six sigma green belt training handout_iihmr

Indian Institute of Health Management ResearchJAIPUR

Indian Institute of Health Management ResearchJAIPUR

D e ce mb e r 2 0 1 0

www.qimpro.com

T A B L E O F C O N T E N T S

1. Process, Defects, and Variation

2. Six Sigma Overview

3. Cross-Functional Teams

4. DMAIC Breakthrough Strategy

5. Define Phase

Develop Problem Statement

Map High Level Process Map (SIPOC)

Determine Critical to Quality Characteristics (CTQ’s)

Develop Project Charter

6. Measure Phase

Develop Detailed “AS IS” Process Map

Determine What to Measure (Process Y)

Validate Measurement System

Quantify Current Performance

7. Analyze Phase

Cause and Effect Diagram

Why? Why? Why? Analysis

Testing and Validation of Theories

Validating the Root Causes

Finalizing the Charter

8. Improve Phase

Determine Solutions to Counteract the Root Causes

Provide Statistical Evidence that Solutions Work

Prepare the “Should Be” Process Map

9. Control Phase

Prepare and Implement the Control Plan

Control Charts

Improvement Dashboards

Final Project Report

Lean Six Sigma Overview

Certified Lean Six Sigma Green Belt 1 © Qimpro Consultants, 2009

SIX SIGMA TRAINING

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SIX SIGMA GREEN BELT

Quality is a state in which

value entitlement is realized

Quality – The Definition

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by the customer and provider

in every aspect of the

business relationship.

Any sequence of activities that use a set of INPUTS to produce an OUTPUT is called a PROCESS

A Process is a means for doing work

What is a Process??

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Every Process has a CUSTOMER. A Customer is the immediate recipient of the Output from the Process



Components of a Process??Supplier: The provider of inputs to your process

Input: Materials, resources or data required to execute your process

Process: A collection of activities that takes one or more kinds of input and creates

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output that is of value to the customer

Output: The products or services that result from the process

Customer: The recipient of the process output –may be internal or external

Graphical Representation of a Process

Process

InputVariables

Outputs

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Process Variables

Variables

What Can Go Wrong in a Process??A Process may not produce the desired output leading to CUSTOMER DISSATISFACTION.

The output from a process may have defects or errors in it and this leads to REWORK or REJECTION. This leads to the generation of WASTE

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WASTE.

The produced output may be unpredictable in its ability to meet customer requirements and this is caused due to high VARIATION in a Process.

The process may be unstable and this leads to generation of WASTE in the process itself



What are the Implications of Variation and Waste

The key deficiencies of any Process include:

VARIATION

WASTE

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Both these deficiencies have the following implications:

CUSTOMER DISSATISFACTION

INCREASE IN COSTS OF DELIVERING SERVICES

Identify Chronic Problems (diseases) in the ProcessEnsure that adequate Measurement Systems have been defined to accurately measure the damage i.e. Rework, Rejections, Variation, etc caused by these Chronic Problems

How to Prevent Variation and Waste

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etc caused by these Chronic ProblemsUse structured Problem Solving Methodologies such as Six Sigma to permanently eliminate or minimize the Waste and VariationImprove the Capability of the Process to meet customer requirements Consistently at Optimized Costs

Process Deficiencies are solved by a Project by Project approach.

Each Project needs to address a specific PAIN(deficiency) in the process

Each Project is a structured approach to

How to Achieve Process Improvement

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j ppProblem Solving involving the five steps;

Defining the Problem – Define Phase

Measuring the Problem – Measure Phase

Analyzing the Root Causes – Analyze Phase

Implementing the Improvements – Improve Phase

Sustaining the Gains – Control Phase



Each Project needs to have a specific GOALfor improvement in terms of either eliminating or minimizing the deficiency.

Each Project needs to be conducted by a CROSSFUNCTIONAL TEAM consisting of

b f h f i ff d


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members from the functions most affected by the pain.

Each Project needs to be TIMEBOUND

Each Project must have a goal to generate

savings as ELIMINATING OR MINIMIZING

DEFICIENCIES will always REDUCE COSTS.

This reduction in costs translates to


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This reduction in costs translates to

SAVINGS TO THE BOTTOMLINE

Sigma is used in statistics to denote standard deviation.

A sigma value is used to relate the ability of a process to perform defect free work.

The lower the value of Standard Deviation the

What is Sigma?

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better the process is performing and the lower the probability that a defect will occur.



The higher the Sigma Level i.e. 3σ, 4σ, etc the better the process is performing and the lower the probability that a defect will occur.

What is Six Sigma?

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At Six Sigma (6σ) level of performance the probability of a defect occurring is reduced to 3.4 out of 1 million and that is considered to be virtual perfection.

What is Sigma? Standard Deviation:Metric that displays variation from it’s “target”.

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One standard deviation around the mean is about 68% of the total “opportunities” for meeting customer requirements!

1 Std. Dev.(“Sigma”)

If we can squeeze six standard deviations in between our target and the customer’s requirements...

What is Six Sigma?

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then:99.99966% of “opportunities” to meet customer requirements are included!

1 2 3 4 5 6123456



PPM/DPMOSigma Level

691,4621

308,5382

Defect Rates and Sigma Levels

10 Times Improvement

3σ - Historical Standard

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66,8073

6,2104

2335

3.46

1800 TimesImprovement

6σ – New Standard

4σ - Current Standard

Six Sigma in Practical Terms99% GOOD (4σ) 99.99966% GOOD (6σ)20,000 LOST ARTICLES OF MAIL PER HR.

SEVEN LOST ARTICLES OF MAIL PER HR.

UNSAFE DRINKING WATER 15 MIN. PER DAY

UNSAFE DRINKING WATER FOR ONE MINUTE EVERY SEVEN MONTHS

5,000 INCORRECT SURGICAL OPERATIONS PER WEEK

1.7 INCORRECT SURGICAL OPERATIONS PER WEEK

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OPERATIONS PER WEEK OPERATIONS PER WEEK

2 SHORT OR LONG LANDINGS AT MOST MAJOR AIRPORTS EACH DAY

ONE SHORT OR LONG LANDING EVERY FIVE YEARS

200,000 WRONG DRUG PRESCRIPTIONS EACH YEAR

68 WRONG DRUG PRESCRIPTIONS EACH YEAR

NO ELECTRICITY FOR ALMOST 7 HOURS PER MONTH

NO ELECTRICITY FOR ONE HOUR EVERY 34 YEARS

Reduce Variation

Reduce Waste

Reduce Defects

Focus of Six Sigma

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Delighting Patients

Reduce Cost

Reduce Delivery Time



Cross Functional TeamsCross Functional Teams are made up of individuals who represent the different functions or departments who are impacted by the problem.

They are carefully selected Subject Matter Experts (SME)

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Experts (SME)

The key advantage of cross functional teams is that the representation form all the impacted departments promotes acceptance and implementation of change throughout the organization

Team Meeting Structure1. Develop an agenda and distribute the agenda in

advance

2. Start and finish on Time

3. Appoint a recorder to record the minutes

4 Use visual aids liberally

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4. Use visual aids liberally

5. Summarize key points

6. Review assignments and completion dates and set deliverables for the next meeting

7. Distribute minutes promptly

8. Review meeting effectiveness periodically

Team Facilitator / Leader Must Do:1. Extract balanced participation from all members2. Identify members who need coaching or training

for effective participation and provide the same3. Keep the team on track with the project4 P id t id t l ti

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4. Provide an outside neutral perspective5. Help in securing resources that the team needs6. Resolve conflicts and focus on progress towards

achieving the team goal7. Ensure that all members complete all assigned

tasks between two meetings.



Team Facilitator / Leader Must NOT Do:

1. Being judgmental of team members or their ideas and opinions

2. Taking sides or becoming caught-up in the subject matter

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3. Solving a problem or giving an answer

4. Making suggestions on the task instead of the process

5. Steer the team towards pre-conceived solutions

Black BeltFacilitator:

Six Sigma implementation experts with the ability to develop, coach, and lead multiple cross-functional process improvement teamsUse tools to quickly and efficiently drive improvementFacilitate to keep team focused on the project

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objectiveEnsure that the Six Sigma methods are followedHelp teams learn and understand Six Sigma tools and techniques through regular project reviews Responsible for the ultimate success of the project Trains and develops Green BeltsSpread Six Sigma awareness throughout the organization.

Green BeltProject Team Leaders:

Execute Six Sigma as part of their daily jobs

Form Six Sigma project teams

Process experts

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Part time on Six Sigma Projects

Trained on Six Sigma methods and quality tools.



Team Members are the Process Experts and are vital for success in the Project. The key Roles and Responsibilities of the Team Member include:

Good knowledge of product, process and t i t

Team Roles – Team Member

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customer requirementsWilling to work in teams and dedicate time to work on projectsHigh Participation and Active in Data Collection Responsible for Implementing the Changes and Improvements

Team StagesForming:

Forming is the beginning of team life. Members typically start out by exploring the boundaries of acceptable group behaviour.

Storming:The second stage consists of conflicts and resistance

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The second stage consists of conflicts and resistance to the group’s task and structure. This is the most difficult stage for any team to work through. Team members tend to cling on to their own opinions , based on personal experience and resist seeking the opinions of others. This can lead to hurt feelings and unnecessary disputes. The role of the team facilitator / leader is crucial in this stage.

Team StagesNorming:

During the third stage, a sense of group cohesion develops. Team members begin to focus more on collection and analysis of data rather than experiences. Norming takes place as the team keeps meeting routinely as per a fixed schedule and the

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team becomes more relaxed and steady. Norming is essential. A team cannot perform if it does not norm.

Performing:This is the payoff stage. The team begins to work effectively and cohesively towards achieving the common goal.



Team Stages

ANCE

NORMING:Members: Cooperate, talk things out, focus on objectives

PERFORMING:Members: Show maturity, focus on the process, achieve goals and operate smoothly

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FORMING:Members are: Inexperienced, excited, anxious and proud

STORMING:Members have: confrontations, divided loyalties and individual thinking,

PERF

ROM

A

TIME

Establish focus to ensure improvements will make a strategic difference.

Identify the product or process to be improved and top few critical to quality (CTQ) customer requirements.

Quantify how the process performs today and set improvement goal

Recognize

Define

MeasureProcess

Characterization

DMAIC Breakthrough Strategy

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and set improvement goal.

Identify the input variables that affect the CTQ’s the most.

Determine solutions for controlling the key process input variables, quantify their impact and compare to goal.

Implement process design modifications and standardization methods for maintaining the improved performance level over time.

Integrate intoDaily Work

Analyze

Improve

Control

Characterization

ProcessOptimization

Key Objectives are…..

Identify the factors that are critical to Customer Satisfaction (CTS).

Define Project Boundaries

DEFINE PHASE

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Define Project Boundaries.

Define the project objective and impact.




Prepare the “AS IS” process map and determine outputs.

Determine what to measure Reported by:Date of study:Gage name:

Gage R&R (ANOVA) for NO. OF DAYS

MEASURE PHASE

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and validate the

measurement system.

Quantify current

performance and estimate

improvement target.

Misc:Tolerance:

0

10

5

0

321

Xbar Chart by ENGINEER

Sam

ple

Mea

n

Mean=4.083UCL=4.773LCL=3.394

0

1.0

0.5

0.0

321

R Chart by ENGINEER

Sam

ple

Ran

ge

R=0.3667

UCL=1.198

LCL=0

10 9 8 7 6 5 4 3 2 1

10

5

0PROJECT

ENGINEERENGINEER*PROJECT Interaction

Aver

age

1 2 3

321

10

5

0ENGINEER

By ENGINEER10 9 8 7 6 5 4 3 2 1

10

5

0PROJECT

By PROJECT%Contribution %Study Var

Part-to-PartReprodRepeatGage R&R

100

50

0

Components of VariationPe

rcen

t


Identify causes of variation and defects.

