1

MTCP ProgramSix Sigma Introduction

15th June 2009

Malaysia Productivity Corporation(Statutory Body under MITI)P.O Box 64, Jalan Sultan, 46904 Petaling JayaWebsite: www mpc gov my

Topic: Six Sigma Introduction

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Website: www.mpc.gov.my

Consultant: Mohd Azlan AbasTel: +6 012 308 7421Email: Mohdazlan.abas@gmail.com

Why Does One Need a Quality Initiative?

Meet customer expectations for higher quality

Provide a competitive differentiator in the service market

Build greater pride and satisfaction in the team

Tangible Costs Intangible Costs- Inspection - Expediting- Scrap - Lost Customers- Rework - Longer Cycles- Warranty - Lower Morale

Drive other key goals: productivity and growth

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Enormous opportunityEnormous opportunity

2

Vital Few CTQs that apply to all Customers:

– Responsiveness

– Marketplace Competitiveness

Six Sigma Provides focus on

Critical to Quality (CTQ) Metrics in businesses

p p

– On-time, Accurate and Complete Deliverables

– Product/Service Technical Performance

Key CTQs for a company:

– Post Sales Issue resolution

– Service Delivery Span

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– Contract Fulfillment

– Parts Fulfillment

– Pricing

– Customer Escalation Cycle Time

PracticalProblem Traditional

Approach

D fi & MD fi & M

Six Sigma Provides focus on

Critical to Quality (CTQ) Metrics in businesses

StatisticalProblem

StatisticalSolution

6Quality Methodology

Systematic Approach Focusing

Define & MeasureDefine & Measure

AnalyzeAnalyze

ImproveImprove

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Driving Customer & Shareholder BenefitsDriving Customer & Shareholder Benefits

PracticalSolution

Systematic Approach Focusing on Statistically Significant Root

Causes & Solutions

pp

ControlControl

3

What is Six Sigma?Process to reduce defects per million opportunities

• From current levels to “Six Sigma”

• “Sigma” is standard deviation from the ideal

• Can be applied to all business functions

2

3

308,537

66 807

B DPMO

• Can be applied to all business functions

» Manufacturing, Products, Transactions

» Service, Sales Support

Quantitative methodology

• Uses measurements and scientific process

3

4

56

66,807

6,210

233

3.4

3 to 620 000 times improvement

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... 20,000 times improvement ... ... A true quantum leap

Process = Hose

Four Important Properties:(1) Centering(2) Spread(3) Shape(3) Shape(4) Stability Over Time

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Y axis = Weight (lbs)

10.5 10 9.5

4

Every Human Activity Has Variability...

MeanUpper

C tLower

C t

Six Sigma Concept

1 p(defect)

Customer Specification

Customer Specification

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Reducing variability is the essence of six sigma

Target

1

Some Chance of

Failure

Mean

Th hi h th

Specification LimitWhat is Sigma? 

1

3

Much Less Chance of

Failure

The higher the number (Z) in front

of the sigma symbol the lower the chance

of producing a defect

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6

Reducing variation is the key to reducing defects

5

Reducing Variation is the Key

Starting Point After Project

Order by Order Delivery TimesWhat GE sees

28 29

Meanh

What Customers feel

13 17

2818

623

58

1619

296

1012

4101310

(Days)

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Big Change

VarianceNo Significant Change

30% improvement

193311

17

102013

13Average

Reference: Six Sigma Performance

Six Sigma99.99966% Good

• 20,000 lost articles of mail per hour

• Seven articles lost per hour

3.8 Sigma99% Good

• Unsafe drinking water for almost 15 minutes each day

• 5,000 incorrect surgical operations per week

• Two short or long landings at

• One unsafe minute every seven months

• 1.7 incorrect operations per week

• One short or long landing

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• Two short or long landings at most major airports each day

• 200,000 wrong drug prescriptions each year

• One short or long landing every five years

• 68 wrong prescriptions per year

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Key Terms: Process or Activity

OutputsProcess X’sor Factors

X1

XY1

For any given product, procedure or transaction, there are inputs, a process, and outputs. You will need to measure the outputs to quantify how well you satisfy a CTQ requirement; the output measures are Ys To

PROCESSX2

X3

X4

1

Y2

Y3

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Find and control the critical X’s

well you satisfy a CTQ requirement; the output measures are Ys. To change the process performance however, you must find and change the critical Xs.

