six sigma 3 - analyze - optimized

7/27/2019 Six Sigma 3 - Analyze - Optimized

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industrial engineering ui - where the science of engineering and management blends 1TEKNIK INDUSTRIUNIVERSITAS INDONESIA

D M A I C

Analysis

Deliverables of the Analyze Phase:

1) Establish the capability of the current process (baseline)How good are we today at meeting customer CTQs?

What is the probability of making a defect for each CTQ? What sigma level does this translate into?

2) Define the performance objectives for measurable Ys (benchmark)

How good do we want to be at meeting customer CTQs?

3) Identify sources of variation

Based on analysis of historical (sample) data, which Xs might be affecting

the product (or process) quality?

AnalyzeAnalyze -- OverviewOverview


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D M A I C

Analysis

Analyze

Six Sigma RoadMap


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D M A I C

Analysis Tools of the Analyze Phase:AnalyzeAnalyze -- OverviewOverview

Basic graphical tools (run chart, histogram, pareto chart, boxplot,

scatter plot)

Fishbone diagram (cause-and-effect diagram)

Correlation & regression analysis

Capability indices

Confidence intervals

Process mapping (in more detail) value analysis

Variance component analysis


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D M A I C

Analysis Analyze - Baseline

1) Establish the capability of the current process (baseline)- What is the probability of making a defect for each CTQ?

If Y is a continuous r.v.,

P(defect) = P(Y>USL) + P(Yz) = P(defect)


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D M A I C

AnalysisAnalyze - B

Example 1: Viscosity of Aircraft Primer Paint

Batch Paint Viscosity

1 33.75

2 33.05

3 34.00

4 33.815 33.46

6 34.02

7 33.68

8 33.27

9 33.4910 33.20

11 33.62

12 33.00

13 33.54

14 33.1215 33.84

Data taken from:

Montgomery, D., (2001),

Introduction to Statistical Quality Control.John Wiley &Sons

P-Value: 0.704

A-Squared: 0.247

Anderson-Darling Normality Test

N: 15

StDev: 0.335552

Average: 33.5233

34.033.533.0

.999

.99

.95

.80

.50

.20

.05

.01

.001

Probabilit

y

Paint Viscosity

Normal Probability Plot

34.033.933.833.733.633.533.433.333.233.133.0

3

2

1

0

Paint Viscosity

Frequency

Histogram


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D M A I C


Minitab output:

Descriptive Statistics: Paint Viscosity

Variable N Mean Median TrMean StDev SE Mean

Paint Visc 15 33.523 33.540 33.525 0.336 0.087

Variable Minimum Maximum Q1 Q3

Paint Visc 33.000 34.020 33.200 33.810

Minitab input: Stat > Basic Statistics > Display Descriptive Statistics

Example 1 (contd)


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D M A I C

AnalysisAnalyze - B

Example 1 (contd)

LSL = 33.00, USL = 34.00

P(defect) = P(Y 34.00)

= P(Y


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D M A I C

AnalysisAnalyze - B

Example 1 (contd)

Find z s.t. P(Z>z) = .1375

Z = 1.09

Calculating sigma level:

P(defect) = .1375 137,500 DPMO

If the sample data only represents short-term variation in the process,

then this is the short term z. If long term variation is represented,

then the short term z = 1.09 + 1.50 = 2.59 (assuming a 1.5 shift).