Provide statistical 0 1 0 2 0 3 0

0

1

2

3

4

5

6

7

8

9

1 0

N o . o f D ay s = 0 .201 735 + 0 .19 153 9 No . O f E r ro r + 0 .0 031 606 No . O f E r r o r * * 2

S = 0 .66 489 1 R -S q = 96 .4 % R -S q (a d j) = 95 .3 %

R eg res s ion P lo t

ANALYZE PHASE

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evidence that causes are real.

Commit to improvement target.

Fishbone Diagram for Internal Logistics

Cost of InternalLogistics of Imported

Equipment is veryHigh.

Method Material

Men Machine

Salary for the storekeeperrequired to manage Warehouse

All inland transportation of importedequipment is done through Air Freight.

Cost of Rent paid for the Warehouse

Cost of Insurance premium paid forthe Insuring the Warehouse.

Cost of Inventory of Material Storedin Warehouse.


Determine solutions (ways to counteract causes) including operating levels

Control Chart for the cause of high cost of Internal Logistics

1,000,000 1,000,000 1,000,000

600,000

800,000

1,000,000

1,200,000

cess

DPM

O

Current DPMO Target DPMO

IMPROVE PHASE

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and tolerances.

Install solutions and provide statistical evidence that the solutions work.

142,800 142,800

06,210 6,210 6,210 6,210 6,210 6,2100

200,000

400,000

Sep-01 Oct-01 Nov-01 Dec-01 Jan-02 Feb-02

Period in Months

Pro

Current DPMO 1,000,000 1,000,000 1,000,000 142,800 142,800 0

Target DPMO 6,210 6,210 6,210 6,210 6,210 6,210

Sep-01 Oct-01 Nov-01 Dec-01 Jan-02 Feb-02




Put controls inplace to maintainimprovementover time.

543210

-1ndiv

idua

l Val

ue

Mean=1.65

UCL=4.450

LCL= 1 150

Control Chart for the sustained process control

CONTROL PHASE

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Provide statisticalevidence that theimprovement issustained (3months of data).

2010Subgroup 0

1-2

I

11No. Of Days

LCL=-1.150

4

3

2

1

0

Mov

ing

Ran

ge

R=1.053

UCL=3.439

LCL=0

Effo

rt

Champion Black Belt/Green Belt and Team Team and Process Owner

Effort Over a Project Life Cycle

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Define Project M A I C Integrate into Daily Work

Leve

l of

E

SIX SIGMA DEFINE PHASE

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Define Phase Contents1. Develop Problem Statement

2. Map High Level Process (SIPOC)

3. Determine Critical to Quality Characteristics (CTQ’s)

4 Develop Project Charter

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4. Develop Project Charter

Problem StatementDescription of the “pain”

What is wrong or not meeting our customer’s needs?

When and where does the problem occur?

How big is the problem?

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How big is the problem?

What’s the impact of the problem?

Problem StatementKey Consideration/Potential Pitfalls

Is the problem based on observation (fact)

Does the problem statement prejudge a root cause?

Can data be collected by the team to verify and

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Can data be collected by the team to verify and analyze the problem?

Is the problem statement too narrowly or broadly defined?



Problem StatementKey Consideration/Potential Pitfalls (conti...)

Is a solution included in the statement?

Is the statement blaming any person or function?

Would customers be happy if they knew we were working on this?

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working on this?

Problem Statement – ExamplesExample 1

Poor StatementBecause our customers are dissatisfied with our service, they are late paying their bills.

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Problem Statement – ExamplesExample 1 (conti...)

Improved StatementIn the last 6 months (when) 20% of our repeat customers – not first timers (where) – were over 60 days late (what) paying our invoices. When surveyed all of these customers reported extreme

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surveyed, all of these customers reported extreme dissatisfaction with our service (what). The current rate of late payments is up from 10% in 1990 and represents 30% of our outstanding receivables (how big). This negatively affects our operating cash flow (impact)



Problem Statement – ExamplesExample 2

Poor StatementCustomers are unable to access the call centre half the time leading to high revenue losses.

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Problem Statement – ExamplesExample 2 (conti...)

Improved StatementDuring the year 2003, (when) 40% of our customers (extent) were unable to access the call centre at the first attempt (what). This causes dissatisfaction to our customers and a loss of

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dissatisfaction to our customers and a loss of revenue opportunities to the organization (impact).

High Level Process Mapping

PPSS II OO CCSuppliers Inputs Process Outputs Customers

CTP CTQ

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pp p

ProcessMap

MeasuresMeasures MeasuresMeasures



Credit Decision Cycle Time Customer’s Perspective

OI Internal View

Initial Metric Stop

Process Boundaries - Example

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View Process From The Customer’s PerspectiveNot The Internal Perspective

S

Completed Application Received From Customer

Decision Sent To The Customer

New Metric

Customer Sends Application

Customer Receives Decision

SIPOC Worksheet

Supplier

PS I O CInput (Use nouns)

Process (Use verbs) Output (Use nouns) Customer

1

2

3

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3

4

5

6

7

Gather VOC Data

Project Team 1

Surveys

Personal Visits

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Customer

Project Team 2

Project Team 3

Questionnaires

Interviews

Phone Calls



Gather VOC DataKey Considerations In Collecting Customer Data:

Collector’s bias may affect what is heardWhat contact/relationship do you have with the customer?What are your time constraints?

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What budget is available?How much certainty to do you need to move forward with the project?Ensure customer expectations are aligned with our intentions/actions

Managing Customer ExpectationsManage customer expectations throughout VOC data collection

Select customers carefully

Explain your intent for gathering the information

Clarify your ability to act on information

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Clarify your ability to act on information gathered

Communicate next steps to the customer

Asking For Information Does Not Translate To A Promise To Act

Steps To Determining CTQsA Process To Identify Customers And Understand Their CTQs

IdentifyCustomers

Voice Of TheCustomer (VOC)

Determine CTQs

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• List customers• Define customer

segments• Narrow list

• Organize all customer data

• Translate VOC to specific needs

• Define CTQs for needs• Prioritize CTQs• Contain problem if

necessary

• Review existing VOC data

• Decide what to collect/ select VOC tools

• Collect data



Effective BrainstormingBrainstorming is used to establish common method for a team to creatively and efficiently generate high volume of ideas on any topic

Brainstorming encourages open thinking

Gets the involvement of all the team members

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without the dominance of anyone team member

Allows team members to build on each others creativity while staying focus on the joint mission

Affinity DiagramRecord each VOC on a post it note in bold letters

Without talking sort the ideas simultaneously as a team into 5 –10 related groupings

For each grouping create summary or header cards using consensuses

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Draw the final affinity diagram connecting all finalized header cards with their grouping

Affinity Diagram - ExampleFEEDBACK&RESPONSIVENESS

Action plan for pending STO

Advance intimation regarding availability of material

Dispatch intimation

MATERIAL

DELIVERY

Quality of packing

Cycle time for 100% fulfillment of STO requirements

Weekly dispatch

MATERIAL

FULFILLMENT

Stores to punch entire STO in SAP

Common tracking no. for all material issues

Material balancing

SYSTEMS

MANAGEMENT

Communicating new part codes and part numbers to users

Streamlining of part codesin all database systems

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Dispatch intimation as per STO

List of obsolete or discontinued parts

Reconciliation with balance STO’s

Response time for acknowledgement of requirement

Weekly dispatch schedule

Material balancing across all lines

Stores and Production should have part lists for equivalent components

All accessories for new models should bebundled with 1st dispatch

Alternate process to be standardized for urgent requirements

Availability of obsolete or discontinued parts for repeat orders



Kano ModelTo identify & prioritize the full range of the customers needs

Kano model helps to describe which needs, if fulfilled contribute to customer dissatisfaction neutrality or delight

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Kano Model Identifies • Must be needs - Critical to customer

expectation• More is better – Critical to customer

satisfaction• Delighter – Converting wants to needs

CTQ Prioritization MatrixProcess: Invoicing

Primary output (product or service): Invoices sent to customers’ accounts payable departments

Potential Project Y Metrics

Strong relationship

M d l i hi

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CTQ Output Characteristic Dev

iatio

nIn

Del

iver

y

Erro

rsPe

r In

voic

e

Tota

l Cyc

leTi

me

Cust

omer

Clar

ifica

tions

Rs.

Non

-Re

ceiv

able

Cycle Time for Invoicing

Accuracy of Invoices

Legible Invoices

Potential Project Y MetricsModerate relationship

Weak relationship

What is a Pareto Diagram?A diagram that shows 20% of the inputs (Xs) cause 80% of the problems with dependent process outputs (Ys)

A Pareto diagram allows a team to:Discover what type of categories relate to the problem

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problemFocus on the most important items



Pareto DiagramA Pareto diagram is a bar chart organized with the largest bar to the left and the smaller bars to the right in order of frequency.

60

Pareto Chart for Type

100

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Coun

t

Defect

50

40

30

20

10

0

Perc

ent

80

60

40

20

0

Pareto Diagrams – Key Points!Pareto diagrams are typically used to prioritize competing or conflicting problems and to distinguish the “vital few” from the “trivial many.”

Pareto diagrams determine which of several classifications have the most count or cost

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classifications have the most count or cost associated with them.

The base data gathered must be in terms of either counts or costs.

Pareto Diagrams – Key Points!Do not use terms that can't be added, such as percent yields or error rates.

Remember to use Pareto Diagrams creatively.

If the first one doesn’t show an 80-20 pattern, then reconsider the problem and try again.

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CTQ TreeWhy use it

Identifies critical to quality (CTQ) characteristics, features by which customers evaluate our product or service that is to be used as the measure for our project.

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A useful CTQ characteristic has the following features:• It is critical to the customers perception of

quality• It can be measured• A specification can be set to tell whether the

CTQ characteristic has been achieved.

What does the CTQ tree do…

Links customer needs gathered from the voice of customer data with process drivers and with specific, measurable characteristics.

Enables the project team to transform general

CTQ Tree

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data into specific data.

Makes the measuring process easier for the team.

Gather the sorted customer needs from the VOC data

List the major customer needs on the left hand side of the tree structure

View each need from the customers point of view

Setting up a CTQ Tree

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For each need ask “what would that mean” from the customers stand point

Each answer becomes the driver for the CTQs

Keep asking “what would that mean” until you reach a level where it would be absurd to continue

Your answer at this level is the CTQ



Alignment of Project YBUSSINESS Y

CORE PROCESS Y’S

PROCESS

Key output metrics that are aligned with strategic goals/objective of the business. Big Ys provide a direct measure of business performance

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MANAGEMENT

PROJECT Y

INPUT PARAMETERS THAT INFLUENCE THE “Y”

X1 X2 X3

Key output metrics that summarize process performance

Key project metric defined from the customer perspective

Think Outside-In

For your key CTQ, how does the customer define process performance?

Select The Project Y

SSupplier P O CI OutputProcessInput CustomerCTQs

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y=_______

What is the exact definition the customer recognizes for this metric?

How does this compare with existing performance metrics?

Select The Project YKey Questions To Address

If the Project Y changes, will my customer feel the impact?

Does the Project Y match with how the customer describes the process?

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Does the Project Y link to one at the Big Ys for your business?



One of the most important things necessary to get a team started on a footing is a charter

A Charter:

Clarifies what is expected of the project

Keep the team focused

What is a Charter?

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Keeps the team aligned with organizational priorities

Transfers the project from the Champion to the Improvement Team

Used as a tool by the Apex Council to review project progress

SIX SIGMA MEASURE PHASE

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1. Develop Detailed “AS IS” Process Map

2. Determine What to Measure (Process Y)

3. Validate Measurement System

4. Quantify Current Performance

Measure Phase - Steps

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Start

Step 2A Step 2B Step 2C

Step 1

Process flow diagram that visualizes how work is done.