Q

GM GlobalQuality

Master

The People

GreenbeltsApply Six Sigma toolsand methodology in

everyday work.

Quality Leaders

Help choose projects, interview Black Belt candidates, tie projects to business needs. Remove barriers and

Master Black Belts

Develop tools and teaching materials. Conduct training and communication sessions. Mentor Six Sigma

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Remove barriers and drive Six Sigma into the culture of their functions.

Black Belts and their projects.

Project leaders, change agents, expert application of tools, mentor Green Belts and their projects.

gBlack Belts

7

ObjectivesObjectives• DEFINE Phase Purpose

– Step A: Customer & Project CTQs

– Step B: Team Charter (4‐Blocker)

St C Th Hi h L l P M

DMAICStep A

– Step C: The High Level Process Map 

• Change Acceleration Process (CAP)

– E = Q x A

– The Model

– Key CAP tools: 

• ARMI

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ARMI

• GRPI

• Threat/Opportunity Matrix

• In/Out of the Frame

CTQ Definition and CTQ Elements

DMAICStep A

Cycle Time to Deliver Drawings

Product/Process

Characteristic

Customer & Project CTQsCustomer & Project CTQs

From Notice To Proceed To Delivery Time of Drawings

(Weeks)

On Time Delivery

Measure

Specification/Tolerance

Target13 Weeks

CustomerNeed

CTQ

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ToleranceLimit(s)

A performance standard translates customer needs intoA performance standard translates customer needs intoquantified requirements for our product or processquantified requirements for our product or process

15 Weeks

8

A Project Team CharterA Project Team Charter DMAICStep B

Business Case (Problem statement) Potential Issues/ Speed Inhibitors

Project Team

•Multilin has a small market share in Indonesia 

compared to the more established European relays 

manufacturer. Need to improve our service to 

customer and increase sales in Indonesia

• Data collection 

Milestones

Goal Statement

Name Org. Role % Ded.

Owner Date

Vince Tullo Manager         ChampionStuward Thompson Manager ChampionW.N. Yew          Sales                 Leader          70%Daniel Sutando Sales leader Member 10%W.Y. Tan Sr App Engr Member 10%Steven Tao    BB                  Member         5%

customer and increase sales in Indonesia.  

•To increase sales figures in Indonesia in 2004 to  

$1.8M.

• To ensure relevant projects are pursued and to 

improve the market coverage for distributors, EPCs, 

and end users.

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esto es

Scope Included:

Deliverables 

Date

Project Charter Approved         YWN /Tao        Apr 30

Measure /Baseline                      YWN/Tan          July 30

Analyze                                         WN/Tao Aug 30

Improve                                       YWN/Tao       Sept 30

Control                                          YWN/Tao   Oct 30

Close                                              YWN/Tao   Nov 30

•Multilin relays, Indonesia Market

Order growth for 2004

11 9 8 5 4 3

1

6 7 10 2 12

correct size

out of round

wire on pulley

damaged pulley

measurement accuracy

cold weld stand

change reel

wire speed# feet per spool

correct size

out of round

wire on pulley

damaged pulley

measurement accuracy

wire build on reel

proper die l b i ti

Input Legend

WIRE MILL PROJECT

Xs

DMAICStep C

14 15 16 17 18 19 20 21 22 23 13

1) Start of shift2) Change final capstan felt3) Check for excessive slivers/fines4) Check size5) Check surface quality6) Check stand supply

13) Wire size change14) Stop machine15) Replace dies (as required)16) Restring new setup17) Check wire size18) Attach wire to spool

correct size

out of round

accurate tension setting

lubrication

direction of lubricant flowpH level

fat level

pressuretemperature

A) DiameterB) Out-of-round

Legend

CTQ’s

critical

controllablenoise

Ys

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6) Check stand supply7) Is reel spooled 8) Connect wire to new reel9) Check size10) Check surface quality11) Check for acceptable spool build12) Store in enamel room

) p19) Set dancer air pressure20) Crack valve21) Check lubricant flow22) Start spooler23) Start capstan

)C) LoopsD) TanglesE) PinchoutsF) Surface quality

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Objectives• Introduction to Measure

- Measure Phase Deliverables

- Using Statistics to Solve Problems

• Measure Step 1: Select CTQs

- Quality Function Deployment (QFD) Process

DMAIC

- Quality Function Deployment (QFD) Process

- Process Mapping

- Failure Modes & Effect Analysis (FMEA)