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D M A I C

AnalysisAnalyze - Baseline

Other capability indices

stp

LSLUSL

C 6

=

st

pu

USLC

3

=

st

pl

LSLC

3

=

Based on short term variability: Based on long term variability:

ltp

LSLUSLP

6

=

lt

pu

USLP

3

=

),min( plpupk CCC = ),min( plpupk PPP =

lt

pl

LSLP

3

=

D M A I C


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D M A I C


Minitab input

Example 1 (contd)

D M A I C


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D M A I C

AnalysisAnalyze - B

34.534.033.533.032.5

USLLSL

Process Capability Analysis for Paint Viscos

PPM Total

PPM > USL

PPM < LSL

PPM Total

PPM > USL

PPM < LSL

PPM Total

PPM > USL

PPM < LSL

Ppk

PPL

PPU

Pp

Cpm

Cpk

CPL

CPU

Cp

StDev (Overall)

StDev (Within)

Sample N

Mean

LSL

Target

USL

144200.53

81444.07

62756.47

241398.67

131676.29

109722.38

66666.67

66666.67

0.00

0.47

0.51

0.47

0.49

*

0.37

0.41

0.37

0.39

0.341593

0.426165

15

33.5233

33.0000

*

34.0000

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability

Potential (Within) Capability

Process Data

Within

Overall

Minitab output:

Example 1 (contd)

D M A I C


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D M A I C

AnalysisAnalyze - B

Example 2 : Cycle time for Insurance Underwriting

CT = Date of UW decision Date that application data is submitted

USL (goal) = 14 days

100500

50

40

30

20

10

0

Submit to Approval CT

Freque

ncy

Histogram(Graph > Histogram > X=CT)

P-Value: 0.000A-Squared: 8.943


N: 353StDev: 21.3234

Average: 28.9717

9080706050403020100

.999.99

.95

.80

.50

.20

.05

.01

.001

Probability

Submit to Ap


(Stat > Basic Statistics > Normality Test)

D M A I C


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D M A I C

Analysis

100

90

80

70

60

50

40

30

20

10

0

6/25/20026/18/20026/10/2002

SubmittoApprovalCT

Date/Time

Analyze - B

Graphical analysis

of the data over time:

6/28

/200

2

6/27

/200

2

6/26

/200

2

6/25

/200

2

6/24

/200

2

6/22

/200

2

6/21

/200

2

6/20

/200

2

6/19/200

2

6/18/200

2

6/17/200

2

6/14/200

2

6/13/200

2

6/12/200

2

6/11/200

2

6/10/200

2

6/7/20

02

6/6/20

02

6/5/20

02

6/4/20

02

6/3/20

02

6/1/20

02

100

90

80

70

60

50

40

30

20

10

0

SUBMIT_DATE

Submitto

ApprovalCT

Run Chart

(Graph > Time series plot > Y=CT, Date/time stamp = submit date)

Dont use Time series plot if withinsubgroup order isnt known

(as in this case). Without a timestamp,

Minitab assumes the sample order

within each date is the same as theorder of the data set.

Boxplot of subgroups

(Graph > Boxplot > Y=CT, X=date)

Example 2 (contd)

D M A I C


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D M A I C

AnalysisAnalyze - B

Since CT is not normally distributed, we need to either transform

CT to normalize it, or find the appropriate probability distribution.

Box-Cox Power Transformation:Minitab input: Stat > Control Charts > Box-Cox Transformation

Example 1 (contd)

D M A I C


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D M A I C

AnalysisAnalyze - B

Minitab output:

3.02.52.01.51.00.50.0-0.5-1.0

70

60

50

40

30

20

95% Confidence Interval

StDev

Lambda

Last Iteration Info

17.858

17.873

17.932

0.282

0.225

0.169

StDevLambda

Up

Est

Low

Box-Cox Plot for CT

Example 1 (contd)

D M A I C l


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D M A I C

AnalysisAnalyze - B

Comparing the recommended transformation with the more common ln transform :

P-Value: 0.000

A-Squared: 2.041


N: 353

StDev: 0.456757

Average: 2.18922

321

.999

.99

.95

.80

.50

.20

.05

.01

.001

Probability

BoxCox CT (power of .25)


P-Value: 0.000

A-Squared: 3.231


N: 353

StDev: 0.877256

Average: 3.04177

43210

.999

.99

.95

.80

.50

.20

.05

.01

.001

Probability

LN CT


Example 1 (contd)

