.2

106104102100989694

Median

Mean

10110099989796

A nderson-Darling N ormality Test

V ariance 13.116Skew ness 0.367278Kurtosis -0.959324N 20

M inimum 94.000

A -Squared

1st Q uartile 96.000M edian 98.5003rd Q uartile 102.500M aximum 106.000

95% C onfidence Interv al for M ean

97.505

0.36

100.895

95% C onfidence Interv al for M edian

96.235 101.000

95% C onfidence Interv al for S tDev

2.754 5.290

P -V alue 0.425

M ean 99.200S tDev 3.622

9 5 % Confidence Inter vals

Summary for C1

Therefore, the measurement device has inadequate precision.

Treqna Base Manual


EV and AV

Total variation (R&R) in a measurement system is further classified as:

Equipment Variation: The variation within operator, within equipment or gage, within the method. This variation comes from the parts of measurement system or process. This is also termed as Repeatability variation.

Appraiser Variation: The variation introduced between different operators, different parts, and different methods. This is also termed as Reproducibility variation.

Total variation (R&R) = EV + AV

The mathematical equation used for representing the relationship between total variation, EV and AV is

(Std. Dev (R&R))2 = (Std. Dev (Repeatability))2 + (Std. Dev. (Reproducibility))2

Treqna Base Manual


How a gage plays with Spec Limits

What is the challenge with having high R&R error ?

Following scenario explains why..

Centre circle is the true data point and the limits on left and right show the measurement variation

The gage variation might cause this data to pass on lower specification limit

The gage variation might cause this data to fail on the upper specification limit

The gage variation might cause this data to fail on the lower specification limit

The gage variation might cause this data to pass on upper specification limit

LSL USL

Treqna Base Manual


Gage ANOVA - Objectives

Gage ANOVA study:

Quantify amount of measurement variability

Identify amount of measurement variation from different sources

Data Type: Continuous

Treqna Base Manual


Gage ANOVA - Data Format

The data should be arranged in columns as in the following example. The recommended numbers of operators, parts and trials are 3, 10 and 3 respectively. Which would give one 90 data points. (3*10*3=90)

Operator Part Trial Response1 1 1 20.02 1 1 19.13 1 1 19.54 1 1 18.21 1 2 21.22 1 2 20.03 1 2 19.04 1 2 22.01 2 1 17.02 2 1 19.53 2 1 19.64 2 1 18.01 2 2 19.52 2 2 20.13 2 2 21.04 2 2 18.9

Treqna Base Manual


Gage ANOVA Minitab

Choose Stat> Quality Tools> Gage Study> Gage R&R Study (Crossed).

Treqna Base Manual


Gage ANOVA – Minitab

Operator Part Trial Response1 1 1 20.02 1 1 19.13 1 1 19.54 1 1 18.21 1 2 21.22 1 2 20.03 1 2 19.04 1 2 22.01 2 1 17.02 2 1 19.53 2 1 19.64 2 1 18.01 2 2 19.52 2 2 20.13 2 2 21.04 2 2 18.9

Select method of analysis as ANOVA

Treqna Base Manual


Minitab Session Output

Gage R&R Study - ANOVA Method

Two-Way ANOVA Table With Interaction

Source DF SS MS F PPart 9 18343.8 2038.20 31.5583 0.000Operator 2 530.8 265.40 4.1093 0.034Part * Operator 18 1162.5 64.59 3.9663 0.000Repeatability 30 488.5 16.28Total 59 20525.7

Gage R&R %Contribution

Source VarComp (of VarComp)Total Gage R&R 50.475 13. 30Repeatability 16.283 4.29Reproducibility 34.192 9.01Operator 10.041 2.65Operator*Part 24.151 6.37Part-To-Part 328.936 86.70Total Variation 379.411 100.00

Study Var %Study VarSource StdDev (SD) (6 * SD) (%SV)Total Gage R&R 7.1046 42.627 36.47Repeatability 4.0353 24.212 20.72Reproducibility 5.8474 35.084 30.02Operator 3.1687 19.012 16.27Operator*Part 4.9144 29.486 25.23Part-To-Part 18.1366 108.820 93.11Total Variation 19.4785 116.871 100.00

Number of Distinct Categories = 3

P-value < 0.05 says significant variation. In the example Parts, operator and the interaction all are significant factors

Look for percentage contribution for Total Gage R&R, which is addition of Repeatability and Reproducibility percentage contribution. In the example it is 13.3% which is more than acceptable 10%

Percentage contribution:It represents the percentage of variation contributed by gage in the process.Recommended percentage contribution from Total Gage R&R should ideally be less than 10%. However one should consult with BB/MBB if the value is between 10-15%, where one might accept the gage error and gets go ahead with the project. Project should be evaluated by the mentor and acceptance would depend on the process, business and the project champion.If tolerance is beyond 15% it is recommended that the gage be corrected before repeating the gage study.

No. of Distinct Categories:This number represents the number of distinct groups in the data. For example if you have 20 part being evaluated and the number of distinct categories are 2. This means that the most of the parts are not different enough, and the data can be divided into two groups. In such a case the precision of the gage is not enough for the process. Minimum number of distinct categories should be at least 5.

Treqna Base Manual


Gage ANOVA – Graphical Output

Per

cent

Part-to-PartReprodRepeatGage R&R

100

50

0

% Contribution

% Study Var

Sam

ple

Ran

ge

16

8

0

_R=4.7

UCL=15.36

LCL=0

1 2 3

Sam

ple

Mea

n

100

75

50

__X=80.85UCL=89.69

LCL=72.01

1 2 3

Part10987654321

100

75

50

Operator321

100

75

50

Part

Ave

rage

10 9 8 7 6 5 4 3 2 1

100

75

50

Operator

1

23

Gage name:Date of study :

Reported by :Tolerance:Misc:

Components of Variation

R Chart by Operator

Xbar Chart by Operator

Weight by Part

Weight by Operator

Operator * Part Interaction

Gage R&R (ANOVA) for Weight

In By part graph, there are large differences between different parts.

Components of variation graph shows percent contribution by category

In by operator graph, there isn't much difference between operators

X bar graph by operator shows most of the points out of control, which says most of the variation is due to parts

Treqna Base Manual


Destructive Testing

Destructive testing is unique in the sense that the measured characteristic is different after the measurement process. Few examples of destructive events are:

Crash testing

Tensile strength of material

Call quality evaluation for call centre (unless it is done on recorded call)

Destructive Testing is a unique case since an operator can measure a part multiple times in the earlier case where we used Gage ANOVA

Treqna Base Manual


Destructive Testing and Gage

Assumptions and restrictions:

In such a setup the event happens once and can not be repeated. However if the event is recorded than the measurement can be done multiple times. E.g. call quality check done on recorded calls in call centers.

Each operator measures unique batch.

One must be able to assume that all parts in one batch are identical. The reason it is necessary is otherwise the part to part variation will mask the measurement variation. This means that none of the part is measured by multiple operators

Treqna Base Manual


Topics Covered

MSA Concepts

Understand Accuracy and Precision and their components.

Understand sources of variation

•Perceived vs. True process variation

•Equipment vs. appraiser variation

Why gage error is a challenge

Gage standards

Types of MSAs

Attribute gage

Test retest

Gage R&R

Treqna Base Manual


Measure Phase



Identify gage error


Step M.2

Tools

Deliverables

Objective

Step M.3Step M.1






Treqna Base Manual


Topics

Data Collection Plan

Data Segmentation

Sampling

Treqna Base Manual



Following are the steps involved in data collection plan

1. Data Collection Goals

2. Data definition and

procedures

3. Validate measurement

system

4. Collect data and

monitor

•Why collect data?

•What data to collect?

•Establish operational definitions

•Establish data collection procedures

•Pilot operational definitions and procedures and refine

•Establish sampling strategy

•Conduct MSA and validate measurement system

•Collect data

•Monitor for data consistency and make final adjustments

Treqna Base Manual



Till now we have established:

Metric for the project - What is it that we are trying to measure? E.g. If the metric is‘No of New Accounts each day’. One might have to collect data items like – Touch time per application, day of week, No. of applications reworked etc. as additional data that will help us segment and analyze later.

Operational Definitions – We know how to define operational definition. Also we know that operational definition needs to be piloted so that we can fix loose ends in the definition.

Measurement system validation – Depending on the type of data and measurement system setup we know what type of gage to use.

Treqna Base Manual


Data Collection Sheet

What should one capture while collecting data?

Data – Project metric Y or segmentation factor X

Data Type – Continuous vs. Discrete

Data Source – Source/s of data. E.g. Application, process step

Data Range – Possible set of values data can take

Segmentation Factors – All the factors which come out of brainstorming

Time Period – For what time period data is collected

One should also capture if there are any special changes in process during the time period. Such reasons might produce outliers in the data

Monitoring Data Collection

Question collectors for the understanding of operations definitions.

Verify collected data with source, use sampling or ad hoc QC

Ensure that the procedures are followed.

Treqna Base Manual


Topics


Data Segmentation

Sampling

Treqna Base Manual


Data Segmentation

What is Data Segmentation?

Segmentation involves dividing data into logical categories for analyzing data. For instance, while recording the errors made by a data entry process, the project manager may choose to capture the step at which the error occurred, the operator who made the error and so on.

Tools Used for Data Segmentation:

Brainstorming- Members of the process and project team

SME- Subject matter expert for the process can give valuable inputs

Treqna Base Manual


Data Segmentation

Example:

A project is being done on Accuracy of Application processing, the possible segmentation factors are

AccuracyVintage of processor

Work type

Touch time

Day of WeekNo of Processors

These segmentation factors are logical groups that may point to be significant x’s during the analyze phase.

Treqna Base Manual


Topics


Data Segmentation

Sampling

Treqna Base Manual


Sampling - Objectives

Understand sampling and why is it required

Advantages of sampling

Different sampling techniques

Treqna Base Manual


Population vs. Sample

Population:

The entire set of data, the universal set.

Symbol used is N

The population mean represented by µ

Standard deviation is represented by s

Sample:

The part or subset of a population, the universal subset

signifies the sample mean

s signifies standard deviation of a sampleX

Sampling tries to answer few critical questions asked while doing a project:How much data is required?How and when to collect data?

Sampling also reduces the cost involved in collecting data by reducing the amount of data required.

Treqna Base Manual


Sampling

Sampling is the process of collecting subset or portion of data from population and predicting population characteristics

Population N=1000

Sample N=50

Treqna Base Manual


Why Sample ?

When to sample

The cost associated with data is very high

We are measuring a high volume process

When not to sample

When the subset of data may not be able to predict population characteristics. E.g.. If each unit of data is unique

Apart from other reasons to do sampling, one of the critical reasons is the time required to collect population data. Sampling is an efficient way to collect data for any kind of project or analysis.

Treqna Base Manual


Representative Sample

Sample is Representative:

When the sample has same statistics as of the population

How to guarantee a representative sample:

Suitable sampling strategy based on the process

Understand the nature of process

Understand the characteristics of population

Sample must be “representative” of the population, as the data collected otherwise would not deliver any results and might give misleading inferences about the population.

Treqna Base Manual


Sampling Bias

Bias occurs when systematic differences are introduced into the sample as a result of the selection process.

A sample that is biased will not be representative of the population

A sample that is biased will lead to incorrect conclusions about the population

A biased sample would have incorrect information about the population and will lead to biased conclusions. A bias in the sample can not be eliminated with increasing the sample size.

Treqna Base Manual


Sampling Bias Types

Convenience sampling:

This is also called as accidental bias. It occurs we use the data what is available instead of making as effort to collect data. E.g. interviewing the first person you met, pick friends and neighbors for survey.

Systematic sampling:

Collecting data at a particular time, or following a pattern in collecting data which has interference with underlying process. E.g. sampling process on Sunday when only one person works in the process.

Judgmental sampling:

When the data collector or surveyor collects data using his judgment or opinion.

Treqna Base Manual


Sampling Bias Types

Bias by Environment:

This type of bias is introduced when the environmental conditions surrounding process have changed since the sample was collected. E.g. When the call handle time data was collected it was tax season.

Measurement Bias:

Measurement bias could arise if the operational definitions are not correct or the data collectors have interpreted the operational definition differently.

Non-Response Bias:

Non-response bias happens when the respondents to a survey tend to differ systematically from respondents to the survey.

Treqna Base Manual


Sampling Strategy – Random Sampling

Random Sampling:

Samples picked up from assembly line without any order or system. Each item has equal probability of getting selected in the sample.

Production Line

Sample

This is the most commonly used method of sampling. Use random sampling when information about stratification is unknown. Random sampling is a population approach and so care must be taken when the process is cyclical or if the data can be stratified.In random sampling each unit has equal probability of being selected in the sample. Using random sampling method avoids bias being introduced in the sampling process.For practical purpose one can number the data coming out of process and generate random list in excel or on minitab and accordingly sample data.

Treqna Base Manual


Stratified Random Sampling

Stratified Random Sampling

Production Line

Sample 1.1

Sample 1.2

Assembly data stratified in to two categories and random samples collected for both

Stratified random sampling is used when the population has different groups (strata). In such situation it is necessary that both groups are represented in the sample and samples are collected from each group (it is like doing random sampling for each group). The size of the sample depends on population size of each the group. E.g. To sample from a assembly line preparing nuts of two sizes A and B respectively. The two sample sizes for nuts sized A and B would be calculated based on production of size A and size B nuts respectively.

Treqna Base Manual


Systematic Sampling

Systematic Sampling:

Production Line

Sample

Every fourth item selected for sample

Random sampling and stratified sampling are done with historical data. When we have real time data coming in systematic sampling is done.

Unlike random sampling the frequency of collecting data is fixed in systematic sampling.

E.g. selecting every fourth call in the call centre for call barging, selecting 2 application every alternate hour for quality check.

Care must be taken and process must be studied for any underlying structures.

Treqna Base Manual


Rational Sub grouping

Random Sampling:

Production Line

Sample

Three items selected with a frequency of one hour. In this case sample has subgroup size of three.

1st hour2nd hour3rd hour

Rational sub-grouping is a process based sampling strategy. The rational subgroups depend on the nature and type of process from where the data is being selected.

Rational sub-grouping assists us to understand the shift, which is the difference between the long term variability and short term variability of the process. We will study this in capability analysis under Analyze phase.

Treqna Base Manual


Sampling Strategy - Tips

Use following pointers for sampling strategy for a given process:

It is always better to collect small sample spread over longer time period than one large sample over a shorter time period.

Sample more frequently for unstable process and less frequently for stable process

Sample more frequently for process with short cycle time and less frequently for process with long cycle time

To understand the sampling frequency one should understand the objective of data collectionThe most important issue to remember when considering sample frequency is the data collection objective. The sampling frequency is driven by the objective of data collection, e.g. if the data collected is for monitoring process one might want to sample data daily. However if the objective is to collect data for the same process to study capability one might want to collect data for few months by sampling few data points each week or month.

Treqna Base Manual


Sample Size Calc - Continuous Data

Sample represents population characteristics. We can use confidence interval formula and solve it for n to get sample size:

As standard error is also represented by delta, hence:

Solving for n we get:

The equation for 95% confidence becomes (using Z table):

Standard errorXCI nX *2α/Z σ±

n/2Z α=Δ σ

22

Zn

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

Δ

∗=

σ/α

σ x 1.96 n2

⎟⎠⎞

⎜⎝⎛=

Δ

Where, Δ error or precision required from sample in representing the populationis standard deviation

N is sample sizeThe value of Zα/2 depends on confidence level we choose, the corresponding value can taken out from Z table.