- Pareto Chart

- Cause & Effect Diagram

• Measure Step 2: Define Performance Standards

- Performance Standard / Defect

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/

- Basic Nature of Data

• Measure Step 3: Measurement System

• Introduction to Measurement Systems Analysis (MSA)

The Statistical ProblemThe Statistical ProblemGoal: Find the Relationship

Y = f(X1, …, Xn) Process - BProcess - A

DMAIC

Shape of the Curves CHARACTERIZES the ProcessShape of the Curves CHARACTERIZES the Process

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ppProcess B is Better than Process A*Process B is Better than Process A*

* Assumes same scale

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Select CTQ CharacteristicsSelect CTQ Characteristics

Functional Requirements(HOW’s)

DMAICStep 1

Quality Function Deployment (QFD)Quality Function Deployment (QFD) Process Mapping (Flow Chart)Process Mapping (Flow Chart)

Map Customer Needs to Potential Hows

Cu

sto

mer

Req

uir

emen

ts

(WH

AT

’s)

Identify Critical Few Identify Critical Few -- Resource PlanningResource Planning Map “Information” FlowMap “Information” FlowIdentify All Touch PointsIdentify All Touch Points

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Select CTQ CharacteristicsSelect CTQ Characteristics DMAICStep 1

Anticipate Potential Failures in Process / Products & Develop Proactive Mitigation PlansAnticipate Potential Failures in Process / Products & Develop Proactive Mitigation Plans

Process Step

OR

Part Number

Potential Failure Mode

Potential Failure Effects

SEV

Potential Causes

OCC

Current Controls

DET

RPN

Action Recommended

Owner

Failure Modes & Effects Analysis (FMEA)Failure Modes & Effects Analysis (FMEA)

20% of causes account for 80% of the problem

Anticipate Potential Failures in Process / Products & Develop Proactive Mitigation PlansAnticipate Potential Failures in Process / Products & Develop Proactive Mitigation Plans

PE FLOWP FLOW

0

500000

1000000

0

20

40

60

80

100

Pe

rce

nt

Co

unt

Defects by Operation

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MA CH. SHA PE

FINA L STA GE FLO

COA THOL E 1

X-RA Y INSP

HOLE 2INSP

BENCHHOLE 3

FINAL W A TER FLO

276144130844127204102599101491 93353 82861 54110 49643 3670726 .2 12.4 12 .1 9 .7 9 .6 8.8 7 .9 5 .1 4.7 3.5

26 .2 38.6 50 .6 60 .4 70 .0 78.8 86 .7 91 .8 96.5 100.0

Defect

C ountP ercentC um %

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Performance Standards Objectives

• Determine the Performance Standard

• Define a Defect- What are the customer’s acceptance criteria for the part/product or process?

DMAICStep 2

• Established How to Measure the Quality of the Part / Product or Process

- Where are the data coming from?

- How do you measure the process?

- What are the units of measure?

- Is it a discrete or continuous measure?

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• Gained Consensus On the Performance Standard

• Are Requirement(s) or Specification(s)Requirement(s) or Specification(s) Imposed by the

Customer on a Specific CTQ

• Translate Customer Needs into Measurable Measurable

What’s Performance StandardsDMAICStep 2

CharacteristicCharacteristic– Have Clear Operational Definition, i.e. Specifies What to Measure, How to

Measure & Collect the Data

– Specifies Target or Mean

– Impose Specification Limits

– Have Clear Defect Definition

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CTQs Quantified CTQs Quantified –– Everybody on Same PageEverybody on Same Page

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More Performance Standards . . .DMAICStep 2

Good Product

Target

LSLLower Spec Limit

USLUpper Spec Limit

Tolerance

= USL - LSL

Defective ProductDefective Product

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Specification limitsSpecification limits are set in order to divide customer satisfaction from customer disappointment. While the exact limits may not be explicitly stated by the customer (and captured in Step 1), their specific values come from what the customer defines as a defect.

Lower Spec Limit Upper Spec Limit

The Basic Nature of Data•• Continuous DataContinuous Data

- Characterizes a product or process feature in terms of its size, weight, volts, time, or currency

- The measurement scale can be meaningfully divided into finer and finer increments of precision

DMAICStep 2

-- Distributions: Distributions: To apply the normal distribution, one must necessarily use continuous data

•• Discrete DataDiscrete Data- Counts the frequency of occurrence: e.g., the number of times something

happens or fails to happen - Is not capable of being meaningfully subdivided into more precise

increments The validity of inferences made from discrete data are highly dependent

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- The validity of inferences made from discrete data are highly dependent upon the number of observations. The sample size required to characterize a discrete product or process feature is much larger than that required when continuous data is used.