What is a Process Map?

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End

Step 3

Good?Rework YesNo

Process Map Symbols

Activity or Process Step

Start or End of Process

MeaningSymbol

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Direction of Flow

Connector

Decision or Inspection Point

Why Create a Process Map?A Cross Functional Process Map shows “AS IS” process.

Process start and end points are identified and made measurable.

Makes process steps visible and keeps the team from drifting outside the project boundaries

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from drifting outside the project boundaries.

Non-valued-added steps become clear and can be discarded or minimized.

Rework and repair is obvious. They are the hidden factories. Hidden Factories have to be shut down.

Is a consensus on how work is done.



1.Examine Each Decision SymbolIs this a checking activity?Is this a complete check, or do some types of errors go undetectedIs this a redundant check?

Analyzing a Flow Diagram

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2.Examine Each Rework LoopWould we need to perform these activities if we had no failure?How ‘long’ is this rework loop (steps, time lost, resources consumed, etc?)Does this rework loop prevent the problem from reoccurring?

4.Examine Each Document or Database Symbol

Is this necessary?How is this kept up to date?Is there a single source for this information?How can we use this information to monitor and improve the process?

3.Examine Each Activity SymbolIs this a redundant activity?What is the value of this activity relative to its cost?How have we prevented errors in this activity?

Learn to Recognize WasteWaste of correction (rework)

Waste of waiting

Waste of inventory

Waste of over production

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p

Waste of transportation

Waste of motion

Waste of over processing

Types Of Data

Discrete DataBinary (Yes/No, Defect/No Defect)Ordered categories (1-5)Counts

E l

Continuous DataCan be broken down into incrementsInfinite number of possible values

E l

Data Type Is An Important Consideration

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ExamplesNumber of incomplete applicationsPercent of responding with a “5” on surveyNumber of Green Belts trained

ExamplesCycle time (measured in days, hours, minutes, etc.)Weight (measured in tons, pounds, etc.)



Data Collection Plan

Develop

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Ensure Data Consistency & Stability

Develop Operational Definitions & Procedures

Collect Data & Monitor Consistency

Establish Data Collection Goals

Breaking Down the Overall Variation

Part-to-PartVariation

Measurement SystemVariation

Variation due Variation due

Overall Variation

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Variation dueto gage-

Repeatability

Variation dueto operator-

Reproducibility

Operator Operatorby part

Interaction

Which variationcomponent do we want

to be large?

Variable Gage R&R - MethodTo conduct a variable gage R&R study….

At least two operators (persons doing the measuring) should participate. Two or three operators are typical.At least 10 parts should be measured. These are 10 units of the same type product that represent the full

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yp p prange of manufacturing variation.Each operator will measure each part two or three times.Parts should be measured in random order.

It is very important that an operator not be aware of his or her earlier measurement when doing a repeat measurement on the same part.



Attribute Gage R&RIt is also important to have good repeatability and reproducibility when obtaining attribute data.

If one operator, for example, decides a unit has an “appearance” defect and another operator concludes the same unit has no defect, then there is a problem with the measurement system

© 2009, Qimpro 79

is a problem with the measurement system.

Similarly, the measurement system is inadequate when the same person draws different conclusions on repeat evaluations of the same unit of product.

An attribute measurement system compares each part to a standard and accepts the part if the standard is met.

The screen effectiveness is the ability of the attribute measurement system to properly discriminate good from bad

Attribute Gage R&R

© 2009, Qimpro 80

discriminate good from bad.

Attribute Gage R&R - MethodSelect a minimum of 30 parts from the process. These parts should represent the full spectrum of process variation (good parts, defective parts, borderline parts).

An “expert” inspector performs an evaluation of each part classifying it as “Good” or “Not Good ”

© 2009, Qimpro 81

each part, classifying it as Good or Not Good.

Independently and in a random order, each of 2 or 3 operators should assess the parts as “Good” or “Not Good.”

Enter the data into the Attribute Gage R&R.xls spreadsheet to quantify the effectiveness of the measurement system.



Attribute Gage R&R - ExampleSCORING REPORT

Attribute Legend DATE:1 G NAME:2 NG PRODUCT:

SBU:TEST CONDITIONS:

Known Population Operator #1 Operator #2Sample # Attribute Try #1 Try #2 Try #1 Try #2

Y/N Y/NAgree Agree

1 G G G G G Y Y2 G G G G G Y Y3 G G G G G Y Y4 G G G G G Y Y5 G G G G G Y Y6 G NG G G G N N This is the

© 2009, Qimpro 82

SCREEN % EFFECTIVE SCORE (3) -> 85.00%SCREEN % EFFECTIVE SCORE vs. ATTRIBUTE (4) -> 85.00%

7 G G G G G Y Y8 G G G G G Y Y9 NG G G NG NG N N

10 NG NG NG G G N N11 G G G G G Y Y12 G G G G G Y Y13 NG NG NG NG NG Y Y14 G G G G G Y Y15 G G G G G Y Y16 G G G G G Y Y17 NG NG NG NG NG Y Y18 G G G G G Y Y19 G G G G G Y Y20 G G G G G Y Y% APPRAISER SCORE (1) -> 95.00% 100.00%

% SCORE VS. ATTRIBUTE (2) -> 90.00% 95.00%

This is theoverall measure of consistency

among operatorsand “expert.”100% is best!

Interpreting the Results% Appraiser Score is the consistency within one person.

% Score vs. Attribute is a measure of how well the operator’s evaluation agrees with that of the “expert”.

© 2009, Qimpro 83

Screen % Effective Score is a measure of how well the operators agree with each other.

Screen % Effective Score vs. Attribute is an overall measure of consistency between operators and agreement with the “expert”.

Role of Defect-Based MetricsWhen Using Attribute Data...

These Metrics Quantify Process Capability:

DPMO - Defects per Million Opportunities

PPM - Parts per Million

© 2009, Qimpro 84

Sigma Levelfor the Process

convert to...



Defects versus Defective ItemsOut of these 12 Marble Slabs… there are...

3 Defective Slabs

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6 Defects

Estimate Process CapabilityA cutting operation cuts tubes to a target length. PPM represents the number of defective items per million items inspected.

9% DefectiveUSLLSL

Variable Data: Length in mm

© 2009, Qimpro 86

or

90,000 PPM

9% Defective

or

90,000 PPM

2%7%

Attribute Data:Go/No Go Length Gage

( )( ) 09.0Inspected500NoGo45 =

Why Count Number of DefectsWhenever a number of things can go wrong, or things can go wrong at any of several steps, then…

Counting number of defects provides a more meaningful indicator of process capability than merely counting the number of defective items

© 2009, Qimpro 87

merely counting the number of defective items at the end of the process.

First, we must determine the opportunities for defect.



If we measured the outcomes of our processes (products, services and information) like volume... then, the combined volume... should equal???

Determine the Total Opportunities

© 2009, Qimpro 88

SuccessesDefects

Either a defect or a success:

The Outcomes of our Process

© 2009, Qimpro 89

Defects Successes

?

Not Good!!!!

© 2009, Qimpro 90

Defects Successes



Better Output

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But good enough???Defects

Successes

If... each glass can hold one million drops...

and, our process generates one million drops...

then the number of drops

Defects Per Million Opportunities

© 2009, Qimpro 92

in the “defects” glass represents...

Defects Successes

DPMO!

3 4

999,996.6

DPMO Converts to Sigma

© 2009, Qimpro 93

3.4 DPMO is equal to 6σ

SuccessesDefects

3.4



Measures of Central TendencyPlacement Time for Technical Positions (in days)

22, 26, 26, 31, 33, 37, 37, 42, 52, 52, 52, 57, 59

Mean or AverageThe sum of the values in a data set divided by the number of values.

ModeThe most frequently

X = 40.5 days

© 2009, Qimpro 94

Mode = 52 days

Median = 37 days

The most frequently occurring data value.

MedianThe middle observation in the data set that has been arranged in a ascending or descending order.

Sample vs. Population

Samplex s s2

Populationμ σ σ2

© 2009, Qimpro 95

Sample Statistics

x = Mean

s = Standard Deviation

s2 = Variance

Population Parameters

μ = Mean

σ = Standard Deviation

σ2 = Variance

HistogramsA histogram is a frequency polygon in which data are grouped into classes. The height of each bar shows the frequency in each class.

2020

© 2009, Qimpro 96

10 15 20 25 30 35 40 Days0

10

1

4

1012

3

Does a histogram preserve the time order in which the data was collected?



Shapes of Data Sets

Bell Shape – The Normal Distribution

Right Skewed (Positively Skewed)

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Left Skewed (Negatively Skewed)

Uniform Distribution

Bimodal Distribution

Histograms to Evaluate ShapeWhen creating a histogram, the data must be properly grouped in order to understand the shape of the data

Number of Number of Data Points Classes

Under 50 5-7

50 – 100 6-10

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distribution.

For the given sample size, the right number of classes should be used.

100 – 250 7-12

Over 250 10-20

The Normal DistributionSince many process outputs have this shape, the properties of the normal curve can be used to make predictions about the process population.

Data that is non-normal can sometimes be transformed to the normal distribution, to use the properties of the normal curve to make predictions.

© 2009, Qimpro 99



Properties of the Normal Distribution

Standard Deviation

© 2009, Qimpro 100

68%

95%

99.73%

Average

-3σ +3σ-2σ -1σ +1σ +2σ

What is Process Capability?Seat Track Rolling Mill Hiring Process

Inner Dimension of Seat Track (mm) Placement Time (in Days)

USLLSL USL

The capability of a process to

© 2009, Qimpro 101

Product exceedsSpecification Limits!

Placements thattake too long!

of a process to meet customer requirements.

PPM (Parts per Million)

LSL USL

Inner Dimension of Seat Track (mm)

USL

Placement Time (in Days)

© 2009, Qimpro 102

3%3%

6% of the seat tracks do not meetspecifications.This translates to… 60,000 PPM

15%

15% of the time, we take too longto fill the open positions.This translates to… 150,000 PPM



A Stable ProcessLSL USL

IndividualMeasurements

Mean

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A process is said to be stable when the distribution of all individual measurements are contained within ± 3σ from the mean.

Stable processes provide the most reliable estimates of process capability.

6σMeasurements

Four Stable Processes

What can be said about the capability of these stable processes?

A

LSL USL

B

LSL USL

© 2009, Qimpro 104

processes?

C

LSL USL

D

LSL USL

Average & Standard DeviationFor example: The average of all data = 178.6 and the average range = 8.4 from a stable control chart that used a sample size of 5.

48RPopulation

© 2009, Qimpro 105

6.3326.24.8

dRThen, σ

2

===

X = 178.6

If the target = 171, is the process centered on target?



Process VariationWe expect that 99.73% of the time, we will produce product that falls between 167.8 and 189.4

USL

= 1

82

LSL

= 1

60

Target

Estimating Process Capability

© 2009, Qimpro 106

Specification LimitsAccording to the specifications, we want all product to fall between 160 and 182.

If centered, would this process be capable of meeting specifications?

189.4178.6167.8σ+σ- 3xx3x

171

Determine the Potential Capability (CP)The Cp index reflects the potential of the process if the average were perfectly centered between the specification limits.

Cp = 1

USLLSL

The larger the C index

© 2009, Qimpro 107

Cp > 1

Cp < 1 For a Six SigmaProcess, Cp = 2

The larger the Cp index,the better!

σ-=ˆ6LSLUSLCp

Estimate Percentage Beyond SpecsTo estimate the percentage of product (or PPM) that falls outside the specification limits, we must first compute Z upper and Z lower.

USL

= 1

82

LSL

= 1

60

© 2009, Qimpro 108

189.4178.6167.8

Z lower is the numberof standard deviations

between the Process Averageand the Lower Specification

Limit.