Finite Population CorrectionThe central limit theorem and the standard errors of the mean and of the proportion are based on the premise that the samples selected are chosen with replacement. However, virtually in all scenarios finite population sampling is conducted without replacement from populations that are of a finite size N.When sample is more than 5% of population size we use Finite population correction factor which is:The sample size is than:N (finite) = n(1 + n/N)

1−−

=N

nNFPC

Treqna Base Manual


Estimating Standard Deviation

Use control limits from an existing X chart

= (UCL – X) / 3 or (X – LCL) / 3

Collect some data from population and calculate std deviation (recommended – 30 data points)

Get realistic estimate from business (based on past experience)

Treqna Base Manual


Estimate Δ

Take estimate from business. It may be based on the resolution of measurement. For instance, if the business measures cycle time in days, do not set Δ in minutes or hours

Collect some data from population and calculate Δ using the sample

Treqna Base Manual


Sample Size Calc - Discrete Data

The formula to calculate sample for proportions data is:

nP1P

ZP /2⎟⎠⎞⎜

⎝⎛ −

± α

⎟⎠⎞⎜

⎝⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= − P1PZn

2/2

Δα

Again if the sample is more than 5% of population finite population correction should be used

Z is the Z score (normal data) and P represents proportionate defective and a represents confidence required from sample. Za/2 is 1.96 for 95% confidence.

This uses the confidence interval formula for attribute (discrete) data:

Treqna Base Manual


Estimating p and Δ

Estimate p

Calculate proportionate defective using small sample

Use historical control charts to estimate

Use subject matter expertise to estimate

Estimate Δ

Use subject matter expertise to estimate

Estimate using formula:

( )n

P1PZ BB/2

−= αΔ

Treqna Base Manual


Topics Covered


Data Segmentation

What is segmentation?

Why segment?

Sampling

What is sampling?

Why sample?

Sampling challenges – Types of Bias

Types of Sampling

Treqna Base Manual


DEFINE

MEASURE

ANALYZE

IMPROVE

CONTROL

Map project



Baseline process

Screen for vital Xs

Define Improved Process

MSA on Xs

Approve project

Data collection



Study interaction between Xs



Treqna Base Manual


Benchmarking

-Concept of Benchmarking

-Benchmarking Types-Benchmarking as

process

Improvement goal for project Y

Performance Objective

Step A.2

Tools

Activities

Deliverables

Objective

Step A.3Step A.1

-Root Cause Analysis (RCA)-Process map analysis-Graphical analysis-Statistical Analysis

-Study data for shape, stability and normality

-Capability analysis-Short Term vs. Long Term

sigma-Understanding shift,

Common cause variation, special cause variation

1-Sample T-test, 2-Sample T-test, One-way ANOVA, Mood’s Median, Homogeneity of Variance, Simple Linear Regression, Correlation/Scatter Diagrams, Chi Square–Test of Independence, Chi Square–Test for Goodness of Fit, Pareto, Cause and Effect diagram, VA/NVA analysis

Descriptive test, run chart, capability pack

List all statistically significant X’sProcess capability for project Y

Identify drivers of variationBaseline Process

Analyze Phase


Treqna Base Manual


Baseline Process - Objectives

• Study data for stability, shape

• Statistically indicate the nature of the problem

• Calculated the baseline capability of the process.

Describe the process by its

• Descriptive statistics

• Nature of distribution

• Understand Specification Limits and Centering or Target Values

• Calculate: probability of a defect and process capability

• Use Minitab for these purposes

Treqna Base Manual


Stability, Shape and Normality

Stability

Tool Used: Run Chart

Stability is lack of excessive variation.There should be no trends, clusters, mixtures or oscillations.

Shape

Tool Used: Descriptive Stats,Histogram

Study distribution characteristics

Normality

Tool Used: Descriptive test, NormalityTest

Check if the data follows a normaldistributions

Treqna Base Manual


Important thing to remember is that data should be in a time order before a run chart is plotted. If the data is sorted or it does not follow the time order in any other way, run chart loses its significance. Run chart studies the stability of process over a period of time by studying any abnormality is data like trends, clusters and so on.

Run chart can be plotted for:Individual valuesMeans or Medians of subgroups (if subgroups are present)

Apart from looking for process stability over a period of time, run chart can also give graphical representation of pre and post process changes comparison as it is plotted on time scale.

The only difference between run chart and control chart comes from the control limits.

Stability - Run Chart

Tool Utility: To track process over a period of time for stability.Tests for if there are any trends, clusters, oscillations in the process. Indicates any special cause variation in the process.

How: Minitab. STATS > QUALITY TOOLS > RUN CHART

Treqna Base Manual


Run Chart - Minitab

MINITAB FILE: RunChart.mtw

Treqna Base Manual


The graph you see in the output window of Minitab is the run chart. Run chart is used for stability and helps in identifying if there is any special cause in the process and when does it appear on time scale. Below the graph you would see hypothesis tests for different measures.Run Chart provides two tests for randomness:Based on the number of runs about the median (Mixtures and Clusters)Based on the number of runs up or down. (Trends and Oscillations)

P-values for the following special cases should be read from run chart out put:Trend:Ho: No fewer runs observed than expectedHa: Fewer runs observed than expectedA trend is a sustained drift in the data, either up or down. Might indicate if the process is about to go out of control or is out of control.Oscillations:Ho: No more runs observed than expected Ha: More runs observed than expectedOscillation occurs when the data fluctuates up and down rapidly, indicating that the process is not steadyClusters:Ho: No fewer runs observed than expected. Ha: Fewer runs observed than expectedClusters are group to group variability which may indicate variation due to special causes, such as measurement problems or sampling from a bad group of parts.Mixtures:Ho: No more runs observed than expected. Ha: More runs observed than expectedMixture can be identified by absence of points near the center line. Mixtures often indicate combined data from two populations, or two processes operating at different levels.`

Run Chart - Subgroup Size 1

• Choose ‘C2’ for Data• Set Subgroup Size to ‘1’• Click Ok

Treqna Base Manual


Studying Stability

Ho: Data is random, special causes not presentHa: Data is not random, special causes present

Treqna Base Manual


Studying Stability

Treqna Base Manual


If you have done rational subgrouping in your data. It can be used for run chart as well. In the input window you can mention subgroup size or column representing subgrouping in the data.

The run chart would than plot mean or median depending on your choice. It also plots the variation within the subgroup apart from the stability over a period of time.

Run Chart – Subgroup Size more than 1

Treqna Base Manual


Shape - Descriptive Stats

Click on Stat > Basic Statistics > Display descriptive Statistics

MINITAB FILE: DescriptiveStats.mtw

Descriptive stats helps studying the shape of data distribution, measures of central tendency and dispersion.It also helps to find out what kind of issue we have with the process: whether it is issue with centering or issue with variation ?

Treqna Base Manual


Tabular Output

1.Double click on “C1 Agent A”2.Click Ok

Results for: DescriptiveStats.MTW

Descriptive Statistics: Agent A

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3

Agent A 250 0 50.424 0.535 8.460 19.000 45.750 51.000 56.000

Variable Maximum

Agent A 71.000

Treqna Base Manual


Graphical Output

Click on Stat > Basic Statistics > Graphical Summary


1. Double click on “C1 Agent A”2. Click Ok

Graphical summary from minitab lists all the basic statistics of the data which includes measures of central tendency, variation(spread) and there graphical representation.Following are the key statistic output from graphical summary.Normality P valueMeanMedianStandard DeviationVarianceKurtosis (measure of skew ness of data)Quartiles

In graphical representation:Histogram (with o without normal curve)Box plot and Dot plot

In the following pages we would cover few basis statistic tools.

Treqna Base Manual


Different Shapes

Normal

Skewed

Central Tendency: Mean

Dispersion: Standard Deviation

Central Tendency: Q1 or Q3

Dispersion: Stability Factor, defined as Q1/Q3

Treqna Base Manual


Different Shapes

Bi-modal

Central Tendency: Median

Dispersion: Range or Span

Such situation suggests data coming from two processes and not one. One should go back and have a look at the processes, separate the data by process and than analyze.

Long Tailed

Treqna Base Manual


Normality

One can test normality of data using:

• Descriptive test

• Normality test

Hypothesis used for the test is:

H0: data follow a normal distribution

H1: data do not follow a normal distribution

Treqna Base Manual


99.73%

95.46%

Standard Deviations

3210- 1- 2- 3

68.26%

Area under a Normal Curve

The probability of a randomly selected value of being within 2 Standard Deviations from the mean is 95.46%

+-

Treqna Base Manual


Z - Value

For any value of X in a distribution there is an equivalent Z – value. The Z – value is a measure of the number of Standard Deviations that will fit between X and the Mean.

σμX-=Z

z

x 3 σ 2 σ 1 σ μ

Statistically,

The Z-value is used to transform any normal distribution in terms of the standard normal distribution with a Mean of 0 and Standard Deviation of 1.The Z – value is important as it allows us to compare to dissimilar distributions by using standard deviation as the unit of measure.

Note : Z Value and Z capability are not the same.

Treqna Base Manual


Z - Value

43210- 1- 2- 3- 4

18161412108642

Standard Deviations

Units of Measure

USLUSL

ZUSL

LSLLSL

ZLSL

Χ

2 24

210-14

sX- USL ZUSL ====

3 26

24-10

s LSL-X ZLSL ====

10X =

2s =

A Simple Z Capability CalculationFor this calculation assumeUSL = 14 LSL = 4Nominal = 10Note :

Nominal is also called Target ValueHow the calculation changes for LSL and USL, this is done to ensure that the resulting

number is always positive.The total area under any distribution is always 1.The Shaded Region represents the probability of a value being outside specification limits.

Treqna Base Manual


The Total Probability of a defect is calculated by adding the probability of defects that will occur at values lesser than the LSL and greater than USL. These values can be obtained by using the Z capability values you calculated earlier for both ZLSL and ZUSL.. Using the Z table, then find the Z-value that corresponds to this total probability of defect, this is ZBench and it represent long term process capability.To calculate process capability for the short term, just add Z Shift to the long term capability.

Note :Z Shift is empirically set at 1.5If it is not mentioned whether the data used is for sort or long term, always assume it to be long term. If the data is for short term, your Z – Bench will be short term capability, then subtract Z shift to obtain Z long term.1 – Z bench is the probability of a conformance also called yield, this yield can directly be converted to Sigma

by using a sigma conversion table.

Calculating Z – Bench value

USLLSLTotal P(d)P(d)P(d) +=

ZLT = from Z table

ZST = ZLT + Z shift

LSLP(d) USLP(d)

USL T X LSL

Treqna Base Manual


Single-Tail Z Table A (Values of Z from 0.00 to 4.99)

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.00 5.00e-001 4.96e-001 4.92e-001 4.88e-001 4.84e-001 4.80e-001 4.76e-001 4.72e-001 4.68e-001 4.64e-0010.10 4.60e-001 4.56e-001 4.52e-001 4.48e-001 4.44e-001 4.40e-001 4.36e-001 4.33e-001 4.29e-001 4.25e-0010.20 4.21e-001 4.17e-001 4.13e-001 4.09e-001 4.05e-001 4.01e-001 3.97e-001 3.94e-001 3.90e-001 3.86e-0010.30 3.82e-001 3.78e-001 3.74e-001 3.71e-001 3.67e-001 3.63e-001 3.59e-001 3.56e-001 3.52e-001 3.48e-0010.40 3.45e-001 3.41e-001 3.37e-001 3.34e-001 3.30e-001 3.26e-001 3.23e-001 3.19e-001 3.16e-001 3.12e-0010.50 3.09e-001 3.05e-001 3.02e-001 2.98e-001 2.95e-001 2.91e-001 2.88e-001 2.84e-001 2.81e-001 2.78e-0010.60 2.74e-001 2.71e-001 2.68e-001 2.64e-001 2.61e-001 2.58e-001 2.55e-001 2.51e-001 2.48e-001 2.45e-0010.70 2.42e-001 2.39e-001 2.36e-001 2.33e-001 2.30e-001 2.27e-001 2.24e-001 2.21e-001 2.18e-001 2.15e-0010.80 2.12e-001 2.09e-001 2.06e-001 2.03e-001 2.00e-001 1.98e-001 1.95e-001 1.92e-001 1.89e-001 1.87e-0010.90 1.84e-001 1.81e-001 1.79e-001 1.76e-001 1.74e-001 1.71e-001 1.69e-001 1.66e-001 1.64e-001 1.61e-001





Treqna Base Manual


Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09






Single-Tail Z Table A (Values of Z from 5.00 to 9.99)

Treqna Base Manual


Standard Norm

al D

istribution Table BZ

This Is K

nown A

s The Standard N

ormal D

istribution W

hich H

as A M

ean Of Zero (=

0) An

d A Stan

dard D

eviation of On

e (s = 1)

Treqna Base Manual


Standard Norm

al D

istribution Table B

This Is K

now

n A

s The Stan

dard Norm

al Distribu

tion Wh

ich Has A

Mean O

f Zero (= 0) A

nd A

Standard

Deviation of O

ne (s =

1)

Z

Treqna Base Manual


The Total Probability of a defect is calculated by adding the probability of defects that will occur at values lesser than the LSL and greater than USL. These values can be obtained by using the Z capability values you calculated earlier for both ZLSL and ZUSL.. Using the Z table, then find the Z-value that corresponds to this total probability of defect, this is ZBench and it represent long term process capability.To calculate process capability for the short term, just add Z Shift to the long term capability.

Note :Z Shift is empirically set at 1.5If it is not mentioned whether the data used is for sort or long term, always assume it to be long

term. If the data is for short term, your Z – Bench will be short term capability, then subtract Z shift to obtain Z long term.1 – Z bench is the probability of a conformance also called yield, this yield can directly be

converted to Sigma by using a sigma conversion table.

Process Capability - Objectives

• Calculate Process Capability for Discrete Data

• Calculate Process Capability for Continuous Data

• Understand rational subgroups and use it for sampling and data analysis

• Perform the following calculations:

• within, between and total sum of squares

• the long and short-term standard deviation and Z-values

• understand the difference between short-term process capability and long-term process capability

• establish whether the process has control issue or requires technology improvement

Treqna Base Manual


Choosing a Capability Tool

Start

Is data discrete ?

Run Discrete Data Process Capability

report (excel spreadsheet)

ZST = ZLT + 1.5(ZShift = 1.5)

Is data normal ?

Treat data as discrete for this step and run Discrete Data Process Capability

report (see notes)

Run Capability Analysis (normal data)

Is target specified?

Read ZLT from Capability Analysis

report and 1.5 to arrive at ZST

Run Capability Sixpack (see next page for

interpretation)Is sub group size

> 1?Read ZLT from Capability Analysis report and 1.5 to

arrive at ZST

No

No

No

No

Yes

Yes

Yes

Yes

To convert continuous data to discrete follow the following steps1. Minitab>Stat>Tables>Tally Individual variables2. Under Variable select column that has data on project Y3. Select “Count” and “Cumulative percent”4. Look for yield @ USL or LSL in session window5. Calculate Z value using Abridge table

Treqna Base Manual


Process Capability for Discrete Data

ZLT : Long term capability can be calculated using excel formula normsinv(yield)

ZST : Short term capability is computed by adding 1.5 (standard shift) to the long term

sigma

Treqna Base Manual


Process Capability - Continuous Data

• Objective: Practice generating a Minitab Capability Sixpack

• Directions:

• Open file Penlength.mtw

• The capability of a Pen manufacturing plant is being calculated. The ‘length of the pen’ is the measure.