-- Distributions:Distributions: The Poisson and binomial models are used in connection with this type of data

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Making Data Driven Decisions• Six Sigma is all about reducing defects for the customer.  Fewer defect result in a more satisfied customer.

• The project team must decide what needs to be done to improve quality for the customer based on actual data – measurements of the product or process.

• The measurement system (gauge) used to collect the project data has to be

DMAICStep 3

• The measurement system (gauge) used to collect the project data has to be sufficiently good to allow the project team to make the correct decisions.

• A measurement system must deliver data that accurately represents the project or product. It is defective if it does not.

• The Six Sigma project team becomes the customer for the measurement process. There are many CTQs a project team must consider when evaluating the quality of a gauge…

If th i ’t d h f th d f th j tIf th i ’t d h f th d f th j t

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If the gauge isn’t good enough for the needs of the project, If the gauge isn’t good enough for the needs of the project, you have to fix it (using DMAIC) before you can move on!you have to fix it (using DMAIC) before you can move on!

In order to improve a product or process, we must measure it. We have submit the output from that process to a second measurement process.

ProcessInputs Outputs

Parts(Example)

DMAICStep 3

As a result, all of our observations of the original process are distorted by

The Measurement Process

MeasurementProcess

Outputs

• Observations• Measurements• Data

ocess

Inp

uts

p yerrors in our measurement system. We need to make sure these error don’t dominate our view of the process!

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14

DMAICStep 3

+ =

ProcessInputs Outputs Inputs MeasurementProcess

Outputs

Accuracy (Bias) ‐ Shift in the Average

True Avg Bias Obs. Avg

Actual(Part) + Meas. System = Observed(Total)

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Measurement System Bias Measurement System Bias ––Determined through “Calibration Study”Determined through “Calibration Study”

Product Variability Total Variability

DMAICStep 3

Measurement

Measurement System Precision

ProcessInputs Outputs Inputs MeasurementProcess

Outputs

Product Variability (part)

Total Variability (Observed total)

actual(part) +

meas. system = observed(total)

Measurement Variability

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Measurement System Variability Measurement System Variability ––Investigated through “R&R Study”Investigated through “R&R Study”

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Accuracy vs. PrecisionDMAICStep 3

xxxxxxxxxx

xxx xxxxxx

No

Accurate?

Precise?

Yes

Yes

No

No

Accurate?

Precise?

Yes

Yes

No

No

Accurate?

Precise?

Yes

Yes

No xx x

xxx

xx

x

x

x

xx

x

x

xx

x x

Measured Value

The True Value

No

Accurate?

Precise?

Yes

Yes

No

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xx

xx

Accuracy: the difference between the observed average and the truth.Precision: the amount of inconsistency between measurements.

Characteristics of a Measurement System

•• AccuracyAccuracy : Differences between observed average measurement and a standard.

•• ResolutionResolution : The smallest scale of the measurement.

•• StabilityStability : Do measurements change with time?

•• LinearityLinearity : Is the measurement proportional to the magnitude (size, 

DMAICStep 3

yy p p g ( ,weight, etc) of the sample.

•• PrecisionPrecision : Noise of the measurements.

– Repeatability: variation when one person repeatedly measures the same unit with the same measuring equipment.  Also called Equipment Variation (EV).

– Reproducibility: variation when two or more people measure the same unit with the same measuring equipment.  Also called Appraiser Variation (AV)

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Variation (AV).

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WHAT IS MINITAB?• Statistical software package• Has many of the tools needed to successfully analyze data with

rigor- Graphs- Statistical tools for data analysis- Six Sigma Reports

• Descriptive Statistics

• Gage R & R

• Capability Analysis (ZST/ZLT)

• Graphing - Many Types! (Try them all!)

• Pareto, Fish bone

• Hypothesis Testing

• Product & Process Six Sigma Reports

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• Generation of Test Plans for Designed Experiments

• Analysis of DOE results

• Statistical Process Control

A Great Toolbox for Six Sigma Projects!A Great Toolbox for Six Sigma Projects!

What does Minitab Look Like?What does Minitab Look Like?Menu Bars: For quick access to common commands.