Z upper is the numberof standard deviations

between the Process Averageand the Upper Specification

Limit.



Estimating % Beyond Specifications

USL

= 1

82

LSL

= 1

60

From a Z table, we find that Z = 0.94 corresponds to proportion = 0.1736This converts to 17.36% Defective or 173,600 PPM=2.4 σ (from Sigma Table)

© 2009, Qimpro 109

189.4178.6167.8

Z upper = 0.94

Zupper = USL – Xσ

Zlower = X – LSLσ

Process Capability Metrics

ProcessO tp t

Attribute

Data

PPM, DPU, DPODPMO, RTY

Sigma

© 2009, Qimpro 110

OutputY

Variable

Type

CP, CPK,PP, PPKPPM

gLevel

SIX SIGMA ANALYZE PHASE

© 2009, Qimpro 111



1. Cause and Effect Diagram

2. WHY? WHY? WHY? Analysis

3. Testing and Validation of Theories

4. Validating the Root Causes

Analyze Phase - Steps

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5. Finalize the Charter

A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect

Cause and Effect Diagrams

EffectEffect

Measurement Methods Machinery

Potential High Level Causes (Xs)

© 2009, Qimpro 113

YY

Mother Nature People Materials

Potential High Level Causes (Xs)

Summarize potential high-level causesProvide visual display of potential causesStimulate the identification of deeper potential causes

Cause and Effect Diagram

Process Map AnalysisLet us

Brainstorm???Why Is There

Difference In The V i i I C l

Why Is There Difference In The V i i I C l

© 2009, Qimpro 114

Data Analysis

Variation In Cycle Time Between Line 1

and Line 2

Variation In Cycle Time Between Line 1

and Line 2



Cause and Effect DiagramBrainstorm the “major” cause categories and connect to the centerline of the Cause & Effect diagram

Measurement Methods

Why Is There Why Is There

© 2009, Qimpro 115

People Machinery

yDifference In The Variation In Cycle

Time Between Line 1 and Line 2

yDifference In The Variation In Cycle


Cause and Effect DiagramMeasurement Methods

No tracking of in process rejection of

components

Speed of individual conveyor belts

not known

No. of components inserted per operator

on either line

No. of boards reworked

Why Is There Why Is There

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People Machinery

Line 1 has more temporary operators

Untrained Inspectors in Final Inspection

Breakdown time are different for either line

Difference In The Variation In Cycle


Difference In The Variation In Cycle


Cause and Effect Diagram-Example 1

UNDERUTILIZATION

MACHINE MAN

Irregular prev.maintenance

Mismatched cycle timeImproper data in

comp.library

Dirty line &surrounding

Time loss for PCB inspection

Time loss for Magazine setup

© 2009, Qimpro 117

UNDERUTILIZATIONOF SMT LINE

METHOD MATERIAL

No program protection

Alternate Feeder Banknot used

Implementation of ECRs/Mod.notes

Time loss formagazine setup

Insufficient bufferat input

No control of loading list

Unnecessary checksduring model change Time loss for PCB

setup



Cause and Effect Diagram–Example 2

Interpretation of customer specs byBranch Engineer

Men Machine

Information by Sales Engineeris Incorrect

Submission of Offer isHasty Interpretaion of branch

information by CoEE

New Bunch of fresh Engineers in CoEE

Lack of experience of CoEE engineer inexecuting applications at site

Resource not there

Flooding of Projects to

Overloaded BranchEngineers

Branch Engineer is notavailable most of the time

Response Time to Queryis very Large

Branch does not fill DITOcorrectly

Resistance to Changes inway of working

Frequent Revisions in theStandard Formats

© 2009, Qimpro 118

Start ofProduction by

CoEE takes toolong

Method Material

Flooding of Projects toCoEE

Too many Fast Track jobs

There is lack of communication betweenbranch and CoEE

Too many Assumptions are made byCoEE regarding the Design

Too many questions required to beasked by CoEE to Branch

Branch Engineer wastestime in rework

Transfer information from Branchformats to CoEE formats

There are standard CoEE formatsapplicable to all branches

Low confidence on theDITO provided by Branch

No documented procedureto fill the DITO

DITO has to be checkedfor errors

Stagerred Information fromthe Branches

Irregurality in despatch ofInformation from the Branches

Information availability at theBranches is not organised

Incorrect and Incomplete informationfrom Branches

Information passesthrough many hands invarious formats

CoEE Standard Formatsnot being used from theSales stage itself

Non-Controllable Causes: These are causes that the team unanimously conclude are beyond the control of the present process boundaries or outside the physical location of the process execution.

Lack of Solution OR Direct Improvements: These are causes that are actually solutions that can be

Sorting the Possible Causes

© 2009, Qimpro 119

causes that are actually solutions that can be implemented directly and need no further analysis. They are usually stated as lack of resources, equipment, tools or training.

Likely and Controllable Causes: These causes are the causes that have passed the above two filters and need further analysis.

The immediate next step after the segregation is to attack the likely and controllable causes and ask at least 3 – 5 why’s?….. for each cause. This is called root cause drill down.

Only after we have asked why 3 - 5 times to each of the likely causes we will be able to arrive at the

Asking 5 Why’s? 4.2.1

© 2009, Qimpro 120

the likely causes, we will be able to arrive at the possible root cause, also known as KPIV.



WHY do we have poor and declining participation in improvement programs?1. Because people resist change .

Why do people resist change?2. Because they fear making mistakes.

Why do people fear making mistakes?

5 Why’s? – Example

© 2009, Qimpro 121

Why do people fear making mistakes?3. Because they are criticized for mistakes.

Why are people criticized for mistakes?No ideas, let’s move on.

Okay, then Why else do people fear making mistakes4. Because they are penalized for mistakes.

There are two tools that are widely used for the prioritizing of the possible root causes that are obtained from the Cause and Effect diagram.

Cause and Effect Matrix (C&E Matrix)

Failure Mode Effect Analysis (FMEA)

Prioritizing the Possible Root Causes

© 2009, Qimpro 122

Desired Output List of Prioritized Possible Root Causes

The Cause & Effect Matrix is a team tool used to prioritize the …

key process input variables (KPIV) that affect key process output variables (KPOV)

What is a Cause & Effect Matrix?

© 2009, Qimpro 123

Process Outputs2 2 7 9 6 7 9 3

Process Step Process InputBlending % ISO 2 2 8 8 2 2 3 3 198Blending Time 0 0 3 4 7 9 0 0 162Blending Temperature 1 2 5 5 6 2 0 0 136Molding Fill Time 8 6 3 1 7 1 6 7 182Molding Pressure 9 5 5 4 6 6 9 3 267Molding Mold Temperature 0 0 3 0 5 9 2 6 150

Pad

Stiff

ness

Pad

Wid

th

IL D Void

s

Tear

s

Flas

h

Pad

Thic

knes

s

Burn

s

Tota

ls



Process Outputs2 2 7 9 6 7 9 3

ess

ness

Process Steps

Customer Importance Rating

Key Process Output

V i bl

Process Input

Variables

Anatomy of a Cause and Effect Matrix

© 2009, Qimpro 124

Process Step Process InputBlending % ISO 2 2 8 8 2 2 3 3 198Blending Time 0 0 3 4 7 9 0 0 162Blending Temperature 1 2 5 5 6 2 0 0 136Molding Fill Time 8 6 3 1 7 1 6 7 182Molding Pressure 9 5 5 4 6 6 9 3 267Molding Mold Temperature 0 0 3 0 5 9 2 6 150

Pad

Stiff

ne

Pad

Wid

th

IL D Void

s

Tear

s

Flas

h

Pad

Thic

kn

Burn

s

Tota

ls

Cross Multiply & Prioritize

Variables

Strength of Correlations

Rating of Importance to Customer ==> 3 10 10 5 10 5

Ou

tpu

ts

high

m/c

PPM

Brea

kdow

n

Del

ay in

rel

oadi

ng o

f di

ffer

ent

layo

uts

Inco

mpl

ete

kit

wro

ng c

ompo

nent

s

PCB

brea

kage

Process Step Inputs Total

Un-necessary checks during model change

1 1 7 1 1 1 103

Cause and Effect Matrix - Matrix

© 2009, Qimpro 125

No control of loading list 1 1 3 1 3 1 83No program protection 1 1 3 1 7 1 123Irregular Preventive Maintenance. 7 7 5 1 1 1 161Dirty line & surrounding 3 3 3 1 1 1 89Improper data in comp.library 5 3 3 1 1 1 95

Program change due to ECR/Mod notes Implementation of ECRs/Mod.notes 1 1 3 1 3 1 83

Insufficient buffer at I/p 1 1 10 10 1 1 178Time loss for PCB inspectionTime loss for PCB setup 3 1 7 1 1 1 109Time loss for magazine setup 1 1 5 3 1 1 93

model change Model changeover

Breakdown

Component replenishment Alternate Feeder Bank not used 3 1 7 1 1 1 109

Run time loss

Other losses

A Failure Mode and Effects Analysis is a systemized group of activities intended to:

Recognize and evaluate potential failure and its effects

Identify actions which will reduce or eliminate the

What is FMEA?

© 2009, Qimpro 126

chance of failure

Document analysis findings



Identify the high priorityfailure modes and causes of defects in a process.

Identify high priority input variables (Xs) that impact important output variables

Objectives of FMEA in Six Sigma

© 2009, Qimpro 127

important output variables (Ys).

FMEA is designed to prevent failures from occurring or from getting to internal and external customers.

Therefore, FMEA is essential for situations where failures might occur and the effects of those failures occurring are potentially serious

When to use FMEA?

© 2009, Qimpro 128

failures occurring are potentially serious.

FMEA can be used on all Six Sigma projects. It serves as an overall control document for the process.

FMEA – Worksheet

Process Step/Part Number

Potential Failure Mode

Potential Failure Effects

SEV

Potential Causes

OCC

Current Controls

DET

RPN

Actions Recommended Resp.

Actions Taken

SEV

OCC

DET

RPN

0

0RPN

© 2009, Qimpro 129

0

0

0

RPN = Severity

X Occurrence

X Detection



FMEA – Severity Rating Scale

109876

Severity – The consequences of a failure should it occur.

Rating Criteria – A Failure CouldInjure a customer or employeeBe illegal / cause controllership issuesRender the product or service unfit for useCause extreme customer dissatisfactionResult in partial malfunction

© 2009, Qimpro 130

654321

Result in partial malfunctionCause a loss of performance which is likely to result in a complaintCause minor performance lossCause a minor nuisance, but be overcome with no performance lossBe unnoticed and have only minor effect on performanceBe unnoticed and not affect the performance

Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to true differences in the samples

Used to test the theories established during the Cause and Effect analysis

Hypothesis Testing

© 2009, Qimpro 131

Cause and Effect analysis.

Increases your confidence that probable Xs are statistically significant

Used when you need to be certain that a statistical difference exists

Number Of ScrappedPrototype Seats

Why Do Hypothesis Testing?

Is the observed

difference real?

© 2009, Qimpro 132

Program A Program B



Continuous dataDifferences in averagesDifferences in variationDifferences in distribution shape” of values

Discrete data

Kinds Of Differences

© 2009, Qimpro 133

Differences in proportions

Definition Of TermsNull Hypothesis – H0

The Null Hypothesis is the antithesis to our claim regarding the relationship of two or more data sets.

Hypothesis Testing

© 2009, Qimpro 134

Alternate Hypothesis – H1 or HA

The Alternate Hypothesis is our claim statement. This is the theory that we want to test.

The Null Hypothesis and Alternative Hypothesis Are Mutually Exclusive and

Complimentary.

Sampling from a distribution must be representative or independent

Random sampling is the key assumption

Normality is not the key assumption

The random sampling assumption is also known as

Hypothesis Testing – Assumptions

© 2009, Qimpro 135

The random sampling assumption is also known as the statistical independence assumption



As a result of the hypothesis test, we will either….