• USL = 10.2 cms

• LSL = 9.8 cms

• The data was collected in batches of 10(Subgroup size = 10)

• Stat > Quality Tools > Capability Sixpack > Normal

• In ‘Options’ – Enter Target = 10

If subgroup size = 1, the short term sigma value reported in the Capability Analysis report is invalid as there are no sub groups and hence no sub group variation.

If upper and lower specification limits are provided without a target, Minitab assumes that the target is the mid point of the specification range. If only one specification limit is entered and the target is left blank, then Minitab approximates the target with the mean of the data.

Treqna Base Manual



Treqna Base Manual


Interpreting the Capability Sixpack

Always check for S Chart stability to judge whether rational sub grouping is acceptable- S chart in control indicates sub groups are acceptable- S chart out of control indicates sampling is not acceptable

-If the graph shows an R Chart instead of S then,If R chart is out of control, Xbar chart interpretation may not be reliable as the control limits on the Xbar chart are arrived at using the Rbar value from the R chart.If the R chart is not in control, the rational sub grouping is not correct. Within subgroup variation is higher than between sub group variation.

Treqna Base Manual

First Edition 176 © All Rights Reserved TreQna 2005Note: Subtract 1.5 to get long-term Sigma level

Abridged Yield to Sigma Conversion TableLong-Term

YieldST Process

SigmaDefects Per 1,000,000

Defects Per 100,000

Defects Per 10,000

Defects Per 1,000

Defects Per 100

99.99966%99.9995%99.9992%99.9990%99.9980%99.9970%99.9960%99.9930%99.9900%99.9850%

99.9770%99.9670%99.9520%99.9320%99.9040%99.8650%99.8140%99.7450%99.6540%99.5340%

99.3790%99.1810%98.930%98.610%98.220%97.730%97.130%96.410%95.540%94.520%

93.320%91.920%90.320%88.50%86.50%84.20%81.60%78.80%75.80%72.60%

69.20%65.60%61.80%58.00%54.00%

50%46%43%39%35%

31%28%25%22%19%16%14%12%10%8%

3.4581020304070100150230330480680960

1,3501,8602,5503,4604,6606,2108,19010,70013,90017,80022,70028,70035,90044,60054,80066,80080,80096,800115,000135,000158,000184,000212,000242,000274,000

308,000344,000382,000420,000460,000500,000540,000570,000610,000650,000

690,000720,000750,000780,000810,000840,000860,000880,000900,000920,000

0.340.50.81234710152333486896135186255346466621819

1,0701,3901,7802,2702,8703,5904,4605,4806,6808,0809,68011,50013,50015,80018,40021,20024,20027,40030,80034,40038,20042,00046,00050,00054,00057,00061,00065,00069,00072,00075,00078,00081,00084,00086,00088,00090,00092,000

0.0340.050.080.10.20.30.40.71.01.52.33.34.86.89.613.518.625.534.646.662.181.9107139178227287359446548668808968

1,1501,3501,5801,8402,1202,4202,7403,0803,4403,8204,2004,6005,0005,4005,7006,1006,5006,9007,2007,5007,8008,1008,4008,6008,8009,0009,200

0.00340.0050.0080.010.020.030.040.070.10.150.230.330.480.680.961.351.862.553.464.666.218.1910.713.917.822.728.735.944.654.866.880.896.8115135158184212242274308344382420460500540570610650690720750780810840860880900920

0.000340.00050.00080.0010.0020.0030.0040.0070.010.0150.0230.0330.0480.0680.0960.1350.1860.2550.3460.4660.6210.8191.071.391.782.272.873.594.465.486.688.089.6811.513.515.818.421.224.227.430.834.438.24246505457616569727578818486889092

6.05.95.85.75.65.55.45.35.25.15.04.94.84.74.64.54.44.34.24.14.03.93.83.73.63.53.43.33.23.13.02.92.82.72.62.52.42.32.22.12.01.91.81.71.61.51.41.31.21.11.00.90.80.70.60.50.40.30.20.1

Treqna Base Manual


Long Term & Short Term Capability

ZLT = Long term process sigma

Long term sigma is also the sustained process capability

ZST = Short term process sigma

The process at entitlement is performing at its best. This can happen when process short term sigma (Zst) is as high as possible.

ZST = ZLT + Shift

Where shift is the difference between short term process capability and long term process capability.

Shift is taken as 1.5 if the data lacks rational sub grouping*

* Discussed Later

ZST assumes:Theoretically, process performance is more consistent in the short term than the long term, hence short term sigma is always better than the long term sigma.

Treqna Base Manual


Therefore, six sigma is a measure of the short term capability of a process. If a normal process is centered at 6 standard deviations from each specification limit (or is on target) in the short term, assuming standard shift, the process would tend to move 1.5 standard deviations towards either specification limit in the long term. This means, the process will be 4.5 standard deviations from one specification limit and 7.5 standard deviations from the other.

The assumed shift of 1.5 sigma comes from manufacturing industry. Shift compensates for the variation which is non-random in nature and does not get captured while calculating short term sigma. It accounts for the changes in process capability over many cycles of that process.

LSL ± 6s

Centered Distribution

TUSL

4.5sT

mmDistribution Shifted 1.5σ

LSL USL

The Shift

Treqna Base Manual


As discussed in the previous slide, the process mean typically shifts by 1.5 standard deviations around the target. Short term sigma is a measure of the process at a particular point in time whereas long term sigma is a measure of the process over a period of time.

LSL USLT

Time = t

Short-Term capability

Long-Term capability

Visual Representation of ST & LT

Time = t + x

Treqna Base Manual


Non-Random Variation:ShiftsTrendsCycles

Types of Variation

Common Cause variation• Random process variation• Also called as inherent variation of any given process• Variation comes from

– People– Materials– Methods– Machines– Measurements– Mother Nature

Special Cause variation • Non-random process variation• Assignable cause• Can generate outliers

Treqna Base Manual


To create rational subgroups find:A time period that is short enough such that you do not have special causes of variationThis time period will differ from process to process

A subgroup should only contain common cause variation. There is variation between different subgroups. This variation is accounted primarily by special causes (though this might include some common cause variation also)In other words, short term capability should have common cause variation only. Long term capability has common cause and special cause variation

Special Cause Variation – between groups

RationalSubgroups

Common Cause Variation- Within Group

The objective behind doing Rational Subgrouping is to have subgroups with only common cause variation and minimal special cause variation within them. The attempt is made to collect samples of data in such a way that special cause accounts for variation between different subgroups.

Rational Subgrouping

TimeTime

Treqna Base Manual


Rational Subgroups

Characteristics of good rational subgroup:

– Samples to be collected over a large period of time so that each sample represents a rational subgroup defined by some logic(which usually is a one process cycle)

– Attempt to minimize variation within the subgroup and maximize the variation between subgroups

Examples of sampling to create rational subgroups:

– Sample each hour, 3 applications

– Sample each day, 3 applications

– Sample each shift, 3 applications

In high-volume situations, use the Xbar and R-chart to evaluate stability of short/long-term stability.

In low-volume situations, process measurements typically come “one-at-a-time.”Use the X & RM chart.

Treqna Base Manual


SSTotal : deviation of each individual point from the overall meanSSBetween: deviation of each subgroup mean from the overall mean (variation of the means)SSWithin :deviation of each individual point from its corresponding group mean (variation of the individuals within group)Xij : Individual observation

Xj : Subgroup mean

X : Overall Mean

Components of Variation

( ) ( )2

11

2

1

2

11jij

ijj

jij

ijXXNXX

NKKNK

XX −+⎟⎠⎞

⎜⎝⎛ −=− ∑∑∑∑∑

=====

[Samples size n=3 at different times

SSTTotalSST

TotalSSW

WithinSSW

WithinSSB

BetweenSSB

Between

Where K=number of subgroups and N= subgroup size

Total variation representing Long term process capability

The Shift defined by special cause variation

Common cause variation representing Short term process capability

[}}SSW

SST

SSB

Treqna Base Manual


Standard Deviation & Sum of Squares

One Sample

Short-Term

Long-Term

( )1gn

XXσ̂

g

1j

n

1i

2

ij

LT−

−=

∑ ∑= =

( )( )1ng

XXσ

g

1j

n

1i

2 jij

ST −

−=

∑ ∑= =ˆ

( )( )1n

XXσ̂

n

i

2 i

−

−=

∑Where “n” is the sample size

Where “n” is the subgroup size and “g” is the number of subgroups. Numerator denotes SSW

Where “n” is the subgroup size and “g” is the number of subgroups. Numerator denotes SST. X represents overall mean.=

Treqna Base Manual


Z Long-term: Which is the actual capability of the process and what is current. It is always calculated w.r.t. the population mean. SL - m is the distance between specification limits given by customer and the true population mean.

Z Short-term:Z short term is the best process can deliver if the current distribution is assumed around the Target (and not mean). This means assuming the same variation and if the distribution were to centered around Target what will be process capability. For the same reason while calculating Z short term we use Target value and not population mean.SL - T is the distance the specification is from the target.

ZST is bigger than ZLT, so the shift is

Higher the shift bigger the control issue in process. Typical assumed shift when rational subgrouping not present is 1.5 sigma.

The Equation

Z Equation

Z = Specification Limit – Central TendencyStandard Deviation

Variations

Z – Short Term(ZST ) or Long Term(ZLT)

Specification Limit – USL or LSL

Central Tendency – Mean(m) or Target(T)

Standard Deviation – σST or σLT

LTLT σ

μSLZ

−=

STST σ

TSLZ

−=

ZShift=ZST-ZLT

Treqna Base Manual


Relating ST Capability & Process Shift

Short Term Sigma

• Short Term Sigma signifies the best process can deliver as of current.

• Entitlement of process with current technology

• Any attempt to increase the capability would require improvement in current technology

Shift

• Shift in the distribution over a period of time, the difference between long term and short term capability

• Caused by assignable special causes

• Signifies control issues in the process

Seeing Short term Sigma and Shift together provides insight into what needs to be changed to improve Long Term process capability.

Poor Control;Poor Control;Poor TechnologyPoor Technology

Poor Control;Poor Control;

Poor TechnologyPoor TechnologyGood Control;Good Control;

Good TechnologyGood Technology

ZZshiftshift

ZZstst

2.5

2.0

1.5

1.0

0.5

1 2 3 4 5 6

The graph to your right helps identify the issue in your process. Once you baseline your process and understand it’s short term capability and shift, you will be in a position to determine whether your process needs better controls, improved technology or both.

A typical DMAIC project aims at improving controls by eliminating special cause variation. DFSS projects on the other hand are run to improve technology so that the process can reach higher capability.

Treqna Base Manual


ZST is based on the analysis of subgroups. If special cause variation is also present along with common cause variation, ZST will not reflect the correct (best) picture of present technology.

A small ZShift does not necessarily indicate good control, but consistency among the subgroups or need to revisit sub groups. However, if ZShift is greater than 1.5, this is a definite indication of a controlproblem.

Summary LT vs. ST

LONG-TERM CAPABILITY (ZLT)

• Actual current process capability

• Way to improve involves improving control (reducing shift) and technology

• 6s means 4.5s with assumed shift of 1.5s, otherwise 6s - (shift)

SHORT-TERM CAPABILITY (ZST)

• Best process performance –Entitlement

• Way to improve involves improving technology as it is the inherent capability of process at current

• 6σ means ZST = 6σ

Treqna Base Manual


Step Summary – Baseline Process

Discrete Data Characteristics• Defect, Defectives• DPMO• For capability Use ZLT from Z table corresponding to DPMO

Continuous data characteristics• Central Tendency – mean, median• Variation – variance, standard deviation• For capability use Z values from minitab capability reports

Normality• Process with only random variation will have such distribution• Can always be related to normal distribution which has mean of zero and

standard deviation of oneSample:

• Subset of population which has same characteristics as population.

Treqna Base Manual


Basic Statistics tools:Use graphical summary, box plots, run charts(for stability), normality graph

from minitab to understand process

Rational Subgrouping• Attempt is made to collect samples with only random variation(common

cause variation)• Between subgroup variation is special cause variation• Derive SSB and SSW to understand ZST, ZLT and Shift

Z-value• Signifies number of standard deviation that can be fit between customer

specification limit and mean• Corresponds to probability of defect, which is area under the curve outside

the customer specification limit• Represents process capability


Treqna Base Manual


Shift

• Difference between ZLT and ZST

• Signifies process control issues

• Assume shift to be 1.5s to estimate ZST if rational subgrouping not present

• Attributed by special and assignable causes

What the customer feels is the process Long term capability. Short term capability is the inherent capability of process – “Entitlement”


Treqna Base Manual


Benchmarking



process

Set Improvement goal for project Y


Step A.2

Tools

Activities

Deliverables

Objective

Step A.3Step A.1










Analyze Phase


Treqna Base Manual


Setting a goal for the Y metric

Following are approaches which one could adopt to define the Goal for Y metric:

• Benchmarking: One can target to achieve best in industry

• Learning Curve-Based: One could also use multi level goal in terms of sigma

for the process metric.

• Arbitrary Defect Reduction: This is frequently used with discrete metric.

E.g.reduce DPMO by 50%

Six sigma should always have aggressive but achievable target

Treqna Base Manual


Benchmark and Baseline

Z Long Term

Benchmark is the best in industry, process baseline tells where the process stands against Industry

Benchmark : World Class Performance

Z Short Term : The best performance by the process with current technology

Baseline Process Sigma : The sustained long term sigma for the process

Z Short TermBenchmark

Treqna Base Manual


Benchmarking

Definition:

An improvement process in which a company measures its performance against that

of best in class companies, determines how those companies achieved their

performance levels and uses the information to improve its own performance. The

subjects that can be benchmarked include strategies, operations, processes and

procedures.

Where to use Benchmarking:

• Compare process performance against industry’s best

• Understand market competition

• Establish improvement targets for your process

Benchmarking is a continuous process which gives insight into where does your competitor stand and how do they achieve those levels of service excellence. It also provides a platform for best practice sharing across industry.

The knowledge derived from the process of benchmarking can be used to improve service, products, support functions and systems. It also provides target for process capability improvement.

In the current market scenario where information flows seamless and the access is universal, benchmarking is definitely a tool to facilitate service excellence achievement .

Treqna Base Manual


Types Of Benchmarking

Strategic BenchmarkingIt is used where organizations seek to improve their overall performance by examining the long-term strategies and approach. It involves considering high level aspects such as core competencies, developing new products and services.

Performance/ Competitive BenchmarkingIt is used where organizations consider their positions in relation to performance characteristics of key products and services. Usually focuses is the relevant segment of market.

Process BenchmarkingIt is used when the focus is on improving specific critical processes and operations. Benchmarking partners are sought from best practice organizations that perform similar work or deliver similar services. It helps in driving short term goals of company.

Functional BenchmarkingIt is used when organizations look to benchmark with market players drawn from different business sectors to find ways of improving similar functions or work processes. This sort of benchmarking can lead to innovation and dramatic improvements.

Treqna Base Manual


Types Of Benchmarking

Internal BenchmarkingIt involves seeking information from within the same organization, for example, from business units located in different areas. The main advantages of internal benchmarking are that access to sensitive data and information are easier; standardized data is often readily available; and, usually less time and resources are needed.

External BenchmarkingExternal Benchmarking involves seeking outside organizations that are known to be best in class. External benchmarking provides opportunities of learning from those who are at the leading edge.