Session Window:Shows Minitab text output (One only is present)

Worksheet Window: Kind of like an Excel worksheet (at least one is always present). A tool is available to

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tool is available to manage multiple worksheets.

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ObjectivesObjectives

• Calculate baseline capability of the process using either continuous or discrete data

• Statistically define the improvement goals

DMAIC

y p g

• Generated a list of Statistically Significant Xs based on analysis of historical data

• Identified which Xs to further investigate in the Improve phase

• Gained consensus with the project team on the list of Xs for

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Gained consensus with the project team on the list of Xs for investigation

Step 4: Establish Process CapabilityStep 4: Establish Process Capability

USLUSL

Y = f (X 1 . . . X )n

DMAICStep 4

The variation inherent to any dependent variable (Y) is determined bythe variations inherent to each of the independent variables. (X)

Very Low Probability of

Defects

Very Low Probability of

Defects

ExcellentProcess Capability

Very High Probability of

Defects

Very High Probability of

Defects

PoorProcess Capability

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Low Z High Z

LSL USLLSL USL

Z is a Measure of Process CapabilityZ is a Measure of Process Capability

18

p(x) BenchmarkEntitlement

Baseline

Step 5: Define Performance ObjectiveStep 5: Define Performance Objective

Benchmark: World-Class performance

Entitlement: The level of performance a business should be able to achieve given the investments already made

Defects

Baseline: The current level of performance

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Benchmarking Sets the Ultimate Goal, while Baselining Benchmarking Sets the Ultimate Goal, while Baselining

Takes Current Measurements to Monitor a ProcessTakes Current Measurements to Monitor a Process

Step 6: Identify Sources of VariationStep 6: Identify Sources of Variation

To get results, should we focus our behavior on the Y or X ?

Y= f (X)

DMAICStep 6

n Y

n Dependent

n Output

n Effect

n Symptom

n X1 . . . Xn

n Independent

n Input-Process

n Cause

n Problem

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Historically the Y, … with Six Sigma the XsHistorically the Y, … with Six Sigma the Xs

n Monitor n Control

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1.1. Identify Requirements on the Customer or Internal YIdentify Requirements on the Customer or Internal Y

These are often expressed quantitatively as target values plusspecification limits. - Anything “outside of the specification limits” is a defect.

Determining Process Capability (Steps 1 Determining Process Capability (Steps 1 –– 4)4)

Target ValueUSLLSL

Process CapabilityProcess Capability DMAICStep 4

2.2. Determine Process DistributionDetermine Process DistributionWe expect variation in our process.The Y’s measured on a large number

110Defects

gUSL (upper specification limit)(lower specification limit) LSL

Tolerance

10090Defects

Mean = 102 = 5.0

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The Y s measured on a large numberof parts will form a distribution. Forsimplicity, we’ll assume that they forma normal distribution with a knownmean and standard deviation.

85 90 95 100 105 110 115

3.3. Superimpose your process distribution on to the targetSuperimpose your process distribution on to the targetand specification limits.and specification limits.

USLLSL

Target Mean = 102 = 5.0

Process CapabilityProcess Capability DMAICStep 4

4.4. Apply some Basic Statistics.Apply some Basic Statistics.1. We can relate our distribution to the standardized normal distribution.

• The total area under the standard curve = 1 (or 100%)2 If d i h Z l di ifi i li i

85 90 95 100 105 110 115

USLLSL

Probability of a Defect

Probability of a Defect

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2. If we can determine the Z-value corresponding to a specification limit,then we can calculate the area beyond that limit (out of specification)• The area beyond a given specification limit is the fraction of the

population that is defective wrt that limit.

20

Putting it all together (Steps 1 Putting it all together (Steps 1 –– 4)4)

Total Area Outside of Specification Limits = (0.055 + 0.008) = 0.063Total Area Outside of Specification Limits = (0.055 + 0.008) = 0.0636.3% of what we produce is defective6.3% of what we produce is defective

Process CapabilityProcess Capability DMAICStep 4

USLLSL

Target Mean = 102 = 5.0

0.055y Probabilit

1.65

102110

(USL)Z

0.008y Probabilit

2510290

4.(LSL)Z Notice also that ourNotice also that ourprocess is not centeredprocess is not centered

on the targeton the target

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85 90 95 100 105 110 115

Z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641

0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.42470.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.38590.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.34830.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.31210.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.27760.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.24510.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.21480.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.18670.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.16111 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379