Reject the Null Hypothesis, or

Fail to Reject the Null Hypothesis

Hypothesis Testing – The Decision

© 2009, Qimpro 136

In Hypothesis Testing We Always Work With The Null Hypothesis. The Test Result Will Tell Us If We Can Reject Or Fail To Reject The Null Hypothesis

Whenever a hypothesis test is run, there is a risk associated with the decision that is made. There are two types of errors (risks):

Type I error (also known as alpha risk, denoted by α) – The probability of rejecting the null hypothesis when it is true

Risk of Hypothesis

© 2009, Qimpro 137

when it is true.

Type II error (also known as beta risk, denoted by β) – The probability of accepting the null hypothesis when it is false.

Type I and Type II Errors

Null Hypothesis True Null Hypothesis False

Accept Null Hypothesis

Reality

Correctdecision

Type II error

© 2009, Qimpro 138

Decision

Null Hypothesis

Reject Null Hypothesis

decision error

Type I error

Correct decision



Type I and Type II Errors

I have taken a “β”risk, my test did I have confidence

In fact there is no difference

In fact there is a difference

My test decides there is

Reality

© 2009, Qimpro 139

My test is powerful !

I have taken an “α” risk, could not have enough confidence

in my test

not have enough power

in my test

Decision

there is no difference

My test decides there is a difference

Refer to the exercise A1 in the CSSGB workbook and state the Null and Alternate Hypothesis for the situations provided.

For each of the situations, state …

H0 = ????

Hypothesis Testing – Exercise

© 2009, Qimpro 140

AndHA = ????

1 sample z-test / t-test

2 sample t-test

1 way analysis of variance (ANOVA)

Chi square test for independence

Hypothesis Testing – Common Tests

© 2009, Qimpro 141

1 proportion test

2 proportion test



The z statistic or the t statistic is a ratio of difference in means and variation of the means

The z – statistic is used for samples with;

• Large sample size of more than 30 data points

• Standard deviation of the population is known

z – test Features

© 2009, Qimpro 142

Standard deviation of the population is known

Used to compare average performance of two groups.

Tests the null (H0) hypothesis of “no difference between means of two groups”

Draws critical values from standard normal table or z table and t distribution table respectively.

The t – statistic is used for samples with;

• Small sample size of less than 30 data points

• Standard deviation of population is not known.

Used to compare average performance of two groups

t - test Features

© 2009, Qimpro 143

groups.

Tests the null (H0) hypothesis of “no difference between means of two groups”

Draws critical values from standard normal table or t distribution table.

The 1-sample Z test is used when…

Testing the equality of a population mean to a specific value, and

Sample size is large (n > 30)

Z Test – Example

© 2009, Qimpro 144



You are attempting to assess the cycle time for packaging of goods when utilizing two different methods. The use of a metal strapping has traditionally been assumed to generate the best response, but that assumption is now going to be tested against a process of using self adhesive tape.

Z Test – Example (conti...)

© 2009, Qimpro 145

Historically, when utilizing the metal staple sheets:

Average cycle time = 6 minutesStandard deviation = 2 minutes

A random sample of size 36 was collected from the self adhesive tape process, yielding:

x = 4.7 minutes s = 2.0 minutes

Establish both the Alternative and Null Hypotheses.

H0 : μ = 6 minutes

HA : μ ≠ 6 minutes

Determine the level of significance α : α = 0 05


© 2009, Qimpro 146

Determine the level of significance, α : α = 0.05

Calculate the test statistic, Z : We use the sample standard deviation, s, as our estimate of σ population. Then…


3.940.331.3

26.04.7xz -=-=-=-= σ

μ

T the same

© 2009, Qimpro 147

36n

For a = 0.05 (95% confidence) : z critical = 1.96Since the computed Z value = -3.94 < -1.96;

We REJECT the Null Hypothesis.

Conclusion: Cycle Time for packaging with Self Adhesive Tape is not equal to 6 minutes.

Try the same with y = 5.5

mins



A Scatter Diagram is an Important Graphical Tool

For Exploring the Relationship Between

Predictor Variables (X’s)

And

Scatter Diagrams

© 2009, Qimpro 148

The Response Variable (Y’s)

(i.e., Causes and the Effect)

Use Scatter Diagrams To Study The Relationship Between Two Variables

Analyzing Relationships

40

30

35

© 2009, Qimpro 149

No. Of Components for Insertion (X)

25

20

15

10

5

1K 2K 3K 4K 5K 6K 7K 8K 9K 10K

Warning! Correlation Does Not Imply Causation

Correlation and Causation

80 80100 200 300

)

Correlation Between

Number Of Storks

A d

© 2009, Qimpro 150

Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978

Number Of Storks

50100

70

60

200 30050

70

60Pop

ula

tion

(In

Thou

sand

s )And

Human Population



Look for Patterns

Interpreting A Scatter Diagram

No CorrelationStrong Positive Strong Negative Correlation

11 33 55

© 2009, Qimpro 151

Positive Correlation

Correlation

Other PatternNegative Correlation

22 44 66

For all charts: Y = Participant satisfaction (scale: 1 – worst to 100 – best)X = Trainer experience (# of hours)

The Correlation Coefficient r measures the strength of linear relationships

–1 ≤ r ≤ 1

When a relationship exists, the variables are said to be correlated

Regression Measures Of Correlation

© 2009, Qimpro 152

Perfect negative relationship r = –1.0No linear correlation r = 0Perfect positive relationship r = +1.0

r2 measures the percent of variation in Y explained by the linear relationship of X and Y and is called the Coefficient of Determination.

r2 value will always be smaller than r values

In simple linear regression, you obtain the graph and the equation of the straight line that best represent the relationship between two variables.Given a sample of paired

What is Regression?

150

100

Cost

$k

Best Fit Line

© 2009, Qimpro 153

p pdata, the regression equation

y = β0 + β1x describes the relationship between two variables.

The graph of the regression equation is called the regression line (or best fit line).

302010

50

X:Time (Days)

Y: C



The Regression Equation

Line of

xY 10β+β=Dependent

Variable

y-intercept slopeIndependent

Variable

© 2009, Qimpro 154

Whereβ0 = Predicted Value Of Y

When X1 = 0

β1 = Slope Of Line Change In Y Per UnitChange In X

X

Y

Line of Best Fit

SIX SIGMA IMPROVE PHASE

© 2009, Qimpro 155

1. Determine Solutions to Counteract the Root Causes

2. Provide Statistical Evidence that Solutions Work

3. Prepare “Should Be” Process Map

Improve Phase - Steps

© 2009, Qimpro 156



A counteraction is anything that is done to reduce or eliminate the effect of a cause.

Reduce the Effect of a CauseA helmet (counteraction) reduces the injury (effect) from an impact (cause).

R d h C Th b R d i h Eff

What is a Counteraction?

© 2009, Qimpro 157

Reduce the Cause, Thereby Reducing the Effect.A refrigerator (counteraction) reduces spoilage (effect) by reducing temperature (cause)

Eliminate the Cause, Thereby Eliminating the Effect.Antibiotics (counteraction) eliminate some diseases (effect) by eliminating Bacteria (cause)

Good counteractions are Well defined Actionable

Examples of well defined, actionable counteractions:

Useful Counteractions

© 2009, Qimpro 158

Create quarterly goals for the Six Sigma Implementation PlanAdd cavity pressure transducer to cut off injection pressure at set point.

Examples of less useful Counteractions (too vague, not actionable):

Improve communicationDevelop process focusImprove injection molding quality

Less Useful Counteractions

© 2009, Qimpro 159

Using such counteractions only leads to confusion, since people don’t understand the specific actions to take.

When these kinds of counteractions arise in brainstorming, ask, “What specific actions do we need to take to accomplish this item?”



A Decision Matrix that helps the team to screen possible solutions against three criteria…..

Effectiveness in eliminating or reducing the verified root causes – X’s

Ease of Implementation

Evaluation Matrix

© 2009, Qimpro 160

Cost of Implementation

Evaluation Matrix – ExampleCounteractions –Reducing Cycle Time from Customer Order to Supplier Purchase Order.

Effectiveness

Ease to Im

plement

Cost

Fax from Master Contact List

© 2009, Qimpro 161

Send Supplier E-Mail version of the PO file

Auto-fax: Modify Access Database to fax and e-mail confirm.

Request Call Return from Supplier

Legend: Strong RelationshipModerate RelationshipWeak Relationship

Quiz:Which idea should the team select?

Identify the high priorityfailure modes and causes of defects in a process.

Identify high priority input variables (Xs) that impact important output variables

Objectives of FMEA in Six Sigma

© 2009, Qimpro 162

important output variables (Ys).



FMEA is designed to prevent failures from occurring or from getting to internal and external customers.

Therefore, FMEA is essential for situations where failures might occur and the effects of those failures occurring are potentially serious

When to use FMEA?

© 2009, Qimpro 163

failures occurring are potentially serious.

FMEA can be used on all Six Sigma projects. It serves as an overall control document for the process.

FMEA – Worksheet

Process Step/Part Number

Potential Failure Mode

Potential Failure Effects

SEV

Potential Causes

OCC

Current Controls

DET

RPN

Actions Recommended Resp.

Actions Taken

SEV

OCC

DET

RPN

0

0RPN

© 2009, Qimpro 164

0

0

0

RPN = Severity

X Occurrence

X Detection

Cost/Benefits Analysis – Example

Costs (First Year)

Equipment $3,000

Training 500

Travel and living 250

Team labor 500

Benefits (Yearly)

Increased capacity(reduced cycle time) $750

Reduce rejects by 50% 4,000

Reduce labor hours for the job 500

© 2009, Qimpro 165

Team labor 500

Total Cost $4250

Reduced interest expense 750

Total Benefit $6000



Concentrate on tangible costs and benefits; use indirect costs that are generally acceptable to all stakeholders

Use the process map and personnel in associated departments to identify cost and benefit information

Cost/Benefits Analysis Tips

© 2009, Qimpro 166

information

Keep the analysis simple; focus on cost of implementation and a few key benefits that clearly exceed the cost

Use standard methods and rates in your calculations

List all activities that contribute to either cost or benefit and identify as much as possible how these activities will be measured

Cost/Benefits Analysis Tips (conti...)

© 2009, Qimpro 167

Keep the presentation simple and easy to understand

Take One Final Look at Your Solution Before Implementation

Does it address the root cause?

Can the solution been verified through the data that it will drive your process toward successfully

Outside – In Perspective

© 2009, Qimpro 168

meeting the customer CTQs?

Will your customer be satisfied with the solution?



Pilot SolutionsA Test Of All Or Part Of A Proposed Solution On A Small Scale In Order To Better Understand Its Effects And To Learn About How To Make The Full Scale Implementation More Effective

© 2009, Qimpro 169

Improved solution that meets customer CTQs

Refined implementation plans

Lower risk of failure by identifying and fixing problems

Confirmation expected results and relationships

Benefits Of Piloting

© 2009, Qimpro 170

Confirmation expected results and relationships (of X and Y)

Increased opportunity for feedback and buy-in

Get early version of a solution out quickly to a particular segment

Verification Of Pilot Results

Before After

Statistically Verify The Pilot Results

© 2009, Qimpro 171

Time ToProcess In Days

Time ToProcess In Days

Does The Output Data Show A Significant Difference That Can Be Attributed To The New Solution?



To Assess The Effectiveness Of A Solution:

Calculate the new Process Capability (sigma) and compare it with the improvement goal and the original process.

Compare before and after Visual Tools so you can

Test Effectiveness of Pilot

© 2009, Qimpro 172

analyze the data visually.

Use Hypothesis Testing to see if a significant statistical difference exists between the old versus the new process.