International BenchmarkingIt is used where partners are sought from other countries because best practitioners are located elsewhere in the world and/or there are too few benchmarking partners within the same country to produce valid results

Treqna Base Manual


Benchmarking Plan

Primarily following are the things to be considered in your benchmarking plan:

• Focus of Study

• Current assessment of area requiring improvement

• Selection of process for benchmarking

• Description of current process

• Purpose of study

• Outline of areas/issues for questioning

• Benchmarking partners

• rationale for selection

• initial contact

• development of detailed questions

Treqna Base Manual


• Site Visit

•confirm and arrange site visit

•develop briefing package

•finalize and communicate plans

•conduct visit

• Post Visit

•points of clarification / follow up

•review all data

•initial report sent to partners for confirmation

Benchmarking Plan

Treqna Base Manual


Other sources for setting a goal

Following are few more options which drive the goal for process metric:

• Corporate mandate

• Compliance/legal requirement

• Voice Of Customer

• Industry Standards (e.g. CMM, ISO)

Treqna Base Manual


What is Benchmarking?– Benchmarking is a continuous process– Valuable tool to gather market knowledge and improve services, products and

systems– Process of knowing how competitor is achieving higher levels of service

excellence– Benchmarking is a time consuming and labor intensive process

Common Benchmarking Mistakes:– Not establishing the baseline– Confusing benchmarking with participating in a survey. – Thinking there are pre-existing "benchmarks" to be found.– The process is too large and complex to be manageable– Confusing benchmarking with research– Picking a topic that is too intangible and difficult to measure – Not researching benchmarking partners thoroughly– Not having a code of ethics and contract agreed with partners

Summary – Performance Objective

Treqna Base Manual


Benchmarking



process

Set Improvement goal for project Y


Step A.2

Tools

Activities

Deliverables

Objective

Step A.3Step A.1










Analyze Phase


Treqna Base Manual


Bridging the Gap -Practical to Statistical

Practical Problem

Statistical Problem

Statistical Solution

D

M

A

I

C• MSA on Vital X’s

• Control Plan

• Project Y• Project Charter• MSA• Data Collection

• Process Characteristics

- Centering and Variation

• Establish Process Capability

• Determine Statistical Goal (Benchmarking)

• Critical X’s

• Transfer function Y=f(X)

• Pilot/Implement Solution

Practical Solution

This section is the beginning of statistical problem solving process. By the end of this section we would have established Critical X’s

Treqna Base Manual


Tools to be used in this section

Graphical Tools1. Fishbone analysis

2. Matrices

3. Pareto

4. Histograms

5. Dot Plot

6. Box and whisker plot

7. Process map analysis

• VA/NVA analysis

• Value mapping

8. Hypothesis Tests

Cause and Effect diagram is used in measure for identifying segmentation factors. It is also used to prioritize X’s which affect project Y

Treqna Base Manual


Cause and Effect Diagram (Fishbone)

Use the tool:

• To get a visual map of all causes

• While brainstorming for causes and trying to capture thoughts

• Correctly identify root causes and categorize them

Treqna Base Manual


How to work with a Fishbone

Define your problem statement. It should start with “Why”, for example “Why is the

cycle time high?”

Use the basic categories as framework:

– People

– Materials

– Methods

– Machines

– Measurements

– Mother Nature

Make your core team understand the problem statement and objective of exercise

Cause and Effect diagram is a team tool and so it is important to have members in your team who understand the process well.

Treqna Base Manual


Building the Diagram– Brainstorm possible causes and attach them to appropriate categories– Relate each cause with the problem statement– Try to bucket small related causes and prioritize

The Structure of Diagram:

P u t in y o u rQ u e s t io nh e r e

E n v ir o n m e n t

M e a su r e m e n ts

M e th o d s

M a te r ia l

M a c h in e s

P e r s o n n e l

S a m p l e F i s h b o n e

P u t in y o u rQ u e s t io nh e r e

E n v ir o n m e n t

M e a su r e m e n ts

M e th o d s

M a te r ia l

M a c h in e s

P e r s o n n e l

S a m p l e F i s h b o n e

How to work with a Fishbone

The attached diagram is an example to the structure, which once filled gives complete picture of problem and causes.

Treqna Base Manual


Prioritization Matrix

Few prioritization matrices which can be used are:• Criterion v/s criterion• QFD• Control/Impact

Why use it ?• To narrow down systematically to critical X’s by weighing each option w.r.t. its

importance and effect on Y

How does it help?• Helps six sigma team to focus on X’s on priority• Systemizes the approach of prioritizing as it based on on X’s weighed against each

other w.r.t. to there effect on Y • Quickly surfaces critical X’s from disagreements within the team

The matrix only prioritizes…the output still needs to be ratified with data and an objective outlook

Treqna Base Manual


Fishbone to Prioritization Matrix

Translate the Cause and Effect diagram to a Prioritization Matrix

• Items in Quadrant 1 are ‘Must do’• Items in Quadrant 2 should be dropped as they complicate processes without significant impact• Items in Quadrant 3 should only be implemented if Project Y does not show necessary improvements after

implementing items from Q1• Items in Quadrant 4 are NOT to be done

Treqna Base Manual


Pareto Chart

Use the tool:

To filter vital few from trivial many X’s affecting process Y.

A Pareto is very handy when:

– You want to prioritize which causes to eliminate first

– You want to display information objectively to others

Treqna Base Manual


The Pareto Principle

The 80:20 rule

“ 20% of the causes account for 80% of the effect”

The 80:20 rule originated from Vilfredo Pareto, an Italian economist who studied the distribution of wealth in a variety of countries around 1900. He discovered a common phenomenon: about 80% of the wealth in most countries was controlled by a consistent minority -- about 20% of the people. His observation eventually became known as either the "80:20 rule" or "Pareto's Principle".

While making Pareto the defects grouped by different segments depending on what makes sense to the business. Following are few segments: •By Cost•By Financial defects•By risk•By compliance/ legal errors

Treqna Base Manual


Pareto Chart - Minitab

1) Collect data

S o f t S k i l l s I s s u e P o o r K n o w l e d g e N o P r o b l e m R e s o l u t i o nP r o c e s s A 5 8 5 3 9 4 9 3 9 0P r o c e s s B 8 2 1 5 4 0 8 5 4 8P r o c e s s C 1 4 9 9 9 4 9 9P r o c e s s D 9 4 6 6 3 0 7 6 3 1P r o c e s s E 4 1 5 3 1 1 2 2 7 7

C a l l s M o n i t o r e dS o f t S k i l l s I s s u e P o o r K n o w l e d g e N o P r o b l e m R e s o l u t i o n

P r o c e s s A 5 8 5 3 9 4 9 3 9 0P r o c e s s B 8 2 1 5 4 0 8 5 4 8P r o c e s s C 1 4 9 9 9 4 9 9P r o c e s s D 9 4 6 6 3 0 7 6 3 1P r o c e s s E 4 1 5 3 1 1 2 2 7 7

C a l l s M o n i t o r e d

2). Total results and arrange data by Segmentation Factors

T o t a l d e f e c t sS o f t S k i l l s I s s u e 2 9 1 7P o o r K n o w l e d g e 1 9 2 7 6

N o P r o b l e m R e s o l u t i o n 2 0 4 5

T o t a l d e f e c t sS o f t S k i l l s I s s u e 2 9 1 7P o o r K n o w l e d g e 1 9 2 7 6

N o P r o b l e m R e s o l u t i o n 2 0 4 5

Following are the steps involved in making of pareto chart:

1. Data collection by different defect categories. While doing so we capture:Types or categories of defectsFrequency of defectsFor further analysis we might do a drill down on financial loss, risk, compliance defect and so on. This helps in building an approach towards problem

2. Put sum of frequencies of defects by category

Treqna Base Manual


Pareto

Tool Utility: Useful tool identify factors/segments which contribute to the majority of the effect

How: Minitab > Quality Tools > Pareto Chart

Treqna Base Manual


Pareto Minitab Inputs

Choose ‘Chart defects table’ – Labels in ‘Defects’ and Frequencies in ‘Counts’

Treqna Base Manual


Pareto Minitab Output

Treqna Base Manual


Process Map Analysis

Tool Utility:

Useful tools to approach process from customer perspective. Understand what does customer feel and what customer values. It solves two important purpose:

– Identification of problems and improvement opportunity in the process

– Sense of urgency to improve as it is seen from customer perspective

Types Of Analysis:

What does the customer feel?. “The moment of Truth”

Which parts of the services provided, customer is ready to pay? ”Value to customer”

Wait time in process

Further on the three key components to the process map analysis:•Moments of truth helps us on focusing on customer and this paradigm change in approach changes the comfort level at which the process is operating. With this approach we try to study the customer – process interaction. We also study the touch points of customer with the process and improve the experience.

•Value analysis is process of studying the value add activities and non-value add activities in the process. Every activity within the process is seen as whether it adds any value to customer or not.

•Wait time is related to the process workflow.

Treqna Base Manual


Value Analysis

Value-Added Work

Nonvalue-AddedWork

Value-EnablingWork

Process steps which are non essential but enable or support the Value-Adding Tasks to be done better/faster.

For every activity in the process ask the question

“Is Customer

Willing To Pay For Them?”

Answers to this question amount to Value added work which changes the product/ services physically and so is essential to the process.

This is part of process steps which is Non-Essential for production and delivery product/ service.

Customer Is not willing to pay for process step.

Notes on Value enable work:Value enable work is the category which confuses the most. The only distinguishing factor between non value add and value enable work comes from customer’s perspective where customer is definitely not ready to pay for non-value added work.

Given the current condition of any given process we might not be able to take out the value enable steps from the process. They aid in delivery of product and services.

Indicators of non value add in the process:Approval process involves multiple departmentsToo many supervisorsMultiple reporting

Typical non-value add is rework. Which is a process step repeated, a step which usually takes you back in the process. E.g. Defect caught in downstream step being sent to upstream step in process.

Treqna Base Manual


Types Of Non-Value-Added Work

SetupInitialization

InventoryMovement

Inspection(Quality Check)

Failure(Internal/External)

Wait / Delay

Process failures:• Failures happen two ways, Internal and External. Internal refers to defect found during processing due to upstream process and being corrected. E.g. Rework• External failure are the defects reported by customer.

Inspection(Quality Check):• Internal process step dedicated to check products/ services for defects.

Wait/ Delay:• Products/ services waiting or queuing to get processed in front of process step. It is inventory building in front of a process step. It is usually due to bottlenecks. E.g. Backlogs

Setup / Initialization:• Steps involved in setup or preparation of subsequent step. E.g. Changing settings of machine in manufacturing plant

Inventory Movement:Physical movement of inventory from one point of processing to other point of processing.

Treqna Base Manual


Workflow and Time allocation

Processing Time (Product Touch Time)Wait / Delay Time

Cycle Time

T1 T2

T2+T2

While analyzing workflow for a process one needs to go at product/service unit level and track the flow of that identity. This is very detailed process map with time allocation with each small step. In the process we categorize process step into value add, non value add and value enabling.

Concept of time allocation in process:Cycle TimeTotal time spent from start point of process to end point of process. It is also important to look at this metric from customer point of view. E.g in call centre the average wait time for call might be 60 seconds but customer might be going through longer wait due to IVR, which we don’t capture.

Process TimeIt is the actual spent on any unit of service or product which goes through the whole process. (Note: this also includes steps which are non value add).

Wait / Delay Time:Total idle time spent by any product or service while going through process steps.

Treqna Base Manual


Workflow: Disconnects in Process Steps

Unclear work responsibility

Unclear processing requirements

Redundancies

Tricky handoffs between process steps

Conflict in job goals

Process disconnects more often than not lead to delay and wait time in the process. It also leads to rework or resource under utilization.Most of the disconnects arise due to following reasons:

Unclear work responsibility: Happens when a process step is not owned by a particular person. The processing such environment happens in a very ad hoc manner leading to delay.

Unclear processing Requirements: Operational definitions for process step do not exist. This might lead to rework due to defects caught in later process steps.

Redundancies: When one process step is duplicated amount two or multiple processors. This happens when one processor is unaware of other processor working.

Tricky Handoffs: Work transfer from one person or step to another step or person without any operational definitions in place. Leading to delays or rework.

Conflict in Job goals: When the job goals are overlapping or do not cover complete processing involved leading to conflict or incomplete work.

Treqna Base Manual


Analyzing Workflow: “Track the unit flow”

Agent fills app with customer

Agent fills app with customer

Agent mails app using USPS

Agent mails app using USPS

App received in mail room

App received in mail room

Mail room sorts by department

Mail room sorts by department

Data entry apps placed in data

entry tub

Data entry apps placed in data

entry tub

Apps transferred to data entry

every two hours

Apps transferred to data entry

every two hours

Data entry operator screens app for completeness

Data entry operator screens app for completeness

Is app complete ?

Route to Resolution team

Route to Resolution team

Procure missing information from

agent

Procure missing information from

agent

Complete data entry and forward to audit

team

Complete data entry and forward to audit

team

Is information

entered correct ?

Correct informationCorrect

information

Route to underwriterRoute to

underwriter

Can we issue policy ?

Issue policyIssue policy

Decline policyDecline policy

Order printOrder print

Sort issues and declines

Sort issues and declines

Create policy package for Issued policy and letter for

declined policies

Create policy package for Issued policy and letter for

declined policies

Apply postage and mail to agent using SPS

Apply postage and mail to agent using SPS

Agent receives letter / package and notifies clientAgent receives letter /

package and notifies client

Yes

Yes

Yes

No

No

No

Cycle time is the total time taken from the point at which the customer requests a good or service until the good or service is delivered to the customer.The components of cycle time are processing time, inventory movement time, inspection time,wait time. Cycle time metric should always be seen with caution. Lot of times we might just look at one part of process which might be working at its best. But when the customer might think otherwise as you might have another process step having lot of delays. The customer always looks at total cycle time.

Treqna Base Manual


Value Analysis

Process Step 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total Time % TotalTime Taken (min) 2 2 10 21 120 3 4 5 3 7 9 12 1 2 3 21 240 10 475 100%Value Add 24 5%Value enabling 9 2%Rework 6 1%Transportation 261 55%Inventory / queue 147 31%Audit / Inspection 24 5%Prep / Set up 4 1%

Process Step 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Total Time % TotalTime Taken (min) 2 2 10 21 120 3 4 5 3 7 9 12 1 2 3 21 240 10 475 100%Value Add 24 5%Value enabling 9 2%Rework 6 1%Transportation 261 55%Inventory / queue 147 31%Audit / Inspection 24 5%Prep / Set up 4 1%

Usually, a majority of the time is spent in Non Value add or Value Enabling work

Value analysis breaks the process into small steps categorized into value add and non value add. When we put our cycle time analysis against value analysis it gives tremendous insight into improvement opportunities. It tells exactly where we spent maximum time in process and whether or not it is value added work.

It is an eye opener exercise to understand the process, we might come the data where non-value added work adds to maximum in cycle timeNote: We might come across a situation where for a process step we may not have any data available. In such a scenario it is best to estimate time than skip the step.

Conclusion: Example4 steps (<25% of total steps) provide 100% value and take 24 minutes or 5% of total cycle time.14 steps (>75% of steps) are non-value-added, and consume 95% of cycle time.

How to Interpret the Matrix:

Look for the longest cycle time component. Is it a value-added step? If not, can you still reduce time?

Look for frequent category of non-value add steps in your process?. They might be driven due to things outside

process.

Look for overall breakup of cycle time into value add, value enable, and non-value add. This might give overview of

improvement opportunities.