SingleSingle--Tail Z Table (values from 0.00 to 3.99)Tail Z Table (values from 0.00 to 3.99)

z

1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.11701.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.09851.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.08231.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.06811.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.05591.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.04551.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.03671.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.02941.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.02332 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183

2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.01432.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.01102.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.00842.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.00642.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.00482.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.00362.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.00262.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.00192 9 0 0019 0 0018 0 0018 0 0017 0 0016 0 0016 0 0015 0 0015 0 0014 0 0014

Calculates the probability of a USL defect above the given value of z

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2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.00143 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010

3.1 9.68E-04 9.36E-04 9.04E-04 8.74E-04 8.45E-04 8.16E-04 7.89E-04 7.62E-04 7.36E-04 7.11E-043.2 6.87E-04 6.64E-04 6.41E-04 6.19E-04 5.98E-04 5.77E-04 5.57E-04 5.38E-04 5.19E-04 5.01E-043.3 4.83E-04 4.67E-04 4.50E-04 4.34E-04 4.19E-04 4.04E-04 3.90E-04 3.76E-04 3.62E-04 3.50E-043.4 3.37E-04 3.25E-04 3.13E-04 3.02E-04 2.91E-04 2.80E-04 2.70E-04 2.60E-04 2.51E-04 2.42E-043.5 2.33E-04 2.24E-04 2.16E-04 2.08E-04 2.00E-04 1.93E-04 1.85E-04 1.79E-04 1.72E-04 1.65E-043.6 1.59E-04 1.53E-04 1.47E-04 1.42E-04 1.36E-04 1.31E-04 1.26E-04 1.21E-04 1.17E-04 1.12E-043.7 1.08E-04 1.04E-04 9.96E-05 9.58E-05 9.20E-05 8.84E-05 8.50E-05 8.16E-05 7.84E-05 7.53E-053.8 7.24E-05 6.95E-05 6.67E-05 6.41E-05 6.15E-05 5.91E-05 5.67E-05 5.44E-05 5.22E-05 5.01E-053.9 4.81E-05 4.62E-05 4.43E-05 4.25E-05 4.08E-05 3.91E-05 3.75E-05 3.60E-05 3.45E-05 3.31E-05

21

Problem with SpreadDesiredCurrent

SituationAccurate but not Precise

Goal: Process on Target with Minimum SpreadGoal: Process on Target with Minimum Spread

DMAICStep 6

Identify Variation SourcesIdentify Variation Sources

Situation

LSL USLT

not Precise

DesiredCurrent

SituationPrecise but not

Accurate

Problem with Centering – Not on Target

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LSL USLT

Accurate

Is the Problem Centering, Spread, or Both?Is the Problem Centering, Spread, or Both?

One Sample Two Samples Multiple Samples

Study Stability(Run Chart)

Study Shape

Continuous Data Analysis Road MapContinuous Data Analysis Road Map DMAICStep 6

Study Shape(Histogram, Dot Plot, Normality)

Study Spread(Chi Square-Test)

Data paired?

Study Spread(F-test)

Study Centering(Paired t test)

Study Spread(Homogeneity of Variance)

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(F test)

Study Centering(2 sample t-test)

Study Centering(1 sample t-test)

(Paired t-test)

Study Centering(ANOVA)

22

Descriptive StatisticsDescriptive StatisticsStat > Basic Statistics > Display Descriptive Statistics

Provides summary reportof basic statistical

DMAICStep 6

p-value > .05 Cannot Reject H0

No evidence that data is non-normal

Basic Statistical Information

Dot Plot

Histogram

Minitab Output

of basic statisticalinformation

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Confidence Intervals

X and Y Data CorrelationX and Y Data Correlation

5

10

15

20

25

Y

Strong Positive Correlation

DMAICStep 6

00 5 10 15 20 25

X

10

15

20

25

Y

5

No Correlation

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5 10 15 20 25

X

0

5

0

23

Improve Phase ObjectivesImprove Phase Objectives• The benefits of Design of Experiments (DOE’s)

• Key concepts and terms associated with DOE’s

• Performing a simple full factorial and fractional DOE’s and interpreting the results

• Awareness of screening designs and higher level response surface designs

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What’s Improve Phase About. . .What’s Improve Phase About. . .• Develop an Improvement Strategy

• Determine which candidate x’s identified in the Analyze Phaseare truly “critical X’s”.

• If possible, determine a quantitative transfer function thatrelates your Y to these critical X’s

DMAIC

• Identify Improvement Actions• Determine optimal settings for the X’s• Show the impact of the changes on meeting

project or business objectives.