D M A I C A l B


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D M A I C

AnalysisAnalyze - B

Another approach find anappropriate distribution

In this case, we will

be better off with

the transformation

Example 1 (contd)

D M A I C A l B


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D M A I C

AnalysisAnalyze - B

Capability analysis for CT - Minitab input

Example 1 (contd)

Chooseoptions

D M A I C A l B


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D M A I C

AnalysisAnalyze - B

Example 1 (contd)

Capability analysis for CT - Minitab input (contd)

D M A I C Analyze B


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D M A I C

AnalysisAnalyze - B

Example 1 (contd)

Capability analysis for CT - Minitab output

3.02.52.01.51.0

USL*USL*

Process Capability Analysis for Submit to Ap

Box-Cox Transformation, With Lambda = 0.225

PPM Total

PPM > USL*

PPM < LSL*

PPM Total

PPM > USL*

PPM < LSL*

PPM Total

PPM > USL

PPM < LSL

Ppk

PPL

PPU

Pp

Cpm

Cpk

CPLCPU

Cp

StDev* (Overall)

StDev (Overall)StDev* (Within)

StDev (Within)

Sample NMean*

Mean

LSL*

LSL

Target*

Target

USL*

USL

708442.33

708442.33

*

708792.10

708792.10

*

657223.80

657223.80

*

-0.18

*

-0.18

*

*

-0.18

*-0.18

*

0.3814

21.33850.3807

21.1650

3532.0202

28.9717

*

*

*

*

1.8108

14.0000

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability

Potential (Within) Capability

Process Data

Within

Overall

D M A I C Analyze B


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AnalysisAnalyze - B

Example 1 (contd)

Capability analysis for CT - usingMinitab descriptive statistics todo a manual Z calculation:

Descriptive Statistics: BoxCox CT (power of .225)

Variable N Mean Median TrMean StDev SE Mean

BoxCox CT 353 2.0202 2.0248 2.0237 0.3812 0.0203

Variable Minimum Maximum Q1 Q3

BoxCox CT 1.0000 2.7727 1.7152 2.3248

P(defect) = P(CT.225 > 14.225)

= P( Z > (14.225 2.02)/.3812) )

= P(Z >-.2247) = .5899 589,900 DPMO

D M A I CAnalyzeAnalyze OverviewOverview


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Analysis

Deliverables of the Analyze Phase:

1) Establish the capability of the current process (baseline)How good are we today at meeting customer CTQs?

What is the probability of making a defect for each CTQ? What sigma level does this translate into?







D M A I CAnalyzeAnalyze - OverviewOverview


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Analysis

Generated a list of Statistically Significant Xs based on analysis

of historical data.

Process:1. Brainstorm Xs

2. Use historical data analysis to prioritize which Xs should

be investigated further in the Improve phase

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

investigation

Identified value added & non-value added process steps

(this is especially important if your CTQ is a function of process

cycle time)

By the end of Analyze, you will have:


D M A I CFishbone DiagramFishbone Diagram


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AnalysisFishbone DiagramFishbone Diagram

Begin by brainstorming a list of Xs which may affect the mean and/or

variance of the project CTQ(s). A useful tool for this is the Cause & EffectDiagram (Fishbone Diagram).

Purpose: To provide a visual display

of all possible causes of a specific

problem

When:

To expand your thinking toconsider all possible causes

To gain groups input

To determine if you have correctly

identified the true problem

CauseCause

EffectEffect

Categories

Causes

Problem

Statement

D M A I C

Fishbone DiagramFishbone Diagram


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Analysis

Problem

Statement

Measurements Materials Men & Women

MethodsEnvironment Machines

Draw a blank diagram on a flip chart.

Define your problem statement.

Label branches with categories appropriate to your problem.

Categories can also be Policies, Procedures, People, and Plant

or any other category that will help people think creatively.

The 4 Ps


D M A I CFishbone DiagramFishbone Diagram


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Analysis

Brainstorm possible causes and attach them to appropriate categories.