Treqna Base Manual


Histogram

Tool Utility:Study variation in process. Gives visual display of data distribution as bar graph (frequency graph). Useful tool to determine if distribution is centered around target, and how is the variation against the customer specification limits.

How:Minitab.Histogram can also be made using excel sheet. In order to do so:- create a frequency table with or without defined classes(e.g. age 10-20, or without classes 10, 11 etc.)- Plot the frequency against individual X values or Classes on X-axis.

1 0 09 59 08 58 07 57 06 56 05 5

1 0

5

0

T e s t G r a d e s

# of

Stu

dent

s

1 0 09 59 08 58 07 57 06 56 05 5

1 0

5

0

T e s t G r a d e s

# of

Stu

dent

s

Treqna Base Manual


Histogram – Minitab

MINITAB FILE: DescriptiveStats.mtwClick on Graph > Histograms

1.Click on ‘Simple’2.Click Ok

Treqna Base Manual


Histogram is the graphical representation of the distribution of population plotted. It helps understanding following for any given population:

• Shape: Look for the distribution of bars. Are there multiple modes in the distribution?. This might give us idea if the given data is mix of two or more different population sets.

• Center: Where is the distribution centered?. Is it off the process target?.• Spread: How is the spread of bars in histogram?. Is the spread large compare to

requirement?(look against the specification limits). Note that spread has got nothing to do with Normality of data, as you might have normal data with very large spread when compared against specification limits from customer.

The options at the bottom of histogram input window gives option to put specification limits.

Histogram Output

Treqna Base Manual


Dot Plot

Tool Utility: Another tool to study variation in process. Also used for quick comparison of two or more groups for variation. As a part of descriptive statistical analysis used in initial stages.

How: Use Minitab GRAPH > DOTPLOTClick on ‘Simple’, Click OkDouble Click on C1, Click ok

Treqna Base Manual


Dot plot can be plotted from GRAPHS> DOTPLOTIn Minitab Release 14 the Dotplot from Graphs menu gives multiple option for Single Y, Multiple Y, Single group, Multiple group and there combination.

Dot Plot - Minitab


Treqna Base Manual


When Dotplot plotted for multiple operators (groups) gives us comparative visual representation of their:•Variation•Center• and spread

Dot Plot Output

Treqna Base Manual


Box And Whisker Plot

Tool Utility: Useful tool to compare two or more groups on variation and median. The tool plots:

- Quartiles- Median- Outliers, if any

The box tells about the spread of data and is a visual used for comparing two or more data groups.

How: Minitab > Graph > Boxplot

Treqna Base Manual


Box plot - How to Read ?

Maximum Observation that falls within the upper limit = Q3 + 1.5 (Q3 - Q1)

75th Percentile (Q3)

Median (50th Percentile)

25th Percentile (Q1)

Minimum Observation that falls within the lower limit = Q1 - 1.5 (Q3 - Q1)

Outlierany point outside the lower or upper limit*

Treqna Base Manual


Box plot - Minitab

MINITAB FILE: BoxPlots.mtwMinitab > Graph > Boxplot

• Choose ‘One Y’ ‘With Groups’, Click Ok.

• Use C6 for Data,• C7 for Subscripts• Click ok

Treqna Base Manual


Statistical Hypothesis Testing

Treqna Base Manual


The Nature Of Statistical Problems

DesiredProcess Current

Process

LSL USL

Poor Precision, Focus on reducing Variation

T

Poor Accuracy, Focus on Centering the process

DesiredProcess

CurrentProcess

LSL

T

USL

While working on Six Sigma Projects we come across two types of problems with data. •Variation (Spread)•CenteringThough working on one problem has some impact on other also, more often than not we would target only one problem at a time.

In Analyze phase we run statistical tests to determine which X’s have an effect on the Y. These tests may be testing for variance or for mean depending on what is our Y metric.

Treqna Base Manual


A Statistical Hypothesis

Definition of Hypothesis: Statement about the parameters of the Population

In hypothesis testing there are two hypotheses of interest.

– The null hypothesis (H0)

– The alternative hypothesis (HA)

Treqna Base Manual


Concept Of Hypothesis Testing

1. All processes have variation.

2. Different Samples from the same process may vary

Are these Samples from the same distribution or are they truly from different processes.

3. Hypothesis testing differentiates between sampling error (Precision) and true process differences.

Treqna Base Manual


Why Do Hypothesis Testing?

Identification and validation of factors which impact process performance.

Validate improvement in process

Statistically validate our statement about the characteristics of population

Helps in decision making process. Enabler for data driven approach.

Treqna Base Manual


Hypothesis Testing

In Hypothesis Testing one has to make a decision:– to either to accept null hypothesis or– to reject null hypothesis

The hypotheses are always statements about the population parameters.

To define a statistical Test we– Choose a statistic (called the test statistic)– State your null and alternate hypothesis– Divide the range of possible values for the test statistic into two parts

• The Acceptance Region• The Critical Region

•The Acceptance Region (The range of values of the test statistic that indicate the Null Hypothesis is true.)• The Critical Region (The range of values of the test statistic that indicate the Null Hypothesis is false.)

Treqna Base Manual


Nature of Ho and Ha

Null Hypothesis (Ho ):

Null hypothesis always represents Status Quo, No difference

True unless proven otherwise

Represented by = or > or <

Alternative Hypothesis (Ha ):

It is the conclusion we are trying to make from data

Signs used in Minitab:≠ or < or >

Treqna Base Manual


Criminal Trial Analogy

• In the court defendant is always treated as innocent until proven guilty.

• The hypothesis than is:

• Ho: Person is not guilty.

• Ha: Person is guilty.

• There after once all the evidence(data) is collected we make a decision based on it:

• If there is sufficient evidence(statistically significant) we reject null hypothesis and

accept alternate(defendant is guilty).

• If there is not enough evidence we accept null hypothesis (defendant is innocent)

Hypotheses are statements about population parameters. Relating to the previous example about the height of people from two different countries, we could state: Ho: μB ≤ μA Ha: μB > μA

The statement is about the population means, not the sample means.

Treqna Base Manual


TruthTruth

Ho Ha

Ver

dict

Ver

dict

Ho

HaInnocent,

Jailed

Guilty,Set Free

Innocent,Set Free

Guilty,Jailed

Innocent Guilty

Set

Free

Jaile

d

Based on the evidence there are four possible outcomes of decision we make:

Decision Error

Treqna Base Manual


• 1 - α = Probability of correctly accepting the null hypothesis (detecting no change when there is none).

• 1 - β = Probability of correctly accepting the alternative hypothesis (detecting a change when there is one).

• It is not possible to commit a Type I and Type II decision error simultaneously

Decision Error - Types

TruthTruth

Ho Ha

Ver

dict

Ver

dict Ho

HaType I Error

α

Type II Errorβ

Correct Decision1 - α = Confidence

Correct Decision1 - β = Power

Innocent Guilty

Set

Free

Jaile

d

For any statistical testing procedure define1. α = P[Rejecting the null hypothesis when it is true] = P[ type I error]2. β = P[accepting the null hypothesis when it is false] = P[ type II error]The symbol α is called the level of significance. Usually we have α set at .05, which means we have 95%(1- α) confidence in accepting null hypothesis.The Acceptance Region and The Critical Region are chosen form underneath the sampling distribution of the test statistic when H0 is true.The Critical Region lies in the tails of sampling distribution of the test statistic when H0 is true.

Treqna Base Manual


Types of HypothesisOne Sample Hypothesis

1. Ho : μ = constant = T

Ha : μ ≠ constant = T

2. Ho : σ2 = constant

Ha : σ2 ≠ constant

Ho Ha

T

In this and following slides read:μ as mean and σ as standard deviation

Treqna Base Manual


Types of HypothesisTwo Sample Hypotheses

3. Ho : μ1 = μ2

Ha : μ1≠ μ2

4. Ho : μ1 ≤ μ2

Ha : μ1 > μ2

5. Ho : σ12 = σ2

2

Ha : σ12 ≠ σ2

2

μ1 μ2

σ2

σ1

Treqna Base Manual


Types of HypothesisMulti Sample Hypotheses

6. Ho : μ1 = μ2 = . . . = μn

Ha : at least one not equal

7. Ho : σ12 = σ2

2 = . . . = σn2

Ha : at least one not equal

Treqna Base Manual


4 5 6 7 8 9 10 11 12 13 14 15 16

4 5 6 7 8 9 10 11 12 13 14 15 16

α/2 α/2

α/2

μ = 10

μ = 10

Acceptance Region1 - α

Acceptance Region1 - α

One-Sided Test

Ex. Ho : μ1 < 10Ha : μ1 > 10

Two-Sided Test

Ex. Ho : μ1 = 10Ha : μ1 ≠ 10

One-sided & Two-sided Hypothesis Tests

The symbols used for two-sided tests are = and ≠. The symbols used for one-sided tests are ≥, ≤, < and >

Treqna Base Manual


Alpha denotes the probability of making a Type I error

P-value is the probability value based on which we make judgment on hypothesis.

Any p-value less than 0.05 means we reject the null hypothesis and accept the

alternate hypothesis

The P-Value

p < a: Reject Ho

p > a: Accept Ho

p < a: Reject Ho

p > a: Accept Ho

Treqna Base Manual


Hypothesis Tests Summary

Continuous Y and Discrete X

Test for MEDIAN- Moods Median Test – tests if medians from 2 or more sample means are equal

- HOV (Levene) – Compares 2 or more samples

Test for MEAN- 1-sample T test – tests if a sample means is equal to a known mean or target- 2-sample T test – tests if 2 sample means are equal- One way ANOVA – tests if 2 or more samples have equal means- Two way ANOVA – tests if means from samples classified by 2 categories are equal

- F test – Compares 2 samples- HOV (Levene) – Compares 2 or more samples- χ2 Test – Compares a sample variance to a known population variance

Central TendencyVariation

Test for MEDIAN- Moods Median Test – tests if medians from 2 or more sample means are equal

- HOV (Levene) – Compares 2 or more samples

Test for MEAN- 1-sample T test – tests if a sample means is equal to a known mean or target- 2-sample T test – tests if 2 sample means are equal- One way ANOVA – tests if 2 or more samples have equal means- Two way ANOVA – tests if means from samples classified by 2 categories are equal

- F test – Compares 2 samples- HOV (Levene) – Compares 2 or more samples- χ2 Test – Compares a sample variance to a known population variance

Central TendencyVariation

Y =

Nor

mal

Y =

Non

Nor

mal

Treqna Base Manual


Normal (z) Distribution

When sample size is infinite uncertainty prediction becomes very small, hence we can use Normal distribution for predictions.

df = ∞

σμXZ −=

μ

Sample size infinite

Treqna Base Manual


While working on project if our metric is related to controlling or decreasing spread, we might be interested to know if factor X has an impact on variance in Y.

To compare variance of two or multiple data samples we use Homogeneity of Variance

(HOV) Test.

The hypothesis for the test is:

HO = Variance for all the groups are equal

Ha = At least one group variance is different

HOV is also prerequisite to testing for group means. Some tools which are used to test

means of groups use pooled deviation and so HOV is a tool which used before we

decide which tool we will use before testing for means.

Homogeneity of Variance (HOV)

Treqna Base Manual


HOV - Minitab

If you wish to study variation across 2 or more Groups and you have established that each groups stable and normally distributed. Perform the Homogeneity of Variance Test.

Minitab File: HOV.mtw

Treqna Base Manual


HOV - Input

22

21a

22

21o

σ σ :H

σ σ :H

≠

=

.05 α =

Treqna Base Manual


In the output window the graph on left side represent confidence interval around standard deviation of each group.On the right hand side we get P-values for the test.The test results which we can read from left side window are:F-Test: We get this result only when there are two groups and normal data. For more than two groups and normal data F-test is replaced by Bartlett’s test.Bartlett’s Test: When your data is normal and have more than two groups under evaluation. Do not use this test result when your data is non- normal as Bartlett’s test is not robust to non-normality.Levene’s Test: Use this test result when data is continuous and not necessary normal.

HOV Test - Output

p < a: Reject Ho

p > a: Accept Ho

22

21a

22

21o

σ σ :H

σ σ :H

≠

=.05 α =

Treqna Base Manual


2 Sample t test

HO (Null Hypothesis) : μ1 = μ2

HA (Alternate Hypothesis) : μ1 = μ2

Treqna Base Manual


2 Sample t test - Minitab

Minitab File: HOV.mtw

Treqna Base Manual


Run Homogeneity of Variance test before you indicate to assume equal variances in the input window.

2 sample t - Input

Click ‘Options’ to change your Alternate Hypothesis

Check this box if HOV Indicates that there is no statistically significant difference in Variation among the groups being tested

Treqna Base Manual


2 Sample t -Output

Two-Sample T-Test and CI: Agent A, Agent B

Two-sample T for Agent A vs Agent B

N Mean StDev SE Mean

Agent A 40 70.20 2.19 0.35

Agent B 40 49.58 2.85 0.45

Difference = mu (Agent A) - mu (Agent B)

Estimate for difference: 20.6250

95% CI for difference: (19.4920, 21.7580)

T-Test of difference = 0 (vs not =): T-Value = 36.28

P-Value = 0.000 DF = 73

Accept HA (Alternate Hypothesis) : μ1 = μ2

The p value indicates that the two agents are statically different in their performance.

Treqna Base Manual


Two Sample T-test and One Way ANOVA test the same thing, however the difference comes from the fact that Two Sample T-test can analyze only two sample at a time and so running it formultiple groups is a logistical nightmare. Though Two Sample T-test gives us flexibility of not assuming equal variances

ANOVA v/s Regression:

Analysis of variance (ANOVA) is similar to regression in that it is used to investigate and model the relationship between a response variable and one or more independent variables. There are two ways ANOVA is different from Regression Analysis:•The independent variables are categorical•It doesn’t make any assumption about the the nature of relationship between Y and independent variable.

ANOVA stand for Analysis of Variance. Though the name is misleading

One Way ANOVA is used to compare means of two or more groups. The hypothesis

used is:

Ho: μ1 = μ2 = μ3 = μ4

Ha: At least one m different from the others

Since ANOVA uses pooled standard deviation it is essential to run HOV before this test.

In case HOV fails than one may use Two Sample T-Test.

One Way Analysis of Variance (ANOVA)

Treqna Base Manual


A Test to determine if the means of the number of Queries Resolved by 4 agents is statistically differentHo: μ1 = μ2 = μ3 = μ4Ha: at least one m different from the others

One Way ANOVA - Minitab

Minitab File: Anova.mtw

Treqna Base Manual


One-Way ANOVA – Input/ Output

One-way ANOVA: Average Queries Resolved versus Agent

Source DF SS MS F P

Agent 3 9998.6 3332.9 287.01 0.000

Error 196 2276.1 11.6

Total 199 12274.6

S = 3.408 R-Sq = 81.46% R-Sq(adj) = 81.17%

Individual 95% CIs For Mean Based on

Pooled StDev

Level N Mean StDev --------+---------+---------+---------+-

Agent A 50 19.940 2.234 (*-)

Agent B 50 29.908 2.779 (-*)

Agent C 50 39.874 4.049 (*-)

Agent D 50 28.596 4.164 (-*)

--------+---------+---------+---------+-

24.0 30.0 36.0 42.0

Pooled StDev = 3.408

An ANOVA output gives us:1. P-value for significance2. Confidence band to understand which ones are different

Treqna Base Manual


Non–Parametric Test - Objectives

Understand distribution - Normality Test

Possible reasons for not normal data

Understand interpretation of Mood’s Median Test

Understand HOV Test

Treqna Base Manual


Non-parametric Tests

What if I don’t have normal data?