• Validate the Improvement• Demonstrate the validity of your identified improvement

actions via additional experiments or a pilot study

Y = f(x)

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• Develop a Plan to Implement the Change

It’s More than Just Designed ExperimentsIt’s More than Just Designed Experiments

24

Common “Improve” ToolsCommon “Improve” Tools

BasicBasic Process Map

Fishbone

Box Plot

IntermediateIntermediate DOE

Full Factorial

Fractional

AdvancedAdvancedDOEResponse Surface

Taguchi (Inner /

DMAIC

Box Plot

Time Order Plots

Hypothesis Tests

Linear Regression

Mistake Proofing

Fractional Factorial

Intro to Response Surface

Multivariate Regression

Taguchi (Inner / Outer Array)

Simulation Models

Problem SophisticationProblem Sophistication

Already Covered Covered in Improve Covered in DFSS Adv. Level III e.g. ProModel

LOWLOWLOWLOW

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Problem SophisticationProblem Sophistication

• Complexity

• Business Impact

• Risk

• Data AvailabilityMatch the Tool to the Match the Tool to the

ProblemProblem

LOWLOWLOWLOW

HIGHHIGHHIGHHIGH

Y = f (x1, x2, x3,……xn)

Response (Y)Response (Y) Factors (x’s)Factors (x’s)

DMAICSteps 7-8DOE DOE –– Design of ExperimentsDesign of Experiments

Response (Y)Response (Y)

• The measured outcome of an experiment

• The value observed for the CTQ being explored

Factors (x s)Factors (x s)

• The critical X’s which determine the response,Y

•• They can be categorical or They can be categorical or numericalnumerical

LevelsLevelsRangesRanges

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LevelsLevels

• In DOE’s we investigate the effect of each factor at more than one setting or value

RangesRanges

• The extreme values for each factor determines the range for that factor - the region of interest/investigation

25

Classical ApproachClassical ApproachOFAT OFAT -- One Factor at a TimeOne Factor at a Time

• Change one variable, X2,while holding all others

Benefits of DOEsBenefits of DOEs

90100

DMAICSteps 7-8

constant.

• Find a maximum

• Hold X2 at the“maximum effect” level andrepeat the process for the other variables.

60

7080

Factor X1

OFATOFAT

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OFATOFAT• Requires more experiments than a DOE• Becomes unmanageable as the number of factors increases• Can be very expensive and time consuming – and may not work very well

DOE ApproachDOE Approach

• Select factors and levels

• Select mathematical modeldesigned to obtain maximuminformation for the number

Benefits of Design of ExperimentsBenefits of Design of Experiments

90100

DMAICSteps 7-8

information for the numberof factors/levels selected.

• In your experiments changethe factor levels in a systematicmanner so that all coefficients inthe model can be uniquely computed.(Orthogonality)

• Solve the resulting set of simultaneous equations to obtain the coefficients

60

7080

90

Factor X1

00

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• Solve the resulting set of simultaneous equations to obtain the coefficients.

• Use statistical tests to determine if the coefficients are statistically significant, and if the resulting model (transfer function) is adequate.

• Use the results of your DOE to plan the next DOE (if needed).

26

DMAICSteps 7-8

Screening DesignsScreening Designs

The Team’s understanding atThe Team’s understanding atthe beginning of the projectthe beginning of the project What Mother Nature KnowsWhat Mother Nature Knows

The following 7 Factors The following 7 Factors may bemay be critical X'scritical X's Yield = 64.25Yield = 64.25

A. Temperature (160C A. Temperature (160C -- 180C)180C)B. Monomer Concentration (20% B. Monomer Concentration (20% -- 40%)40%)C. Catalyst Vendor (Sally C. Catalyst Vendor (Sally -- Ed)Ed)D. Stirring Speed ( 50 RPM D. Stirring Speed ( 50 RPM -- 100 RPM)100 RPM)E. Monomer Purity ( 90% E. Monomer Purity ( 90% -- 98%)98%)F. Pressure ( 100 PSI F. Pressure ( 100 PSI -- 500 PSI)500 PSI)G. Acetone/Methanol Ratio G. Acetone/Methanol Ratio -- ( 0.25 ( 0.25 -- 0.50)0.50)

++11.50*A11.50*A

--2.50*B2.50*B

++0.75*C0.75*C

++5.00*A*C 5.00*A*C

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We need an efficient method for screening these"candidate critical X's"

so that we can identify the 'Vital Few"

ObjectivesObjectives

• In the physical world, the law of Entropy explains the gradual loss of order in a system.  The same law applies to business processes. 