The improvement team should be there as much as possible during the pilot process; what they learn and observe will be worth the time they invest

Collect data on process and external factors that may be influential

Piloting Tips

© 2009, Qimpro 173

may be influential

If possible, make sure that the full range of inputs and process conditions are tested in the pilot

Expect “scale-up” issues after even the most successful pilots

Identify critical differences between the pilot environment and the full-scale implementation environment; note potential issues/problems for full scale plan

Piloting Tips (conti...)

© 2009, Qimpro 174

full-scale plan



During the Measure Phase, we collected data on the process output (Y) to establish the baseline performance……x1

During the Improve Phase, we collected data on the process output (Y) after the process has been improved x

Need for Hypothesis Testing

© 2009, Qimpro 175

improved…… x1

Now we need to answer the following…..

Is there really a difference between x1 and x2

Is x2 better than x1

Is x2 worse than x1

Hypothesis Testing gives us the answer…….

Case1 : Higher the better.H0 : x1 = x2HA: x1 < x2

Case 2 : Lower the better.

Hypothesis Testing

© 2009, Qimpro 176

H0 : x1 = x2HA: x1 > x2

Use t Test for Continuous Data and p Test for Attribute Data

SIX SIGMA CONTROL PHASE

© 2009, Qimpro 177



1. Prepare and Implement the Control Plan

2. Provide Statistical Evidence that the Improvements are Sustained. (3 months of data)

Control Phase - Steps

© 2009, Qimpro 178

A written summary description of the system for controlling a process

Describes actions required to maintain the “desired state” of the process and minimize process and product variation

What is a Control Plan?

© 2009, Qimpro 179

p p

A living document which evolves and changes with the process and product requirements

Control Plan StrategyA good control plan strategy…

Minimizes process tampering.

Clearly states the reaction plan to out-of-control conditions.

Describes training needs for standard operating

© 2009, Qimpro 180

g p gprocedures

Describes maintenance schedule requirements.

A good control plan clearly describes what actions to take, when to take them, and who should take them… thereby reducing “fire fighting” activities.



What to ControlY = f ( x1, x2, x3…)

KPOV KPIVs

Monitor Control

© 2009, Qimpro 181

Monitor Control

A control plan controls the X’s to ensure the desired state for Y.

Merely monitoring the output, Y, is not an effective way to control a process.

Why use a Control Plan?Provides a single point of reference for understanding process characteristics, specifications, and Standard Operating Procedures (SOP)

Enables orderly transfer of responsibility for “sustaining the gain”

© 2009, Qimpro 182

sustaining the gain

Developing a Control PlanQuestions to Get Started

What do you want to control?How often do you need to measure the process?Do you have an effective measurement system?Who needs to see the data?

© 2009, Qimpro 183

What type of tool/chart is necessary?Who will generate the data?Who will control the process?Have they been trained?What are the system requirements for auditing & maintenance?



Control ChartsDifferent control charts exist for different types of data.

Common Control Charts

Variable Data:→ X Bar and R Chart

© 2009, Qimpro 184

→ a a d C a t→ Individuals and Moving Range Chart

Attribute Data:→ p Chart (for Binomial Data)→ u Chart (for Poisson Data)

The Value of Process ControlWhen a process is in control:

You can predict what it will do in the future in terms of its average performance and its variation.You can estimate the capability of the process to meet specifications

© 2009, Qimpro 185

to meet specifications.It reduces process variation and process cost.

CAUTION!When a process is not stable, we

cannot draw valid conclusions about the process' ability to meet specifications!

What Control Charts SayIs the processstable?

Should action betaken?

Should the processbe left alone?

6.46.36.26.16.05.95.8D

imen

sion

in m

m

CommonCauses

Special Cause

UCL

x=

© 2009, Qimpro 186

be left alone?

What types of causesare present?

What is the average process output?

What is the variation of the process?

2520151050

5.75.6

Subgroup Number

LCL



Looking at the Data StatisticallyStatistical Control limits have been calculated from the data and are drawn as dashed lines on the graph.

X Bar Control Chart—Average Daily Production Cost by Week

$18,500

$19,000

$19,500

on C

ost

UCL

© 2009, Qimpro 187

$16,000

$16,500

$17,000

$17,500

$18,000

Week Number

Aver

age

Dai

ly P

rodu

ctio

LCL

Since all points are randomly distributed within the statistical bounds, this production system is stable.

Do Not Try to Explain DifferencesThis means that the observed variation in average daily production cost is the natural fluctuation one would expect from a non-changing system


$18,500

$19,000

$19,500

ctio

n C

ost

UCL

6.2.1

© 2009, Qimpro 188

$16,000

$16,500

$17,000

$17,500

$18,000

Week Number

Aver

age

Dai

ly P

rodu

c

LCL

It does not make sense to attempt to explain the difference between any of these points.

Without looking at the data statistically, we wrongly concluded the process was changing -cost was increasing!


$17,000

$17,500

$18,000

$18,500

$19,000

$19,500

Aver

age

Dai

ly P

rodu

ctio

n C

ost

UCL

When we implemented

Ineffective Actions 6.2.1

© 2009, Qimpro 189

$16,000

$16,500

Week Number

A

LCL

pcorrective actions, we wrongly assumed they were effective.

The corrective actions could not produce sustainable improvement because they corrected causes that are not real.



Understanding Types of VariationWithout proper understanding of the types of variation, over-reaction or incorrect actions are taken.

6.2.1

© 2009, Qimpro 190

Special Cause

Type of Variation Definition Characteristics

Common cause No undueInfluence byany of the5M d 1P

• Expected• Predictable• Normal• Random

Two Types of Variation 6.2.1

© 2009, Qimpro 191

Special cause

5Ms and 1P

Undueinfluence byany of the5Ms and 1P

• Chance

• Unexpected• Unpredictable• Not Normal• Not Random• Assignable

Responding to Variation 6.2.1

MEASUREMENTS

MEASURE

CommonCauses

Common or

Special

I ti t ll f th I ti t th ifi

MEASURE

SpecialCauses

© 2009, Qimpro 192

IMPROVE

Develop solutions for the “vital few” process inputs - X’s

MEASURE

Develop solutions for special causes and implement as appropriate

ANALYZE

Investigate all of the variation by identifying the “vital few” process inputs - X’s

MEASURE

Investigate the specific data points related to the special causes



How you treat variation...Common Causes Special Causes

CommonCauses

Mistake 1Tampering

(increases variation)Focus on fundamental

process change

Special and Common Cause Variation 6.2.1

© 2009, Qimpro 193

Causes

SpecialCauses

Mistake 2Under reacting

(missed prevention)Focus on investigating

special causes

What thevariationreally is...

Summary of VariationTo improve any process, it is useful to understand its variation.

All variation is caused by common and/or special causes.

There are two major classifications of causes which help you select appropriate managerial actions:

© 2009, Qimpro 194

help you select appropriate managerial actions:

If all variation is due to “common causes,” the result will be a predictable or stable systemIf some variation is from “special causes,” the result is an unstable or unpredictable system.

Variation causes customer dissatisfaction.

Control Limits

Control Limitsare statistical bounds used to determine

Upper Control limit

© 2009, Qimpro 195

In the X Bar chart, if all the averages stay within these bounds (and fluctuate in a random manner with 2/3 of the points near the center line), then the process is stable.

process stability.Lower Control limit



Specification Limits

Specification Limitsare applied to individualmeasurements.

© 2009, Qimpro 196

LSL USL

We want to know whether or not all foam pads made will fall within the given specification.

Process Not in Statistical Control1. Points beyond Control Limits:Points beyond control limits are isolated high or low points. Usually both the X chart and R chart will show the same point beyond control limits.

© 2009, Qimpro 197

2. Points Hugging Control LimitsPoints are hugging control limits if a chart doesn't satisfy the rule of two-thirds of the points being within one-third of the centerline.

Process Not in Statistical Control3. Points Hugging the CenterlineAlmost all of the points are within one-third (of the distance between the control limits) of the centerline

© 2009, Qimpro 198

centerline.

4. Sudden Shift in LevelSudden shift in level occurs when the points seem to move to a new average over a short period of time.



Process Not in Statistical Control

5. TrendTrends will continue up or down without a well defined end.

© 2009, Qimpro 199

6. CycleA cycle produces a pattern of up and down points, very much as if the values of the points were time dependent.

X Bar & R Chart

The X chart (averages) is accompanied by the range (R) chart (variation).

8 0

12.0

16.0UCL

TheRange

0.02.04.06.08.0

10.0UCL

LCL

The

Chart

© 2009, Qimpro 200

Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:001 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0

Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0

It is important to simultaneously monitor a process' average performance and its variation.

0.0

4.0

8.0 RRangeChart

Construction of X Bar & R Chart1. Compute the average for each subgroup:Add the measurements together and divide by the number of measurements in the subgroup.For the 8:00 subgroup:

Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00

1 10.0 7.0 5.0 9.0 2.0 2.0 5.0

2 1.0 4.0 2.0 3.0 4.0 4.0 6.0

3 4.0 10.0 6.0 7.0 2.0 8.0 4.0

4 9.0 2.0 2.0 3.0 6.0 8.0 10.0

5 8.0 8.0 3.0 1.0 1.0 6.0 3.0

Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6

Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0

© 2009, Qimpro 201

For the 8:00 subgroup:

2. Compute the range for each subgroup:Subtract the smallest measurement from the largest measurement in the subgroup.For the 8:00 subgroup:

( ) 4.60.80.90.40.10.1051x =++++=

0.90.10.10R =-=



Construction of X Bar & R Chart3. Compute X double bar (Average of the Averages):Add all the averages of the subgroups together and divide by the number of subgroups.

Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00

1 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0

Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6

Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0

( ) 05656503636326461X ++++++

© 2009, Qimpro 202

4. Compute R bar (Average of the Ranges):Add all the ranges of the subgroups together and divide by the number of subgroups.

( ) 0.56.56.50.36.36.32.64.67

X =++++++=

( ) 7.60.70.60.50.80.40.80.971R =++++++=

Construction of X Bar & R Chart

5. Calculate the control limits:

For the x bar chart...

RAXLCL

9.8)76577.0(0.5UCLRAXUCL

x

2x

-=

=×+=+=

Sample # 8:00 8:30 9:00 9:30 10:00 10:30 11:00

1 10.0 7.0 5.0 9.0 2.0 2.0 5.02 1.0 4.0 2.0 3.0 4.0 4.0 6.03 4.0 10.0 6.0 7.0 2.0 8.0 4.04 9.0 2.0 2.0 3.0 6.0 8.0 10.05 8.0 8.0 3.0 1.0 1.0 6.0 3.0

Average 6.4 6.2 3.6 4.6 3.0 5.6 5.6

Range 9.0 8.0 4.0 8.0 5.0 6.0 7.0

© 2009, Qimpro 203

SubgroupSize (n) A2 D3 D4

2 1.880 0.000 3.2673 1.023 0.000 2.5744 0.729 0.000 2.2825 0.577 0.000 2.114

1.1)7.6577.0(0.5LCLRAXLCL

x

2x

=×-=

For the R chart...

0.07.6000.0LCL

RDLCL

2.147.6114.2UCL

RDUCL

R

3R

R

4R

=×=

=

=×==

Interpreting an X bar and R ChartData is the dimension of a feature detail on a headliner.

0.7560.7550.7540.7530.7520.7510.7500.7490.7480 747

Mean=0.7512

UCL=0.7551

LCL=0.7473

Xbar/R Chart for Dimension

mpl

e M

ean

© 2009, Qimpro 204

Is the Process in Statistical Control?Is the Process in Statistical Control?

252015105Subgroup 0

0.747

0.015

0.010

0.005

0.000

R=0.00678

UCL=0.01434

LCL=0

Sam

Sam

ple

Ran

ge



Rules of Thumb:

At least 20 subgroups of about n=5 data are required.