When we don’t have Normal data we use non-parametric tests. Nonparametric

means that no assumption for distribution of data exist.

Tools used for analysis are:

Stability : Run Chart

Centre tendency : Mood’s Median Test

Spread (Variance) : HOV – Use Levine's test

Capability : Use DPMO to calculate sigma

It is common to have data which is not not normal. Care should be taken before reaching that conclusion.

Distribution should be check for multiple populationCheck for outliers

Normal data gives flexibility in terms of number of tools available for analysis. However sufficient tools are available for not normal data.

Treqna Base Manual


Non-parametric Tests

The term nonparametric means that no assumption is made about the distribution of

data.

– Non-parametric tests are used when we have no assumption for distribution

of the data to work with.

– Mood’s Median Test is a nonparametric test which is frequently used to

compare medians of two or more groups. One way ANOVA is the

counterpart of this test for Normal data.

Examples of non-normal data:

Cycle time data is usually non normal data. Usually a skewed distribution.

Metric data where only one sided specifications limits are defined.

Treqna Base Manual


Dealing With Non-Normal Data

Do some checks before concluding that data is non normal:

– Normality Test

– Look for resolution of data. The measurement System should be able to capture the unit of data in an adequate fashion.

– Investigate outliers(A word of caution: sometimes while taking out outliers we end up taking out a considerable amount of data from sample, this is not recommended, limit your removal of data to only a few data points).

– Check your sample size. Small sample size (<30 points) might not be able to predict population characteristics correctly.

– Attempt to transform the data. However it should not be used as a compulsion. Consult with MBB/BB before you use transformation. Common transforms include:

– finding the square root of all data points

– finding the log of all data points

– finding the square of all data points

– Box-cox Transformation

Care is required before concluding that data is non-normal. Primarily because more often than not data is supposed to be normal. However we still encounter situations when we come across non-normal data.Use the non-normal tests!

Treqna Base Manual


E.g. File: MoodsMedianStat > Nonparametrics > Mood’s Median Test

– Response = Average Call Handle Time– Factor = Team

Answer the following questions:1. Are the medians different? (interpret the p-value)2. Which medians are different? (interpret the confidence intervals)

Mood’s Median Test

HO = Medians for all the groups are equalHA = At least one median is different

Hypothesis for the test:

To perform a Mood’s Median Test on collected data:Enter Y data in one column in Minitab Second column should define subgroupsChoose test from Stat > Nonparametric > Mood’s Median Test

Treqna Base Manual



Select Stat > Nonparametrics > Moods Median Test

Treqna Base Manual


Mood’s Median Test – Input

Response data or Y

Factors or X’s

Treqna Base Manual


Mood’s Median Test - Output

Mood Median Test: AHT versus Team

Mood median test for AHT

Chi-Square = 26.32 DF = 2 P = 0.000

Individual 95.0% CIs

Team N<= N> Median Q3-Q1 -----+---------+---------+---------+-

A 7 8 280.0 14.0 (----*----)

B 15 0 263.0 10.0 (---*--)

C 1 14 296.0 13.0 (-----*--)

-----+---------+---------+---------+-

264 276 288 300

Overall median = 279.0

P value

Confidence interval

Mood’s Median test output gives a table where it defines by group number of data items below and above group’s median. It then performs a simple Chi-square test on this summary table. Based on the test it gives P value.If you would manually run Chi-square test on the table, you would get the same result.On the right side of table we get a visual of confidence band around group medians. When the test is significant you would see that one of the group confidence band far from others.

Treqna Base Manual


Hypothesis for various tests

Run Charts

Ho : There are no trends, cluster oscillations or mixtures

Ha : There exist trends, clusters, oscillations or mixtures

Normality Test

Ho : Data is normally distributed

Ha : Data is not normally distributed


Ho : X1 = X2 = X3 =…..= Xn

Ha : At least one median is different from the others

Homogeneity of variance

Ho : σ12 = σ2

2 =….. = σn2

Ha : σ12 ≠ σ2

2 ≠ ….. ≠ σn2

∼ ∼ ∼ ∼

Treqna Base Manual


1-sample t test

Ho : μ = T

Ha : μ ≠ T

2-sample t test

Ho : μ1 = μ2

Ha : μ1 ≠ μ2

Paired t test

Ho : Difference between the two means = 0

Ha : Difference between the two means ≠ 0

ANOVA

Ho : μ1 = μ2 = μ3 =….= μn

Ha : At least one mean is different from the others

Hypothesis for various tests

Treqna Base Manual


Continuous Y and X

Continuous Y and Continuous X

• Correlation : Tests Linear relationship between two variables

• Regression : Defines linear relationship between a dependent and an independent

variable

Correlation assumes that both variables can change while regression (typically) assumes that the independent variable is measured without error. A significant correlation means that 2 variables tend to go up or down together (or change in opposite directions), for whatever reason. A significant regression means that the dependent variable can be predicted by the independent variable, again, for whatever reason. Causality is not tested by either method. Though theoretically different, both tests usually give the same answer (significant or not).

Treqna Base Manual


E.g. File: Grades.MTWStat > Basic Stats > Correlation

Correlation - Minitab

Treqna Base Manual


Correlation – Inputs/Outputs

Treqna Base Manual


Regression Minitab

Treqna Base Manual


Regression Minitab Inputs

Treqna Base Manual



Click the ‘Graphs’ button

Treqna Base Manual



Click the ‘Results’ button

Treqna Base Manual


Regression Minitab Outputs

Regression Analysis: Score1 versus Score2

The regression equation isScore1 = - 4.67 + 4.40 Score2

Predictor Coef SE Coef T PConstant -4.6674 0.8572 -5.44 0.001Score2 4.3975 0.3514 12.51 0.000

S = 0.572711 R-Sq = 95.7% R-Sq(adj) = 95.1%

Analysis of Variance

Source DF SS MS F PRegression 1 51.353 51.353 156.56 0.000Residual Error 7 2.296 0.328Total 8 53.649

Treqna Base Manual


Discrete Y & Discrete X

Two Chi-Square Tests:o Goodness-of-Fit Test to test if observed data has expected distributiono Test of Independence to test if two or more proportions are different

• Chi-Square statistic is calculated using formula:

• Critical Value depends on two factors:o a - the confidenceo df – degrees of freedom for data

e

eon

i fff 2

1

⎟⎠⎞

⎜⎝⎛ −

= Σ=

2χ

Treqna Base Manual


Chi-Square Test–χ2

Tool Utility:

Chi-square tests enables us to test whether two or more population can be

considered equal.

There are two types of Chi-square χ2 tests:

- Goodness-of-Fit Test: To test if an observed set of data fits an expected

distribution of data.

- Test of Independence: To test if two or more proportions are associated (Belong

to similar distribution)

Treqna Base Manual


Calculation for Chi-square statistic is:

Where:n = number of categoriesfo = observed frequency of datafe = expected frequency of data

e

eon

i fff 2

1

⎟⎠⎞

⎜⎝⎛ −

= Σ=

2χ

Chi-Square Statistic

Treqna Base Manual


The chi-square uses “degrees of freedom” of data under scrutiny as a parameter while calculating Chi-Square critical value.

For any statistic being computed, the degrees of freedom of a sample are the number of values in the sample which are free to vary without changing the statistic being measured.

Degrees Of Freedom

Treqna Base Manual


The statistical test can be done both manually or using minitab. Steps involved in doing manual calculation are:

• Create frequency table and see if any of the frequency is less than 5(as we have mentioned earlier that avoid small frequency)

• Calculate Chi-square statistic using the formula

• Calculate critical value using the table. Critical value depends on two things, a -the confidence and degrees of freedom(df).

• If the chi-square statistic is less than the critical value in the table, the null hypothesis (good fit) is accepted. If not, the alternative hypothesis (that the data are not typical of the expected distribution) is accepted.

Chi Square Stat Test

A B

Critical Value

Area of Rejection

Chi-Square Distribution

P-value can also be calculated using formula in excel:CHIDIST(statistic,df)

Treqna Base Manual



d f .2 5 0 .1 0 0 .0 5 0 .0 2 5 .0 1 0 .0 0 5 .0 0 11 1 .3 2 3 2 .7 0 6 3 .8 4 1 5 .0 2 4 6 .6 3 5 7 .8 7 9 1 0 .8 2 82 2 .7 7 3 4 .6 0 5 5 .9 9 1 7 .3 7 8 9 .2 1 0 1 0 .5 9 7 1 3 .8 1 63 4 .1 0 8 6 .2 5 1 7 .8 1 5 9 .3 4 8 1 1 .3 4 5 1 2 .8 3 8 1 6 .2 6 64 5 .3 8 5 7 .7 7 9 9 .4 8 8 1 1 .1 4 3 1 3 .2 7 7 1 4 .8 6 0 1 8 .4 6 75 6 .6 2 6 9 .2 3 6 1 1 .0 7 0 1 2 .8 3 2 1 5 .0 8 6 1 6 .7 5 0 2 0 .5 1 5

6 7 .8 4 1 1 0 .6 4 5 1 2 .5 9 2 1 4 .4 4 9 1 6 .8 1 2 1 8 .5 4 8 2 2 .4 5 87 9 .0 3 7 1 2 .0 1 7 1 4 .0 6 7 1 6 .0 1 3 1 8 .4 7 5 2 0 .2 7 8 2 4 .3 2 28 1 0 .2 1 9 1 3 .3 6 2 1 5 .5 0 7 1 7 .5 3 5 2 0 .0 9 0 2 1 .9 5 5 2 6 .1 2 59 1 1 .3 8 9 1 4 .6 8 4 1 6 .9 1 9 1 9 .0 2 3 2 1 .6 6 6 2 3 .5 8 9 2 7 .8 7 7

1 0 1 2 .5 4 9 1 5 .9 8 7 1 8 .3 0 7 2 0 .4 8 3 2 3 .2 0 9 2 5 .1 8 8 2 9 .5 8 8

1 1 1 3 .7 0 1 1 7 .2 7 5 1 9 .6 7 5 2 1 .9 2 0 2 4 .7 2 5 2 6 .7 5 7 3 1 .2 6 41 2 1 4 .8 4 5 1 8 .5 4 9 2 1 .0 2 6 2 3 .3 3 7 2 6 .2 1 7 2 8 .3 0 0 3 2 .9 0 91 3 1 5 .9 8 4 1 9 .8 1 2 2 2 .3 6 2 2 4 .7 3 6 2 7 .6 8 8 2 9 .8 1 9 3 4 .5 2 81 4 1 7 .1 1 7 2 1 .0 6 4 2 3 .6 8 5 2 6 .1 1 9 2 9 .1 4 1 3 1 .3 1 9 3 6 .1 2 31 5 1 8 .2 4 5 2 2 .3 0 7 2 4 .9 9 6 2 7 .4 8 8 3 0 .5 7 8 3 2 .8 0 1 3 7 .6 9 7

1 6 1 9 .3 6 9 2 3 .5 4 2 2 6 .2 9 6 2 8 .8 4 5 3 2 .0 0 0 3 4 .2 6 7 3 9 .2 5 21 7 2 0 .4 8 9 2 4 .7 6 9 2 7 .5 8 7 3 0 .1 9 1 3 3 .4 0 9 3 5 .7 1 8 4 0 .7 9 01 8 2 1 .6 0 5 2 5 .9 8 9 2 8 .8 6 9 3 1 .5 2 6 3 4 .8 0 5 3 7 .1 5 6 4 3 .3 1 21 9 2 2 .7 1 8 2 7 .2 0 4 3 0 .1 4 4 3 2 .8 5 2 3 6 .1 9 1 3 8 .5 8 2 4 3 .8 2 02 0 2 3 .8 2 8 2 8 .4 1 2 3 1 .4 1 0 3 4 .1 7 0 3 7 .5 6 6 3 9 .9 9 7 4 5 .3 1 5

2 1 2 4 .9 3 5 2 9 .6 1 5 3 2 .6 7 1 3 5 .4 7 9 3 8 .9 3 2 4 1 .4 0 1 4 6 .7 9 72 2 2 6 .0 3 9 3 0 .8 1 3 3 3 .9 2 4 3 6 .7 8 1 4 0 .2 8 9 4 2 .7 9 6 4 8 .2 6 82 3 2 7 .1 4 1 3 2 .0 0 7 3 5 .1 7 2 3 8 .0 7 6 4 1 .6 3 8 4 4 .1 8 1 4 9 .7 2 82 4 2 8 .2 4 1 3 3 .1 9 6 3 6 .4 1 5 3 9 .3 6 4 4 2 .9 8 0 4 5 .5 5 8 5 1 .1 7 92 5 2 9 .3 3 9 3 4 .3 8 2 3 7 .6 5 2 4 0 .6 4 6 4 4 .3 1 4 4 6 .9 2 8 5 2 .6 2 0

2 6 3 0 .4 3 4 3 5 .5 6 3 3 8 .8 8 5 4 1 .9 2 3 4 5 .6 4 2 4 8 .2 9 0 5 4 .0 5 22 7 3 1 .5 2 8 3 6 .7 4 1 4 0 .1 1 3 4 3 .1 9 4 4 6 .9 6 3 4 9 .6 4 5 5 5 .4 7 62 8 3 2 .6 2 0 3 7 .9 1 6 4 1 .3 3 7 4 4 .4 6 1 4 8 .2 7 8 5 0 .9 9 3 5 6 .8 9 22 9 3 3 .7 1 1 3 9 .0 8 7 4 2 .5 5 7 4 5 .7 2 2 4 9 .5 8 8 5 2 .3 3 6 5 8 .3 0 23 0 3 4 .8 0 0 4 0 .2 5 6 4 3 .7 7 3 4 6 .9 7 9 5 0 .8 9 2 5 3 .6 7 2 5 9 .7 0 3

4 0 4 5 .6 1 6 5 1 .8 0 5 5 5 .7 5 8 5 9 .3 4 2 6 3 .6 9 1 6 6 .7 6 6 7 3 .4 0 25 0 5 6 .3 3 4 6 3 .1 6 7 6 7 .5 0 5 7 1 .4 2 0 7 6 .1 5 4 7 9 .4 9 0 8 6 .6 6 16 0 6 6 .9 8 1 7 4 .3 9 7 7 9 .0 8 2 8 3 .2 9 8 8 8 .3 7 9 9 1 .9 5 2 9 9 .6 0 7

7 0 7 7 .5 7 7 8 5 .5 2 7 9 0 .5 3 1 9 5 .0 2 3 1 0 0 .4 2 5 1 0 4 .2 1 5 1 1 2 .3 1 78 0 8 8 .1 3 0 9 6 .5 7 8 1 0 1 .8 7 9 1 0 6 .6 2 9 1 1 2 .3 2 9 1 1 6 .3 2 1 1 2 4 .8 3 99 0 9 8 .6 5 0 1 0 7 .5 6 5 1 1 3 .1 4 5 1 1 8 .1 3 6 1 2 4 .1 1 6 1 2 8 .2 9 9 1 3 7 .2 0 8

1 0 0 1 0 9 .1 4 1 1 1 8 .4 9 8 1 2 4 .3 4 2 1 2 9 .5 6 1 1 3 5 .8 0 7 1 4 0 .1 6 9 1 4 9 .4 4 9