For each cause ask, Why does this happen?

Problem

Statement

Measurements Materials Men & Women

MethodsEnvironment Machines

CauseWhy

Analyze results, any causes repeat? As a team, determine the three to five most likely causes.

Determine which likely causes you will need to verify with data.


D M A I C

A lFishbone DiagramFishbone Diagram


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Analysis

Stamp

paperCut Fold

Variation

of CTQApply tail clip

Process Fishbone Example (Helicopter Example)

Fishbone Diagramb ag a

Package

D M A I C

A l iTools for prioritizing XTools for prioritizing Xss


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Analysisp gp g

Once the team has a list of potential Xs, use historical dataanalysis to prioritize their importance.

Simple statistical tools/analytical methods will be very usefulhere, for example:

Pareto charts

Other graphical tools, such as side-by-side boxplots,scatterplots, etc.

ANOVA, variance component analysis

Correlation matrix

D M A I C

A l i


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Analysis

Pareto Chart

Purpose: To separate the vital few from the trivial many in a process. Tocompare how frequently different causes occur or how much each cause costs

your organization.

When: To sort data for determining where to focus improvement efforts.

To choose which causes to eliminate first

To display information objectively to others

Pareto Principle:

20% of causes

account for 80% of

the effect

Pareto Principle:

20% of causes

account for 80% of

the effect

D M A I C

A l iValueValue--Add AnalysisAdd Analysis


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Analysisy

Steps That Are

EssentialBecause They

Physically

Change The

Product/Service,

The Customer IsWilling To Pay For

Them And Are

Done Right The

First Time.

Steps That Are

EssentialBecause They

Physically

Change The

Product/Service,

The Customer IsWilling To Pay For

Them And Are

Done Right The

First Time.

Steps That Are

Considered Non-Essential To

Produce and

Deliver The

Product Or

ServiceTo Meet The

Customers Needs

And

Requirements.

Customer Is Not

Willing To Pay For

Step.

Steps That Are

Considered Non-Essential To

Produce and

Deliver The

Product Or

ServiceTo Meet The

Customers Needs

And

Requirements.

Customer Is Not

Willing To Pay For

Step.

Value-Enabling Work

Steps That Are

Not Essential To

The Customer,

But That Allow

the Value-

Adding Tasks

To Be DoneBetter/Faster.

Steps That Are

Not Essential To

The Customer,But That Al low

the Value-

Adding Tasks

To Be DoneBetter/Faster.

Value-

AddedWork

Non

Value-

Added

Work

D M A I C

Analysis

ValueValue--Add AnalysisAdd Analysis


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Analysis

Types Of Nonvalue-added Work

Internal Failure Delay

External Failure Preparation/Set-Up

Control/Inspection Move

What Does the Customer Value?What Does the Customer Value?

D M A I C

AnalysisValueValue--Add AnalysisAdd Analysis


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Analysis

Cycle TimeCycle Time

Process TimeProcess Time

Delay TimeDelay Time+

D M A I C

AnalysisValueValue--Add AnalysisAdd Analysis


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Analysis

Gaps

Redundancies

Implicit or unclear requirements

Tricky hand-offs

Conflicting objectives

Common problem areas

Process Disconnects (will increase process cycle time):

D M A I C

AnalysisProcess Flow AnalysisProcess Flow Analysis


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Analysis

5. Retrieve

application

and review for

completeness

10. Review

for

completenes

s and make

decision

1. Receive

applicationin mail and

open

envelope

2. Place

application

in mail slot

3. Move

application

to Entry

Dept.

4. Place

application

in

in-box

Isapplication

complete?

7. Enter

application

to computer

system

6. Call to

obtainnecessary

information

8. Score

application

9. Queue

application

for credit

review

Are weextending

loan?