The data within a subgroup should be collected close together in time (for example, 5

i l d d )

Collecting Data for an X Bar & R Chart

© 2009, Qimpro 205

consecutively produced parts).

Longer time intervals are used between subgroups. (Depending on the process and purpose of the study, these time intervals could be 15 min., 30 min., 1hr., 2 hr., or longer).

Key metric to prove improvement from the baseline performance level – Process Capability

A1 A2

Process Capability

© 2009, Qimpro 206

LSL USL LSL USL

Capability of A1CPK, PPM, DPMOSigma Level

Capability of A2CPK, PPM, DPMOSigma Level

<=

ProcessO t t

Attribute

Data

PPM, DPU, DPODPMO, RTY

Sigma

Process Capability Metrics

© 2009, Qimpro 207

OutputY

Variable

DataType

CP, CPK,PP, PPKPPM

SigmaLevel



Control DashboardsA dashboard is a template which gives the top management a snap shot view of the improved process.

A single graph that displays the current performance of the process against the target.

© 2009, Qimpro 208

Each output parameter needs to have one dashboard.

DashboardWhen to use a Dashboard

For the BB from the exit of Improve Phase and to the end of Control Phase

For the process Owner from the hand over of project by BB to lifetime of the process or till

© 2009, Qimpro 209

the next improvement

Dashboard - ExamplesOn Hand Stock Ratio - Cushions

020406080

Bas

elin

e

July

Aug

Sep

t

Oct

Nov

Dec Ja

n

Feb

Mar

Apr

il

May

June

Month

On

hand

sto

ck R

atio

On Hand stock Ratio Cushions Target

On Hand Stock Ratio - CPT

020406080

100

Bas

elin

e

July

Aug

Sep

t

Oct

Nov

Dec Ja

n

Feb

Mar

Apr

il

May

June

Month

On

Hand

Sto

ck R

atio

On Hand stock Ratio CPT Target

© 2009, Qimpro 210

On hand Stock Ratio - Carton

020406080

100

Baselin

eJu

lyAug

Sept

Oct Nov Dec Jan Feb

MarApri

lMay Jun

e

Month

On

Han

d S

tock

Ra

tio

On Hand stock Ratio Carton Target

On Hand Stock Ratio - Cabinet

020406080

100

Bas

elin

e

July

Aug

Sep

t

Oct

Nov

Dec Ja

n

Feb

Mar

Apr

il

May

June

Month

On

hand

sto

ck r

atio

On Hand stock Ratio Cabinet Target



Final ReportAt the end of Control Phase, each BB is required to make a report on the project.

The report should cover all the stages of the Six Sigma project DMAIC

The Report should have the SOP’s & formats

© 2009, Qimpro 211

attached as per the counter measure matrix

The report should end with the Dashboard updated till the end of the 3rd month of Control Phase

Thank You!

© 2009, Qimpro 212

[email protected] 8701

www.qimpro.com Page 1 of 2

Z Table Values (One Tail) from Z = 0 to Z = 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-001

0.10 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-001

0.20 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-001

0.30 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-001

0.40 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-001

0.50 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-001

0.60 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-001

0.70 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-001

0.80 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-001

0.90 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

1.00 1.59e-001 1.56e-001 1.54e-001 1.52e-001 1.49e-001 1.47e-001 1.45e-001 1.42e-001 1.40e-001 1.38e-001

1.10 1.36e-001 1.33e-001 1.31e-001 1.29e-001 1.27e-001 1.25e-001 1.23e-001 1.21e-001 1.19e-001 1.17e-001

1.20 1.15e-001 1.13e-001 1.11e-001 1.09e-001 1.07e-001 1.06e-001 1.04e-001 1.02e-001 1.00e-001 9.85e-002

1.30 9.68e-002 9.51e-002 9.34e-002 9.18e-002 9.01e-002 8.85e-002 8.69e-002 8.53e-002 8.38e-002 8.23e-002

1.40 8.08e-002 7.93e-002 7.78e-002 7.64e-002 7.49e-002 7.35e-002 7.21e-002 7.08e-002 6.94e-002 6.81e-002

1.50 6.68e-002 6.55e-002 6.43e-002 6.30e-002 6.18e-002 6.06e-002 5.94e-002 5.82e-002 5.71e-002 5.59e-002

1.60 5.48e-002 5.37e-002 5.26e-002 5.16e-002 5.05e-002 4.95e-002 4.85e-002 4.75e-002 4.65e-002 4.55e-002

1.70 4.46e-002 4.36e-002 4.27e-002 4.18e-002 4.09e-002 4.01e-002 3.92e-002 3.84e-002 3.75e-002 3.67e-002

1.80 3.59e-002 3.51e-002 3.44e-002 3.36e-002 3.29e-002 3.22e-002 3.14e-002 3.07e-002 3.01e-002 2.94e-002

1.90 2.87e-002 2.81e-002 2.74e-002 2.68e-002 2.62e-002 2.56e-002 2.50e-002 2.44e-002 2.39e-002 2.33e-002

2.00 2.28e-002 2.22e-002 2.17e-002 2.12e-002 2.07e-002 2.02e-002 1.97e-002 1.92e-002 1.88e-002 1.83e-002

2.10 1.79e-002 1.74e-002 1.70e-002 1.66e-002 1.62e-002 1.58e-002 1.54e-002 1.50e-002 1.46e-002 1.43e-002

2.20 1.39e-002 1.36e-002 1.32e-002 1.29e-002 1.25e-002 1.22e-002 1.19e-002 1.16e-002 1.13e-002 1.10e-002

2.30 1.07e-002 1.04e-002 1.02e-002 9.90e-003 9.64e-003 9.39e-003 9.14e-003 8.89e-003 8.66e-003 8.42e-003

2.40 8.20e-003 7.98e-003 7.76e-003 7.55e-003 7.34e-003 7.14e-003 6.95e-003 6.76e-003 6.57e-003 6.39e-003

2.50 6.21e-003 6.04e-003 5.87e-003 5.70e-003 5.54e-003 5.39e-003 5.23e-003 5.08e-003 4.94e-003 4.80e-003

2.60 4.66e-003 4.53e-003 4.40e-003 4.27e-003 4.15e-003 4.02e-003 3.91e-003 3.79e-003 3.68e-003 3.57e-003

2.70 3.47e-003 3.36e-003 3.26e-003 3.17e-003 3.07e-003 2.98e-003 2.89e-003 2.80e-003 2.72e-003 2.64e-003

2.80 2.56e-003 2.48e-003 2.40e-003 2.33e-003 2.26e-003 2.19e-003 2.12e-003 2.05e-003 1.99e-003 1.93e-003

2.90 1.87e-003 1.81e-003 1.75e-003 1.69e-003 1.64e-003 1.59e-003 1.54e-003 1.49e-003 1.44e-003 1.39e-003

3.00 1.35e-003 1.31e-003 1.26e-003 1.22e-003 1.18e-003 1.14e-003 1.11e-003 1.07e-003 1.04e-003 1.00e-003

3.10 9.68e-004 9.35e-004 9.04e-004 8.74e-004 8.45e-004 8.16e-004 7.89e-004 7.62e-004 7.36e-004 7.11e-004

3.20 6.87e-004 6.64e-004 6.41e-004 6.19e-004 5.98e-004 5.77e-004 5.57e-004 5.38e-004 5.19e-004 5.01e-004

3.30 4.83e-004 4.66e-004 4.50e-004 4.34e-004 4.19e-004 4.04e-004 3.90e-004 3.76e-004 3.62e-004 3.49e-004

3.40 3.37e-004 3.25e-004 3.13e-004 3.02e-004 2.91e-004 2.80e-004 2.70e-004 2.60e-004 2.51e-004 2.42e-004

3.50 2.33e-004 2.24e-004 2.16e-004 2.08e-004 2.00e-004 1.93e-004 1.85e-004 1.78e-004 1.72e-004 1.65e-004

3.60 1.59e-004 1.53e-004 1.47e-004 1.42e-004 1.36e-004 1.31e-004 1.26e-004 1.21e-004 1.17e-004 1.12e-004

3.70 1.08e-004 1.04e-004 9.96e-005 9.57e-005 9.20e-005 8.84e-005 8.50e-005 8.16e-005 7.84e-005 7.53e-005

3.80 7.23e-005 6.95e-005 6.67e-005 6.41e-005 6.15e-005 5.91e-005 5.67e-005 5.44e-005 5.22e-005 5.01e-005

3.90 4.81e-005 4.61e-005 4.43e-005 4.25e-005 4.07e-005 3.91e-005 3.75e-005 3.59e-005 3.45e-005 3.30e-005

4.00 3.17e-005 3.04e-005 2.91e-005 2.79e-005 2.67e-005 2.56e-005 2.45e-005 2.35e-005 2.25e-005 2.16e-005

4.10 2.07e-005 1.98e-005 1.89e-005 1.81e-005 1.74e-005 1.66e-005 1.59e-005 1.52e-005 1.46e-005 1.39e-005

4.20 1.33e-005 1.28e-005 1.22e-005 1.17e-005 1.12e-005 1.07e-005 1.02e-005 9.77e-006 9.34e-006 8.93e-006

4.30 8.54e-006 8.16e-006 7.80e-006 7.46e-006 7.12e-006 6.81e-006 6.50e-006 6.21e-006 5.93e-006 5.67e-006

4.40 5.41e-006 5.17e-006 4.94e-006 4.71e-006 4.50e-006 4.29e-006 4.10e-006 3.91e-006 3.73e-006 3.56e-006

4.50 3.40e-006 3.24e-006 3.09e-006 2.95e-006 2.81e-006 2.68e-006 2.56e-006 2.44e-006 2.32e-006 2.22e-006

4.60 2.11e-006 2.01e-006 1.92e-006 1.83e-006 1.74e-006 1.66e-006 1.58e-006 1.51e-006 1.43e-006 1.37e-006

4.70 1.30e-006 1.24e-006 1.18e-006 1.12e-006 1.07e-006 1.02e-006 9.68e-007 9.21e-007 8.76e-007 8.34e-007

4.80 7.93e-007 7.55e-007 7.18e-007 6.83e-007 6.49e-007 6.17e-007 5.87e-007 5.58e-007 5.30e-007 5.04e-007

4.90 4.79e-007 4.55e-007 4.33e-007 4.11e-007 3.91e-007 3.71e-007 3.52e-007 3.35e-007 3.18e-007 3.02e-007

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Z Table Values (One Tail) from Z = 5 to Z = 9.99

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

5.00 2.87e-007 2.72e-007 2.58e-007 2.45e-007 2.33e-007 2.21e-007 2.10e-007 1.99e-007 1.89e-007 1.79e-007

5.10 1.70e-007 1.61e-007 1.53e-007 1.45e-007 1.37e-007 1.30e-007 1.23e-007 1.17e-007 1.11e-007 1.05e-007

5.20 9.96e-008 9.44e-008 8.95e-008 8.48e-008 8.03e-008 7.60e-008 7.20e-008 6.82e-008 6.46e-008 6.12e-008

5.30 5.79e-008 5.48e-008 5.19e-008 4.91e-008 4.65e-008 4.40e-008 4.16e-008 3.94e-008 3.72e-008 3.52e-008

5.40 3.33e-008 3.15e-008 2.98e-008 2.82e-008 2.66e-008 2.52e-008 2.38e-008 2.25e-008 2.13e-008 2.01e-008

5.50 1.90e-008 1.79e-008 1.69e-008 1.60e-008 1.51e-008 1.43e-008 1.35e-008 1.27e-008 1.20e-008 1.14e-008

5.60 1.07e-008 1.01e-008 9.55e-009 9.01e-009 8.50e-009 8.02e-009 7.57e-009 7.14e-009 6.73e-009 6.35e-009