A lp h a

Treqna Base Manual


d f . 9 9 5 . 9 9 0 . 9 7 5 . 9 5 0 . 9 0 0 . 7 5 0 . 5 0 01 . 0 0 0 0 3 9 . 0 0 0 1 6 0 . 0 0 0 9 8 0 . 0 0 3 9 3 0 . 0 1 5 8 0 0 . 1 0 1 5 0 0 . 4 5 5 0 0 02 0 . 0 1 0 0 . 0 2 0 0 . 0 5 1 0 . 1 0 3 0 . 2 1 1 0 . 5 7 5 1 . 3 8 63 0 . 0 7 2 0 . 1 1 5 0 . 2 1 6 0 . 3 5 2 0 . 5 8 4 1 . 2 1 3 2 . 3 6 64 0 . 2 0 7 0 . 2 9 7 0 . 4 8 4 0 . 7 1 1 1 . 0 6 4 1 . 9 2 3 3 . 3 5 75 0 . 4 1 2 0 . 5 5 4 0 . 8 3 1 1 . 1 4 5 1 . 6 1 0 2 . 6 7 5 4 . 3 5 1

6 0 . 6 7 6 0 . 8 7 2 1 . 2 3 7 1 . 6 3 5 2 . 2 0 4 3 . 4 5 5 5 . 3 4 87 0 . 9 8 9 1 . 2 3 9 1 . 6 9 0 2 . 1 6 7 2 . 8 3 3 4 . 2 5 5 6 . 3 4 68 1 . 3 4 4 1 . 6 4 6 2 . 1 8 0 2 . 7 3 3 3 . 4 9 0 5 . 0 7 1 7 . 3 4 49 1 . 7 3 5 2 . 0 8 8 2 . 7 0 0 3 . 3 2 5 4 . 1 6 8 5 . 8 9 9 8 . 3 4 3

1 0 2 . 1 5 6 2 . 5 5 8 3 . 2 4 7 3 . 9 4 0 4 . 8 6 5 6 . 7 3 7 9 . 3 4 2

1 1 2 . 6 0 3 3 . 0 5 3 3 . 8 1 6 4 . 5 7 5 5 . 5 7 8 7 . 5 8 4 1 0 . 3 4 11 2 3 . 0 7 4 3 . 5 7 1 4 . 4 0 4 5 . 2 2 6 6 . 3 0 4 8 . 4 3 8 1 1 . 3 4 01 3 3 . 5 6 5 4 . 1 0 7 5 . 0 0 9 5 . 8 9 2 7 . 0 4 2 9 . 2 9 9 1 2 . 3 4 01 4 4 . 0 7 5 4 . 6 6 0 5 . 6 2 9 6 . 5 7 1 7 . 7 9 0 1 0 . 1 6 5 1 3 . 3 3 91 5 4 . 6 0 1 5 . 2 2 9 6 . 2 6 2 7 . 2 6 1 8 . 5 4 7 1 1 . 0 3 6 1 4 . 3 3 9

1 6 5 . 1 4 2 5 . 8 1 2 6 . 9 0 8 7 . 9 6 2 9 . 3 1 2 1 1 . 9 1 2 1 5 . 3 3 81 7 5 . 6 9 7 6 . 4 0 8 7 . 5 6 4 8 . 6 7 2 1 0 . 0 8 5 1 2 . 7 9 2 1 6 . 3 3 81 8 6 . 2 6 5 7 . 0 1 5 8 . 2 3 1 9 . 3 9 0 1 0 . 8 6 5 1 3 . 6 7 5 1 7 . 3 3 81 9 6 . 8 4 4 7 . 6 3 3 8 . 9 0 7 1 0 . 1 1 7 1 1 . 6 5 1 1 4 . 5 6 2 1 8 . 3 3 82 0 7 . 4 3 4 8 . 2 6 0 9 . 5 9 1 1 0 . 8 5 1 1 2 . 4 4 3 1 5 . 4 5 2 1 9 . 3 3 7

2 1 8 . 0 3 4 8 . 8 9 7 1 0 . 2 8 3 1 1 . 5 9 1 1 3 . 2 4 0 1 6 . 3 4 4 2 0 . 3 3 72 2 8 . 6 4 3 9 . 5 4 2 1 0 . 9 8 2 1 2 . 3 3 8 1 4 . 0 4 1 1 7 . 2 4 0 2 1 . 3 3 72 3 9 . 2 6 0 1 0 . 1 9 6 1 1 . 6 8 8 1 3 . 0 9 1 1 4 . 8 4 8 1 8 . 1 3 7 2 2 . 3 3 72 4 9 . 8 8 6 1 0 . 8 5 6 1 2 . 4 0 1 1 3 . 8 4 8 1 5 . 6 5 9 1 9 . 0 3 7 2 3 . 3 3 72 5 1 0 . 5 2 0 1 1 . 5 2 4 1 3 . 1 2 0 1 4 . 6 1 1 1 6 . 4 7 3 1 9 . 9 3 9 2 4 . 3 3 7

2 6 1 1 . 1 6 0 1 2 . 1 9 8 1 3 . 8 4 4 1 5 . 3 7 9 1 7 . 2 9 2 2 0 . 8 4 3 2 5 . 3 3 62 7 1 1 . 8 0 8 1 2 . 8 7 9 1 4 . 5 7 3 1 6 . 1 5 1 1 8 . 1 1 4 2 1 . 7 4 9 2 6 . 3 3 62 8 1 2 . 4 6 1 1 3 . 5 6 5 1 5 . 3 0 8 1 6 . 9 2 8 1 8 . 9 3 9 2 2 . 6 5 7 2 7 . 3 3 62 9 1 3 . 1 2 1 1 4 . 2 5 6 1 6 . 0 4 7 1 7 . 7 0 8 1 9 . 7 6 8 2 3 . 5 6 7 2 8 . 3 3 63 0 1 3 . 7 8 7 1 4 . 9 5 3 1 6 . 7 9 1 1 8 . 4 9 3 2 0 . 5 9 9 2 4 . 4 7 8 2 9 . 3 3 6

4 0 2 0 . 7 0 7 2 2 . 1 6 4 2 4 . 4 3 3 2 6 . 5 0 9 2 9 . 0 5 1 3 3 . 6 6 0 3 9 . 3 3 55 0 2 7 . 9 9 1 2 9 . 7 0 7 3 2 . 3 5 7 3 4 . 7 6 4 3 7 . 6 8 9 4 2 . 9 4 2 4 9 . 3 3 56 0 3 5 . 5 3 5 3 7 . 4 8 5 4 0 . 4 8 2 4 3 . 1 8 8 4 6 . 4 5 9 5 2 . 2 9 4 5 9 . 3 3 5

7 0 4 3 . 2 7 5 4 5 . 4 4 2 4 8 . 7 5 8 5 1 . 7 3 9 5 5 . 3 2 9 6 1 . 6 9 8 6 9 . 3 3 48 0 5 1 . 1 7 2 5 3 . 5 4 0 5 7 . 1 5 3 6 0 . 3 9 1 6 4 . 2 7 8 7 1 . 1 4 5 7 9 . 3 3 49 0 5 9 . 1 9 6 6 1 . 7 5 4 6 5 . 6 4 7 6 9 . 1 2 6 7 3 . 2 9 1 8 0 . 6 2 5 8 9 . 3 3 4

1 0 0 6 7 . 3 2 8 7 0 . 0 6 5 7 4 . 2 2 2 7 7 . 9 2 9 8 2 . 3 5 8 9 0 . 1 3 3 9 9 . 3 3 4

A l p h a


Treqna Base Manual


This Test is used to check independence of two or more proportions. The hypothesis used is:H0 = all proportions are equalHa = at least one proportion is different from rest

Again as a caution frequency less than 5 not to be used for the test.

To do the test we use Contingency tables. The rows and the columns define the classification of data.

Following is an example of contingency table:

Degrees of Freedom:

Degrees of freedom for the test are calculated using formula:

(M-1)*(N-1)

Where M and N are number of columns and rows respectively.

Test of Independence

fo = 37

fo = 63

fo = 113

fo = 167

Leads

Dead Ends

Tele sales Team A

Total = 150

Total = 230

Total = 100 Total = 280

Tele sales Team A

Treqna Base Manual


The test of Independence includes calculating Chi-Square statistic and Critical value from chi-square table using degrees of freedom and confidence.However, doing the test on minitab is easier:

Test of Independence – Minitab Input

Treqna Base Manual


Test of IndependenceMinitab Input And Results

Ho: No correlation between team and leads generated.

Ha: Correlation between team and leads generated

Treqna Base Manual


Tool picking guide

Treqna Base Manual


Statistical Test Choices

Treqna Base Manual


DEFINE

MEASURE

ANALYZE

IMPROVE

CONTROL

Map project



Baseline process



MSA on X’s

Approve project

Data collection






Treqna Base Manual


Improve Phase Objectives

• Develop and propose a solution

• Identify Vital X’s

• Develop transfer function

• Experiment with possibilities and develop solution

• Confirm that proposed solution will improve the process

• Pilot solution with small scale tests in real business environment

• Run statistical tests on the results to confirm the solution

• Identify and deploy resources to implement the solution

• Deploy solution on the process

Treqna Base Manual


Experiment with various solutions

Develop a transfer functions

Identify Vital Xs

Activities

Control Impact matrix, Regression

Interaction between Xs, Transfer function

Study Interaction between Xs

Step I.2

Tools

Deliverables

Objective

Step I.3Step I.1

FMEA, Process Map, Pareto, Fishbone analysis

Pilot SolutionVital Xs

Define Improved ProcessScreen for Vital Xs

Improve Phase


Treqna Base Manual


Characterization of Xs

Vital X’s or key elements which impact project Y have following characteristics:

• Independent variables

• Can be set at different levels to manipulate the response variable or dependent variable Y.

• Variation in independent variable contributes to variation in dependent variable Y

• Different X’s will have different impact on Y depending on the transfer function

• May be continuous and/or discrete

• Independent variables might not be measurable (E.g. alternative work-flow sequences)

Treqna Base Manual


Screening of X’s is done for various reasons:

• Focus on few factors which make most impact

• Ensure best utilization of resources available for the project

Tools Used:

• FMEA

• Pareto

• Fishbone analysis

• Screening DOE if advanced cases when X’s have interaction

Screening of Xs

Treqna Base Manual


Project Metric: Errors in Application form

Analyze result gave us seven factors which are significant. Now the pareto chart can be used to prioritize or screen further these factors. The output clearly says that Name, DOB and Country field contribute around 80% errors. So working on rest of the factors might not be as beneficial.

Using Pareto

Treqna Base Manual


When all the significant factors are available from Analyze step A3. One might use

FMEA to evaluate corresponding risk associated i.e. Risk priority number.

E.g.

On insurance application form where premium calculation is based on age risk

associated with error in DOB field would be more than error associated with wrong

address as it might result in financial loss to the insurance company.

Using FMEA

Treqna Base Manual




Identify Vital Xs

Activities




Step I.2

Tools

Deliverables

Objective

Step I.3Step I.1




Improve Phase


Treqna Base Manual


Problem Solving Process

Practical Problem

Statistical Problem

Statistical Solution

Practical Solution

Transfer Function Y=F(X)

Treqna Base Manual


Transfer Function

The goal of improve is to develop a solution using the transfer function

Y = {X1, X2, X3…Xn}

The transfer function:

• Relates the vital X’s to the project Y

• Predicts the effect and direction of changes on Y due to changes in X’s

• Helps in fitting a solution which maximizes the effect on Y using all or few of the X’s

Treqna Base Manual


The goal of improve is to develop a solution using the transfer function

Y = {X1, X2, X3…Xn}

Tools that give mathematical transfer function:

• DOE

• Regression

• GLM (General Linear Model)

Transfer Function

Treqna Base Manual


Using the Interaction Matrix – In the following example training has high and positive impact on call quality, while length of the call has low but negative effect on the call quality.

In absence of a transfer function it is a very handy tool to get insight into development of possible solution

Interaction Matrix

High

Low

Influence on Call Quality (Project Y) + -

Subject Knowledge

Training

Length of the call

Finance Background

Treqna Base Manual




Identify Vital Xs

Activities




Step I.2

Tools

Deliverables

Objective

Step I.3Step I.1




Improve Phase


Treqna Base Manual


Tolerance means the allowed variation in a variable

Once we have a a transfer function:

Y = F (X)

We would like to know for given allowed variation in Y what is the variation one would expect for X’s

This process of identifying variation limits for X’s using LSL and USL for Y is called Statistical Tolerancing

Tolerancing

Treqna Base Manual


Assume given transfer function Y= aX + b

Concept of Tolerancing

Y

X

Y = aX + b

USL

LSL

Tolerance for Y

Tolerance for X

The concept can be extrapolated to transfer function involving two X’s by imagining a three dimensions (three axes)

Treqna Base Manual


• Set Tolerance based on customer VOC. E.g. Specification limits defined by

customer

• When multiple X’s are involved. Set Tolerance for all simultaneously, specially when

the interaction between X’s are involved

• Adjust tolerance for measurement variation

More on Tolerancing

Treqna Base Manual


This step may be broken into three steps:

• Ideas generation

• Solution design

• Pilot solution

Solution Identification

Treqna Base Manual


By this step we have established:

• Vital X’s – prioritized

• Transfer function – Either we have a mathematical transfer function or we know how are X’s related to Y, i.e. what should we do to better Y – increase X or decrease X and will it make more impact on Y than any other X ?

• Tolerancing – Based on the transfer function we know how much variation we can allow for each of the X’s

Ideas Generation

While transfer function can exactly tells us the optimum setting for X’s, in its absence one has fair idea about what needs to be done with X’s in order to influence Y positively.

Treqna Base Manual


The project team and process experts can together participate in a team effort to generate ideas for solution.

Following may be used for generating ideas:

• Brainstorming – team tool for generating lots of ideas

• Problem Analogy – use an appropriate analogy for the current problem and try to generate solution for the same

• Best Practices – team might also look for similar processes and make a list of best practices which might be useful

Ideas Generation

Treqna Base Manual


All the ideas and best practices should be than ranked based on following factors in the same priority:

• Impact on Y

• Resource Requirement for implementation

Select ideas which would have maximum impact on Y and minimum resource requirement

Solution Design Selecting the best Ideas

A solution could be:

• One solution

• Set of solution, addressing different X’s or supplementing each other

Treqna Base Manual


The Pilot – Proof of Concept

Pilot is a process in which a solution is tested on existing process with real business environment. The proof of concept – it is important to prove that a hypothetical solution actually delivers what is expected. Helps surface challenges in full scale implementation

The objective of running a pilot is to:

• Analyze the effects of your solution on the process and plan for a successful full-scale implementation

• Establish that the solution would achieve what is desired.

• It is the proof of concept and can help in getting buy in from project champion for resource mobilization required for full scale implementation.

• To identify if there would be any challenges in full scale implementation of solution.

Treqna Base Manual


Running a Pilot

• Prepare a plan to execute pilot

• Do risk assessment of doing the pilot, use FMEA

• Discuss and establish test population, resources, location, duration and timing.