19. Generate

turndownletter

12. Generate

loan packet

13. Place in

out-box

14. Move to

mail room

15. Wait forpostage

16. Postpackage or

letter

17. Place in

outbound

mail basket

18. Post

man picks

up outbound

mail

No

Yes

Yes

No

UnclearUnclearrequirementsrequirements

TrickyTrickyhandhand--offoff

RedundancyRedundancy

UnclearUnclearrequirementsrequirements

TrickyTrickyHandHand--offoff

11. Makeloan

decision

xample loan evaluation process

D M A I C

Analysis


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Analysis

Cake Example Analyze phase

1) Establish the capability of the current process (baseline)






D M A I C

Analysis


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Analysis

Cake % Flour % Sugar % Water % Oil Oven Temp Mixing Time Bake Time Mix Spd Num Eggs FPS height (mm)

1 47.0 20.0 5.0 27.0 373 5 54 low 2 0.40 42.0464

2 47.0 27.0 5.0 20.0 381 3 50 low 2 0.26 44.6038

3 47.0 20.0 5.0 27.0 377 3 52 med 3 0.33 59.1240

4 40.0 27.0 5.0 27.0 383 5 51 high 3 0.42 38.0634

5 40.0 20.0 19.0 20.0 368 4 50 med 3 0.30 35.7231

6 54.0 20.0 5.0 20.0 373 5 49 low 2 0.30 43.0212

7 47.0 27.0 5.0 20.0 361 3 50 high 2 0.37 46.5552

8 40.0 20.0 5.0 34.0 368 5 54 low 2 0.45 11.9006

9 47.0 20.0 5.0 27.0 382 5 50 med 3 0.37 45.6810

110

10 cakes sampled randomly per day for 11 days, measurements made

CTQ

Height LSL = 40

D M A I C

Analysis


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Analysis

Height appears normally distributed.

Sample avg = 43.54, s = 11.7

85756555453525155

99

9590

80706050403020

105

1

Data

Percent 0.453AD*

Goodness of Fit

Normal Probability Plot for height (mm)ML Estimates - 95% CI

Mean

StDev

43.5393

11.6997

ML Estimates

D M A I C

Analysis


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y

Calculating short term capability for Height:

P(height


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y

706050403020100

20

10

0

height (mm)

Frequency

LSL

Need to increase

the mean heightand also possibly

reduce variability

D M A I C

Analysis


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y

1) Establish the capability of the current process (baseline)






D M A I C

Analysis

Fishbone


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Measurements Machines Man/Mother Nature

Material:

Quality

Methods:

Formulation

Methods:

Processing

height

bulk density

viscosity

particle size

sugar

baking powder

salt

eggs

flour

oil

%flour

%sugar

%baking powder

%salt

#eggs

%oil

%water

dry mix time

dry mix speed

wet mix time

wet mix speed

Dry mix vessel

Dry mix blade

Wet Mix Blender

Oven Rack

humidity

Baking time

Baking temp

elevation

Mean

Heighttoo low

D M A I C

Analysis


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Next step: figure out which variables on fishbone are controllable and whichones are uncontrollable

Uncontrollable variables are the noise variables

Controllable variables can either be varied in the experiment or held constant

We need to categorize the xs on the fishbone as follows: (Schmidt andLaunsby, 1994)

control xs (label as a X) noise xs (label as a N)

constant xs (label as a C)

D M A I C

Analysis

Use impact scores from QFD to help decide if a x should be labeled X or C


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Measurements Machines Man/Mother Nature

Material:

Quality

Methods:

Formulation

Methods:Processing

height

bulk density

viscosity

particle size

sugar

baking powder

salt

eggs

flour

oil

%flour

%sugar

%baking powder

%salt

#eggs

%oil

%water

dry mix time

dry mix speed

wet mix time

wet mix speed

dry mix vessel

dry mix blade

wet mix blender

oven rack

humidity

baking time

baking temp

N

N

N

NN

N

N

N

N

N

N

C

C

C

C

C

CC

C

X

XX

X

X

XXX

X

elevation N

Mean

Height

too low

six sigma 3 - analyze - optimized

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