5.70 5.99e-009 5.65e-009 5.33e-009 5.02e-009 4.73e-009 4.46e-009 4.21e-009 3.96e-009 3.74e-009 3.52e-009

5.80 3.32e-009 3.12e-009 2.94e-009 2.77e-009 2.61e-009 2.46e-009 2.31e-009 2.18e-009 2.05e-009 1.93e-009

5.90 1.82e-009 1.71e-009 1.61e-009 1.51e-009 1.43e-009 1.34e-009 1.26e-009 1.19e-009 1.12e-009 1.05e-009

6.00 9.87e-010 9.28e-010 8.72e-010 8.20e-010 7.71e-010 7.24e-010 6.81e-010 6.40e-010 6.01e-010 5.65e-010

6.10 5.30e-010 4.98e-010 4.68e-010 4.39e-010 4.13e-010 3.87e-010 3.64e-010 3.41e-010 3.21e-010 3.01e-010

6.20 2.82e-010 2.65e-010 2.49e-010 2.33e-010 2.19e-010 2.05e-010 1.92e-010 1.81e-010 1.69e-010 1.59e-010

6.30 1.49e-010 1.40e-010 1.31e-010 1.23e-010 1.15e-010 1.08e-010 1.01e-010 9.45e-011 8.85e-011 8.29e-011

6.40 7.77e-011 7.28e-011 6.81e-011 6.38e-011 5.97e-011 5.59e-011 5.24e-011 4.90e-011 4.59e-011 4.29e-011

6.50 4.02e-011 3.76e-011 3.52e-011 3.29e-011 3.08e-011 2.88e-011 2.69e-011 2.52e-011 2.35e-011 2.20e-011

6.60 2.06e-011 1.92e-011 1.80e-011 1.68e-011 1.57e-011 1.47e-011 1.37e-011 1.28e-011 1.19e-011 1.12e-011

6.70 1.04e-011 9.73e-012 9.09e-012 8.48e-012 7.92e-012 7.39e-012 6.90e-012 6.44e-012 6.01e-012 5.61e-012

6.80 5.23e-012 4.88e-012 4.55e-012 4.25e-012 3.96e-012 3.69e-012 3.44e-012 3.21e-012 2.99e-012 2.79e-012

6.90 2.60e-012 2.42e-012 2.26e-012 2.10e-012 1.96e-012 1.83e-012 1.70e-012 1.58e-012 1.48e-012 1.37e-012

7.00 1.28e-012 1.19e-012 1.11e-012 1.03e-012 9.61e-013 8.95e-013 8.33e-013 7.75e-013 7.21e-013 6.71e-013

7.10 6.24e-013 5.80e-013 5.40e-013 5.02e-013 4.67e-013 4.34e-013 4.03e-013 3.75e-013 3.49e-013 3.24e-013

7.20 3.01e-013 2.80e-013 2.60e-013 2.41e-013 2.24e-013 2.08e-013 1.94e-013 1.80e-013 1.67e-013 1.55e-013

7.30 1.44e-013 1.34e-013 1.24e-013 1.15e-013 1.07e-013 9.91e-014 9.20e-014 8.53e-014 7.91e-014 7.34e-014

7.40 6.81e-014 6.31e-014 5.86e-014 5.43e-014 5.03e-014 4.67e-014 4.33e-014 4.01e-014 3.72e-014 3.44e-014

7.50 3.19e-014 2.96e-014 2.74e-014 2.54e-014 2.35e-014 2.18e-014 2.02e-014 1.87e-014 1.73e-014 1.60e-014

7.60 1.48e-014 1.37e-014 1.27e-014 1.17e-014 1.09e-014 1.00e-014 9.30e-015 8.60e-015 7.95e-015 7.36e-015

7.70 6.80e-015 6.29e-015 5.82e-015 5.38e-015 4.97e-015 4.59e-015 4.25e-015 3.92e-015 3.63e-015 3.35e-015

7.80 3.10e-015 2.86e-015 2.64e-015 2.44e-015 2.25e-015 2.08e-015 1.92e-015 1.77e-015 1.64e-015 1.51e-015

7.90 1.39e-015 1.29e-015 1.19e-015 1.10e-015 1.01e-015 9.33e-016 8.60e-016 7.93e-016 7.32e-016 6.75e-016

8.00 6.22e-016 5.74e-016 5.29e-016 4.87e-016 4.49e-016 4.14e-016 3.81e-016 3.51e-016 3.24e-016 2.98e-016

8.10 2.75e-016 2.53e-016 2.33e-016 2.15e-016 1.98e-016 1.82e-016 1.68e-016 1.54e-016 1.42e-016 1.31e-016

8.20 1.20e-016 1.11e-016 1.02e-016 9.36e-017 8.61e-017 7.92e-017 7.28e-017 6.70e-017 6.16e-017 5.66e-017

8.30 5.21e-017 4.79e-017 4.40e-017 4.04e-017 3.71e-017 3.41e-017 3.14e-017 2.88e-017 2.65e-017 2.43e-017

8.40 2.23e-017 2.05e-017 1.88e-017 1.73e-017 1.59e-017 1.46e-017 1.34e-017 1.23e-017 1.13e-017 1.03e-017

8.50 9.48e-018 8.70e-018 7.98e-018 7.32e-018 6.71e-018 6.15e-018 5.64e-018 5.17e-018 4.74e-018 4.35e-018

8.60 3.99e-018 3.65e-018 3.35e-018 3.07e-018 2.81e-018 2.57e-018 2.36e-018 2.16e-018 1.98e-018 1.81e-018

8.70 1.66e-018 1.52e-018 1.39e-018 1.27e-018 1.17e-018 1.07e-018 9.76e-019 8.93e-019 8.17e-019 7.48e-019

8.80 6.84e-019 6.26e-019 5.72e-019 5.23e-019 4.79e-019 4.38e-019 4.00e-019 3.66e-019 3.34e-019 3.06e-019

8.90 2.79e-019 2.55e-019 2.33e-019 2.13e-019 1.95e-019 1.78e-019 1.62e-019 1.48e-019 1.35e-019 1.24e-019

9.00 1.13e-019 1.03e-019 9.40e-020 8.58e-020 7.83e-020 7.15e-020 6.52e-020 5.95e-020 5.43e-020 4.95e-020

9.10 4.52e-020 4.12e-020 3.76e-020 3.42e-020 3.12e-020 2.85e-020 2.59e-020 2.37e-020 2.16e-020 1.96e-020

9.20 1.79e-020 1.63e-020 1.49e-020 1.35e-020 1.23e-020 1.12e-020 1.02e-020 9.31e-021 8.47e-021 7.71e-021

9.30 7.02e-021 6.39e-021 5.82e-021 5.29e-021 4.82e-021 4.38e-021 3.99e-021 3.63e-021 3.30e-021 3.00e-021

9.40 2.73e-021 2.48e-021 2.26e-021 2.05e-021 1.86e-021 1.69e-021 1.54e-021 1.40e-021 1.27e-021 1.16e-021

9.50 1.05e-021 9.53e-022 8.66e-022 7.86e-022 7.14e-022 6.48e-022 5.89e-022 5.35e-022 4.85e-022 4.40e-022

9.60 4.00e-022 3.63e-022 3.29e-022 2.99e-022 2.71e-022 2.46e-022 2.23e-022 2.02e-022 1.83e-022 1.66e-022

9.70 1.51e-022 1.37e-022 1.24e-022 1.12e-022 1.02e-022 9.22e-023 8.36e-023 7.57e-023 6.86e-023 6.21e-023

9.80 5.63e-023 5.10e-023 4.62e-023 4.18e-023 3.79e-023 3.43e-023 3.10e-023 2.81e-023 2.54e-023 2.30e-023

9.90 2.08e-023 1.88e-023 1.70e-023 1.54e-023 1.39e-023 1.26e-023 1.14e-023 1.03e-023 9.32e-024 8.43e-024

ZST PPMLT (-1.5σ) CpkLT ZST PPMLT (-1.5σ) CpkLT

-6.0 1,000,000 -2.5 0.0 933,193 -0.5-5.9 1,000,000 -2.5 0.1 919,243 -0.5-5.8 1,000,000 -2.4 0.2 903,199 -0.4-5.7 1,000,000 -2.4 0.3 884,930 -0.4-5.6 1,000,000 -2.4 0.4 864,334 -0.4-5.5 1,000,000 -2.3 0.5 841,345 -0.3-5.4 1,000,000 -2.3 0.6 815,940 -0.3-5.3 1,000,000 -2.3 0.7 788,145 -0.3-5.2 1,000,000 -2.2 0.8 758,036 -0.2-5.1 1,000,000 -2.2 0.9 725,747 -0.2-5.0 1,000,000 -2.2 1.0 691,462 -0.2-4.9 1,000,000 -2.1 1.1 655,422 -0.1-4.8 1,000,000 -2.1 1.2 617,911 -0.1-4.7 1,000,000 -2.1 1.3 579,260 -0.1-4.6 1,000,000 -2.0 1.4 539,828 0.0-4.5 1,000,000 -2.0 1.5 500,000 0.0-4.4 1,000,000 -2.0 1.6 460,172 0.0-4.3 1,000,000 -1.9 1.7 420,740 0.1-4.2 1,000,000 -1.9 1.8 382,089 0.1-4.1 1,000,000 -1.9 1.9 344,578 0.1-4.0 1,000,000 -1.8 2.0 308,538 0.2-3.9 1,000,000 -1.8 2.1 274,253 0.2-3.8 1,000,000 -1.8 2.2 241,964 0.2-3.7 1,000,000 -1.7 2.3 211,855 0.3-3.6 1,000,000 -1.7 2.4 184,060 0.3-3.5 1,000,000 -1.7 2.5 158,655 0.3-3.4 1,000,000 -1.6 2.6 135,666 0.4-3.3 999,999 -1.6 2.7 115,070 0.4-3.2 999,999 -1.6 2.8 96,801 0.4-3.1 999,998 -1.5 2.9 80,757 0.5-3.0 999,997 -1.5 3.0 66,807 0.5-2.9 999,995 -1.5 3.1 54,799 0.5-2.8 999,991 -1.4 3.2 44,565 0.6-2.7 999,987 -1.4 3.3 35,930 0.6-2.6 999,979 -1.4 3.4 28,716 0.6-2.5 999,968 -1.3 3.5 22,750 0.7-2.4 999,952 -1.3 3.6 17,864 0.7-2.3 999,928 -1.3 3.7 13,903 0.7-2.2 999,892 -1.2 3.8 10,724 0.8-2.1 999,841 -1.2 3.9 8,198 0.8-2.0 999,767 -1.2 4.0 6,210 0.8-1.9 999,663 -1.1 4.1 4,661 0.9-1.8 999,517 -1.1 4.2 3,467 0.9-1.7 999,313 -1.1 4.3 2,555 0.9-1.6 999,032 -1.0 4.4 1,866 1.0-1.5 998,650 -1.0 4.5 1,350 1.0-1.4 998,134 -1.0 4.6 968 1.0-1.3 997,445 -0.9 4.7 687 1.1-1.2 996,533 -0.9 4.8 483 1.1-1.1 995,339 -0.9 4.9 337 1.1-1.0 993,790 -0.8 5.0 233 1.2-0.9 991,802 -0.8 5.1 159 1.2-0.8 989,276 -0.8 5.2 108 1.2-0.7 986,097 -0.7 5.3 72 1.3-0.6 982,136 -0.7 5.4 48 1.3-0.5 977,250 -0.7 5.5 32 1.3-0.4 971,284 -0.6 5.6 21 1.4-0.3 964,070 -0.6 5.7 13 1.4-0.2 955,435 -0.6 5.8 8.5 1.4-0.1 945,201 -0.5 5.9 5.4 1.50.0 933,193 -0.5 6.0 3.4 1.5

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