• Create data collection plan

• Pilot solution and collect data

• Analyze data and establish if the solution meets expectation using statistical test

• Identify resources required for full scale implementation of the solution

Treqna Base Manual


Improve Summary

• Vital X’s – select few which make big impact on Y

• Tools used are Pareto, FMEA, Fishbone Analysis

• Transfer function – what can one do in absence of mathematical transfer function

• Statistical Tolerancing – translating allowed variation in Y to X’s

• Solution Design

• Generating Ideas, prioritizing ideas

• Pilot solution – steps in running of a pilot

Treqna Base Manual


DEFINE

MEASURE

ANALYZE

IMPROVE

CONTROL

Map project



Baseline process



MSA on X’s

Approve project

Data collection






Treqna Base Manual


Control Phase Objectives

• Ensure that the process stays in control after the solution is implemented

• Detect and identify any potential deviation from control state and ensure that a

corresponding correcting procedure is established

• Establish plan to ensure sustenance of improved process performance

Treqna Base Manual


What Does Control Mean

• Monitor X’s using control charts for variation

• Identify potential variation causes and prepare an action plan

• Establish plan to ensure sustenance of improved process performance

Treqna Base Manual


Refer to Step A.1 and A.3

Process capability, Pre-Post data comparison

Improved Process Capability

Step C.2

Tools

Activities

Deliverables

Objective

Step C.3Step C.1

Mistake proofing, Risk management, Statistical process control

FMEA & Control ChartsRefer to step M.3

Control PlanAcceptable gage

Establish Control PlanMSA on Xs

Control Phase


Treqna Base Manual


MSA on Xs

Deliverable for this step:

• Validate measurement system for Xs

• Refer to step M3

Treqna Base Manual





Step C.2

Tools

Activities

Deliverables

Objective

Step C.3Step C.1





Control Phase


Treqna Base Manual



Deliverable for this step:

• Calculate capability for new process

• Compare pre and post data for project Y using tools described in step A.3

Treqna Base Manual





Step C.2

Tools

Activities

Deliverables

Objective

Step C.3Step C.1





Control Phase


Treqna Base Manual


Statistical Process Control (SPC)

• Control charts are used to monitor variation on X’s and process performance over

time. Control charts help in identifying variation caused due to special cause.

• Control charts are not proactive tool as mistake proofing is. They are useful when

X’s can not be mistake proofed and controlled within tolerance.

Treqna Base Manual


Statistical Process Control

• The purpose of using statistical purpose control is to monitor X’s and process

performance over time for variation.

• Post improvements a stable process working at its new capability would have

common cause variation.

• If the process has changed and has special cause variation than action needs

to be taken.

• Control charts are used as tools for statistical process control. They tell us when

X’s go out of control and surface the special cause performance.

Treqna Base Manual


Variation

• Common Cause Variation – is the natural or true variation of process and is inherent

in the process

• Special Cause Variation- is usually of larger magnitude compared to common cause

variation. It is usually due to special causes and happens once in a while.

• Precautionary measure should be taken to avoid recurrence of special causes

Treqna Base Manual


Common cause, Special cause

• Common cause

• Natural, Random

• Inherent to any process

• Variation caused by common cause can be reduced by making changes to the system. This would result in improved capability of the system.

• Special Cause

• Unusual

• Specific and once in a while (sporadic)

• Captured in control charts

• Process stability may be explained as:

• In Control, Stable - Only common cause

• Out of Control, Unstable - Common cause with special cause is present

Treqna Base Manual


Differentiating Variation

Perceived Variation

Common Causes Special Causes

CommonCauses

SpecialCauses

Tampering of process

Focus on process change

Under-reactingOpportunity missed for

taking precautions

Focus on mistake proofing, taking precautions.

True Variation

Precaution should be taken while studying variation, the mistakes in treating common cause as special cause or special cause as common cause causes problem for the process. We usually end up in either creating more variation in the process or not able to rectify the cause of variation.

Treqna Base Manual


Control Charts

A control chart:

• Is a time ordered plot of the data

• Plots the variation of the data in expected range also called control limits

• Identifies when there is a special cause present

Upper Control Limit

Lower Control Limit

Example of Control Chart

Control charts use +/- 3 sigma for control limits. One should calculate the control limits when the process is stable and freeze them. Control charts in the future should be used using the same limits, this would keep an eye on special cause as it should and would also tell if the capability of the process is going down.

Treqna Base Manual


Control Charts – Minitab Tests

Area of any control chart can be divided into different segments in terms of distance from centre line in multiples of standard deviation. Each segment becomes a zone in separated from centre line by multiples of s.

The eight tests defined in Minitab look for position of data points on in the following zones of control charts.

-3σ

-2σ

+2σ

+3σ

-1σ

+1σ

Zone A

Zone A

Zone B

Zone B

Zone C

Zone C

For any control chart, you can find the Minitab Rules under the “test” Button.You can select the rules you want Minitab to use, but you should select all eight tests.Note: Minitab rules only should be used in the exam to evaluate special causes of variation.

Treqna Base Manual


Minitab Tests

Test 1: One point or more points more than 3s from the center line.

Test 2: 9 data points in a row on the same side of center line.

UCL

LCL

Average

ABCCBA

1

UCL

LCL

Average

ABCCBA

2

•Test 1 is positive if there is a shift in the process mean if there is an increase in the process standard deviation, or if there is a “single aberration in the process such as a mistake in calculation, an error in measurement, process breakdown etc

•Test 2 signals a shift in the process mean.

Treqna Base Manual


Minitab Tests

Test 3: Six points in a row, either increasing or decreasing

Test 4: Fourteen points in row, alternating up and down

UCL

LCL

Average

ABCCBA

4

UCL

LCL

Average

ABCCBA

3

•Test 3 signals a drift in the process mean. The causes can include improvement in skill, any kind of deterioration in the process.

•Test 4 signals a systematic effect produced by two different population. The causes could be due to two different operator, two different process etc.

Treqna Base Manual


Minitab Tests

Test 5: Two out of three points greater than 2s on the same side

Test 6: Four out of five points greater than 1s on the same side

UCL

LCL

Average

ABCCBA

5

UCL

LCL

Average

ABCCBA 6

•In the case of charts for variables, the first four tests should be augmented by Tests 5 and 6 when earlier warning is desired.

Treqna Base Manual


Minitab Tests

Test 7: Fifteen points in a row within 1s from center line on either side.

Test 8: Eight points in a row greater than 1s from centre line on either side

UCL

LCL

Average

ABCCBA

8

UCL

LCL

Average

ABCCBA

7

•Tests 7 and 8 indicate stratification (observations in a subgroup have multiple sources with different means). Test 7 is positive when the observations in the subgroup always have multiple sources. Test 8 is positive when the subgroups are taken from one source at a time.

Treqna Base Manual


Control Limits vs. Specification Limits

Control Limits: Control limits are calculated by Minitab based on the data input. They are internal to the process and are calculated using standard deviation. Control limits refer to stability of the process at a given capability.

Specification Limits: Specification limits are defined by the customer. It defines the desired level of performance by customer. Specification limits are not based on any statistic, but is based on what customer expects. Specification limits are used to derive the defect rate of process and hence the capability of the process.

PROCESS A

Process A under control limit and under customer specification limit

LowerSL

UpperSL

PROCESS B

Process B under control limit but has unacceptable variation when evaluated against customer specification limits.

LowerSL

UpperSL

Treqna Base Manual


Process States

The Four possibilities of any Process

The State of Chaos

• Non conforming and non predictable

• Non conformity is also unstable

• Random changes to process would not fix the process

• Need to eliminate effect of assignable causes

The Brink of Chaos

• Confirming yet unpredictable

• Process output is influenced by assignable causes

The Threshold State

• Non Confirming and predictable

• Periodic instability

• Stable but not able to deliver on customer standards fully

The Ideal State

• Confirming and predictable

• Process control limits fall within specification limits

• Process stays inherently stable over time

Treqna Base Manual


Types of Control Charts

Variable Control Chart

• Uses continuous metric like Cycle Time, call handle time, Lengths, Diameters, Drops, etc.

• Generally one characteristic per chart

Attribute Control Chart

• Uses attribute or ordinal data like Pass/Fail, Good/Bad, Go/No-Go

• Could be many characteristics per chart

Variable = ContinuousAttribute = Discrete

Treqna Base Manual


Selecting Control Charts

Get Data

Variable or Attribute

Continuous Data (cycle time, length etc

Attribute Data (Yes / No, Go / No-go, Good/ Bad

Rational Subgroups?

Constant Lot Size?Yes No

Yes

No

X-bar and R for sample of size <8

X-bar and S sample of larger size

I-MR

Defect or Defective

Defect orDefective

c nppu

Treqna Base Manual


Variable Control Charts

Variable Control Chart without rational Subgroups:

• Individuals Chart: a plot of the individual values over time

• Moving-Range Chart: a plot of the moving range over time (Minitab takes the range as two consecutive data points, it can be changed in chart options)

• I-MR Chart: plots individual chart and moving range chart in single window

Variable Control Chart with rational Subgroups:

• S Chart: a plot of sample standard deviations over time

• X-bar Chart: plots of the sample means over time

• R-Chart: a plot of the sample range of a sample over time

• X-bar and R: plots x-bar chart and r chart in the same chart window

• X-bar and S: plots x-bar chart and s chart in the same process window


Treqna Base Manual


Assumptions for Variable Charts

• There are two assumptions about the plotted statistic which control charts make:

• Data is random, each data point is not influenced by past data point value.

• The data has normal probability distribution function

• Though control charts assume normality of data, they give reliable results for non normal data also. However if the data is extremely skewed one might like to transform data. Minitab provides Box-Cox transformation model for transforming data for control charts

Treqna Base Manual


Data Collection

• Data should be in time order as used for run charts

• Use rational sub grouping as discussed in step M.3

• Use team and subject matter experts for rational sub grouping

Treqna Base Manual


X Bar R Chart

• Used for data with subgroup size less than 10, for subgroup size more than 10 use X bar S, which plots subgroup standard deviations instead of range

Sample

Sa

mp

le M

ea

n

191715131197531

600.5

600.0

599.5

599.0

__X=599.548

UC L=600.321

LC L=598.775

Sample

Sa

mp

le R

an

ge

191715131197531

3

2

1

0

_R=1.341

UC L=2.835

LC L=0

Xbar-R Chart of Weight

Central line at Mean

Control Limits

Treqna Base Manual


I-MR-R/S (Between/Within)

Three charts and three perspectives for the process

Subg

roup

Mea

n

191715131197531

601

600

599

_X=599.548

UCL=600.763

LCL=598.333

MR

of

Subg

roup

Mea

n

191715131197531

1.6

0.8

0.0

__MR=0.457

UCL=1.493

LCL=0

Sample

Sam

ple

Ran

ge

191715131197531

3.0

1.5

0.0

_R=1.341

UCL=2.835

LCL=0

I-MR-R/S (Between/Within) Chart of Weight

Individual charts for sample means, control limits are based on moving range of means. Refers to stability of process location

Moving range charts subgroup means. Refers to between sample variation

R chart or S chart showing within sample variation

Treqna Base Manual


I-MR Chart

Used for data with no sub-grouping

Observation

Ind

ivid

ua

l V

alu

e

37332925211713951

0.120

0.115

0.110

0.105

0.100

_X=0.11025

UC L=0.11782

LC L=0.10268

Observation

Mo

vin

g R

an

ge

37332925211713951

0.016

0.012

0.008

0.004

0.000

__MR=0.00285

UC L=0.00930

LC L=0

1

1

1

1

I-MR Chart of Data

Individual values plotted with mean as centre line

Moving range using alternate data values, i.e. length of 2

Treqna Base Manual


Discrete Control Charts


Treqna Base Manual


C Chart

• Charts defects when sub group size is constant and based on Poisson distribution

• C-bar is calculated as (Total defects / Total number of units)

Sample

Sam

ple

Coun

t

191715131197531

8

7

6

5

4

3

2

1

0

_C=2.55

UCL=7.341

LCL=0

C Chart of Data

Treqna Base Manual


u Chart

• Charts defects when sub group size is not constant and based on Poisson distribution

• U-bar is calculated as (Total defects / Total number of units)

Sample

Sam

ple

Coun

t Pe

r Un

it

151413121110987654321

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

_U=0.0478

UCL=0.1134

LCL=0

1

U Chart of Defects

Tests performed with unequal sample sizes

Treqna Base Manual


np Chart

• Charts defectives when sub group size is constant and based on Binomial distribution

Sample

Sam

ple

Coun

t

10987654321

30

25

20

15

10

5

0

__NP=10.8

UCL=20.39

LCL=1.21

1

NP Chart of Rejects

Treqna Base Manual


p Chart

• Charts defectives when sub group size is not constant and based on Binomial distribution

Sample

Prop

orti

on

151413121110987654321

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

_P=0.0478

UCL=0.1118

LCL=0

1

P Chart of Rejects

Tests performed with unequal sample sizes

Treqna Base Manual


Process Control System

• A process control system is a strategy to sustain the improvement in the process. It includes the action plan for any deviation or variation from the control state.

• A process control system includes:

• Risk Management

• Mistake-proofing

• Statistical process control (SPC)

Risk Management

Mistake Proofing

Statistical Process Control

Avoidance

Control

Process control system ensures ongoing process control, which also means that the process keeps delivering the improved capability.

Factors which make a process control system effective:•Clarity of requirements before making the control plan•Clear communication to involved parties•Good training•Buy-in from stakeholders – level of involvement and ownership from stakeholders can help

Treqna Base Manual


Risk Management

• Identify risk which can deteriorate the performance of the process

• Evaluate each risk for probability of happening and impact on the process

• Make action plan to limit or reduce the risk

Treqna Base Manual


Risk Management

• Identify risks in the following categories:

• Technology related

• Financial

• Decision making

• Business

• Use FMEA as a risk assessment tool. (Refer to M.1)

Treqna Base Manual


Mistake Proofing

• A technique to eliminate errors

• Also known as Poka Yoke (Japanese)

• Proactive approach to stop errors from happening

• Example:

• Fuel reserve indicator in vehicles

• Shape of SIM card allows only one way to place it in cell

Treqna Base Manual


Mistake Proofing

• Helps to limit X’s within the tolerance so that the process performance does not go out of control

• Identifies the loopholes and helps implementing proactive steps for warning or avoidance of situation which can lead to X’s stepping out of tolerance

Treqna Base Manual


Mistake Proofing

• How to mistake proof:

• Understand origin of defects

• Identify sources of errors resulting in defects

• Identify process steps where mistake proofing can be done

• Redesign process steps such that they are resistant to errors. The options to make errors are reduced.

Treqna Base Manual


Errors

• Sources of errors:

• Process Variation

• Procedural incorrectness

• Measurement accuracy

• Human errors

• One can use fishbone analysis to brain storm and identify the sources of errors

Treqna Base Manual


Control Plan

• Control plan for a project should include following things:

• CTQ

• Input and out variables

• Specifications and tolerances

• Control measures and tools

• Monitoring and sampling plan

Treqna Base Manual


Control Plan Sheet

• Following is a sample control plane sheet

Date Created:Date Revised:

Measure Process Step Input/Output Specifications TargetSample

Size

Data Collection Frequency

Control Tool

Reaction Plan

Control Plan

Project Y, X’s to be measured

Process step where measured

Whether input or output measure

Specifications and tolerances

Target for the measure

Sample size to be

collected

How often the data is to be

collected

Control charts, Mistake proofing

other tools

Actions to be taken when the measure goes out of control

Treqna Base Manual


Who owns it?

Responsibility plan:

• Who owns the activity?

• Who is the back up?

• Define procedures and operational definitions

• Escalation matrix:

• Escalation matrix as a part of reaction plan

Treqna Base Manual


Control - Summary

• Statistical process control

• Eight tests for control charts

• Variable and Attribute control charts

• Control limits vs. Specification limits

• Risk management and FMEA

• Mistake proofing

• Control plan

• Elements of control plan

• Additional details