• Unless we add “energy” (in the form of documentation and ongoing process controls), processes will tend to degrade over time, losing the 

DMAIC

gains achieved by design and improvement activities.

• The quality plan is the structure through which we add this “energy” to business processes.   This is Control and the main objectives:

– To make sure that our process stays in control after the solution has been implemented. 

– To quickly detect the out of control state and determine the associated special causes so that actions can be taken to correct the problem before

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special causes so that actions can be taken to correct the problem before nonconformance are produced.

27

DefineMeasureAnalyze

• Focus on the Right CTQ• Quantify the Problem• Determine the Drivers

Y = f(X)• Identify Needed Change

Control Control –– Keep It On TargetKeep It On Target DMAIC

• Validate Measurement System (Xs)• Determine Process Capability

AnalyzeImprove

Control

• Identify Needed Change• Implement the Change

• Develop/Modify Quality Plan> Process Documentation

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• Implement Process Controls• Audit Plan Established• Transition to Operating Owners

> Process Controls

On the Lookout for Special CauseOn the Lookout for Special Cause• Common cause variation

– Natural variability

– Random

– Inherent in the process

DMAIC

• Special cause variation– May be caused by operator errors, adjusted machines, or 

defective raw materials

– Generally large when compared to the common cause variation

– Considered an unacceptable level of process performance

• Special causes tend to cause a process to shift out of 

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control where. The output does not meet the desired specifications.

28

What is a Process Control System?What is a Process Control System?•• A Process Control System (PCS)A Process Control System (PCS)

– strategy for maintaining the improved process performance over time

– identifies the specific actions and tools required for sustaining the process improvements or gains 

•• A control system may incorporateA control system may incorporate

DMAIC

y y py y p

– Risk Management

– Mistake‐proofing devices 

– Statistical process control (SPC) 

– Data collection plans 

– Ongoing measurements 

– Audit plans 

– Response plans*

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Response plans

– Product drawings 

– Process documentation 

– Process ownership

Statistical Process ControlStatistical Process Control

StatisticalStatistical -- Probability based decision rules.

ProcessProcess -- Any repetitive task or steps.

ControlControl -- Monitoring of process performance.

DMAICStep 12

SPC will signal when the process is “out-of- control”.

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Your Mission is to find out why and take Your Mission is to find out why and take corrective action!corrective action!

29

Control Chart ComponentsControl Chart Components

0.065

0.060

Average ChartAverage Chartst

ic (

me

an

/de

fect

s)

me

asu

red Upper Control Limit

Lower Control Limit

Grand AverageCentral Line

DMAICStep 12

2520151050

0.055

0.010

0 005

Variation ChartVariation ChartMonitors ShiftMonitors Shift

Sample / Subgroup (time ordered)

Sta

tis Lower Control Limit

Upper Control Limit

e/S

igm

a)

red

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0.005

0.000

Monitors DriftMonitors Drift

Average Range/SigmaCentral Line

Lower Control Limit

Sample / Subgroup (time ordered)Sta

tistic

(R

an

gem

ea

sur

Significance of 3s limitSignificance of 3s limitA Control Chart is a graphic display of a

continuing two tailed test with HO and HAdefined as:

Ho: iHa: i

/2

DMAICStep 12

LCLx

UCLx

/2

/2

X

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• For 3 limits, = 0.00135. approximate confidence level is 99.7%.• 3 limits provide good sensitivity to change with low potential for over-

reacting when the process is stable.

30

Types of Control ChartTypes of Control ChartVariable Chart (Continuous)

• Uses Measured Values

–Cycle Time, Lengths, Diameters, Drops, etc.

• Generally One Characteristic Per

Attribute Chart (Discrete)• Defects: Number of non

conformance in a part• Defective: Pass/Fail,

Good/Bad, Go/No-Go Information

DMAICStep 12

yChart

• More Expensive, But More Information

Information • Can Be Many Characteristics

Per Chart• Less Expensive, But Less

Information

High or Low Volume?

L High

ConstantLot / Unit Size

VariableLot / Unit Size

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Individuals &MovingRange

Low High

X-Bar &Range

cDefects Poisson

BinomialDefective

u

np p

THANK YOU

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