Lean Six Sigma Small Examples

37
Questions and Answers How Relevant Questions Obtain Useful Answers March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 1 Judson B. Estes Fiat Chrysler Automobiles

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Lean Six Sigma

Transcript of Lean Six Sigma Small Examples

Questions and Answers

How Relevant Questions

Obtain

Useful Answers

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 1

Judson B. EstesFiat Chrysler Automobiles

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 2

Weave the wisdom from many available tool sets into a package of training, certification and project work1. Collect

Currently available facts relevant to problem. Listen for what is already known and suspected. Communicate to entire team the current facts to get on the same page.

2. ContrastA Measurable difference in performance.How do you measure the performance?How Big is the difference?

3. ConvergeUse Logical Strategies to isolate the candidate cause.What split are you making?How does that narrow the possible causes?

4. ConfirmTest the candidate cause to prove it is the true root cause.What is your Statistical Confidence?When can we implement the fix?

Focus on the 4 C’s

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 3

Collect Phase

• Describe Problem

• Identify Possible Causes

• Evaluate Possible Measurements

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Collect Phase

Describe the Problem• State the Problem naming the deviation for

which you want to find the cause

• To help stay on track, ask:– What object (or group of objects) has the deviation?

– What deviation does it have?

– What do we see, feel, hear, taste, or smell that tells us there is a deviation?

– Write a short statement in Object/Deviation format• Use one object and one deviation

• Be specific, separate if needed

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Collect Phase

Specify the Problem• Describe the deviation

factually to increase understanding of the deviation

• Ask questions in 4 areas:– WHAT—Identity

– WHERE—Location

– WHEN—Timing

– EXTENT—Size

IS IS NOTDescribe the problem in

detail.

Tighten IS data. Help eliminate

possible causes.

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Other potential lab conclusions could have been but were not "cold shock", "high voltage" & "wear out"

LOP 085032 Needs replacement Some examined from Field, Hot shock is the main conclusion from the Sylvania lab report

2. Defect

Magnums and 300C's. Also WK, PT use same Pt # low beam bulb, All other bulbs in the Click here to see ID of vehicle, subassemblies, bulb and field warranty performance.

low beam bulb # L0009006 used in LX 300 models LXCH48, LXCP48, LXFP48 . Click here to see VIN list

1. ObjectWHAT:

(IS NOT observed/reported)(IS observed / reported)factsNON-PROBLEM AREAPROBLEM ARPEADescription

LX low beam bulb infant failure Problem Statement:

[1] PROBLEM AREA

PROBLEM SOLVING

Collect Phase Example

“I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;”

-Lord KelvinMarch 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 7

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Contrast Phase

0 1 4Length (mm)

CurrentRequired

Freq

uenc

y

0-3 3Flushness (mm)

Current

Required

Freq

uenc

y

-1.5 1.5

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Contrast Phase

Cloth seats

Seat back

Seam A

BOB/WOW seamWOW cushion

Otherstrategies

Seam B

Seat cushion

Driver side Passenger side

Front seat Rear seat

Leather seats

Open seams on DRseats resulting in high

warranty costs

0 1 4Width (mm)

CurrentRequired

Freq

uenc

y

Problem Definition Statement

90% of returns are leather

83% of returns are front seats

71% of returns are driver side seats

92% of returns and narratives are seat cushions

Examination of returned product showsseam B accounts for 42 out of 54 claims

See Strategy Diagram

Find and eliminate the Red Xcausing open seams on the DRfront driver side leather seats

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Contrast Phase

• What is a BOB and a WOW?– Best of the Best and Worst of the Worst

– Not necessarily a good and bad part but really parts that are as different as possible in the way they effect the Customer.

– We are looking for contrast in order to see differences

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Measure twice and get the same answer

on BOB and WOW

Contrast Phase example

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Converge Phase

• Once we make sure our measurement system isn’t fooling us then we start generating clues

• We then use certain tools to begin to converge on the Red X candidate– Concentration diagram

– Component search Stage 1 and 2

– Operation Search

– Paired and Group comparisons

– Event to Energy transform

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5 Whys to the Root Cause

Ishikawa Fishbone Diagram

IS/ IS Not Problem Specifications

Shainin Red X Strategies

Classical and Taguchi

Design of Experiments

Six Sigma

Pure Statistics

TRIZ and Systemology

Reactive Problem Solving Hierarchy

Innovation and Evolution

No Strategy and All Tools

Simple Strategy and Most Tools

Multiple Variables and Interactions

Multiple Strategies, Easy Statistics

Distinctions and Changes

Organized Brainstorming

Simple Questioning

Use the Right Tool for the Problem

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5 Whys to the Root Cause

Ishikawa Fishbone Diagrams

Critical Thinking

Shainin

Classical and Taguchi

Design of Experiments

Six Sigma

Pure Statistics

TRIZ and Systemology

Problem Solving Hierarchy

Easiest to Grasp

Hardest to Grasp

Most Widely Used

Least Widely Used

More Variables and Interactions

Increased Variation and Environment

Changes

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1 2 3 4 5 6 7 8ABCDEF

x

xxxxxxxxxx

xx

xx xx

xxxxxxx

Concentration Diagram example

Paint Craters on “B” pillar

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Component Search Stage 2

• Plotting0

1020

30

Gre

en Y

= lb

s.

Orig. 1st D/R 2nd D/R 3rd D/R S1 orig

* * * *

+ + + +

WOW

BOB

.Stage 1

*

+

+

*

Stage 2

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Confirmation Phase

• Once we identify the Red X candidate it is now time to use statistics to confirm our candidate.

• Some tools types that are used for this:– Six Pack B vs. C

– Tukey test

– Barrier B vs. C

– Spike B vs. C

– 5 Penny test

– Factorial Experiment (DOE)

– Binomial probability

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Six Pack B vs. C

• B

B is the “Better” part or process or sub-assembly or material

• C

C is the “Current” part or process or sub-assembly or material

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Six Pack B vs. C Example 1

The required confidence level is 95%, which therefore requires a sample size of 3 B’s and 3 C’s and an end count of 6.

Run Order B or C Diameter (mm)

1 C 10.6

2 B 8.3

3 C 11.2

4 C 9.8

5 B 9.1

6 B 8.8

B 8.3

B 8.8

B 9.1

C 9.8

C 10.6

C 11.2

Rank Order

The end count equals 6. Therefore, it can be stated with 95% confidence that the B’s are better than the C’s.

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Six Pack B vs. C Test Example

• Distribution of two groups looks something like this.

8.0 8.5 9.0 9.5 10 10.5 11 11.5

B B B C C C

March 2014Confidential and Proprietary to Fiat Chrysler

Automobiles

Reliability by Design

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Reliability

Prediction of Performance

Verification of Performance

Improvement of Prediction

The best Prediction methods are quantative.

The best Verification is actual parts and systems in real usage.

The best Improvement eliminates all discrepancy between prediction and reality.

Deterministic Design

• Design parameters are deterministic, i.e., they have unique values

• CTQ’s are also deterministic, and are calculated as functions of the design variables by transfer functions, Y = f (X1, X2, …, XN)

DesignParameters

(X’s)CTQ’s (Y’s)

Y1...

YN

Transfer FunctionY = f (X1, X2, … XN)

Most engineering design is deterministic

X1

X2

.XN

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Statistical Design• Design parameters are statistical in nature, with mean values and variation

(e.g., standard deviation)

• CTQ variations determined by statistical analysis (e.g., Monte Carlo), using the transfer function and statistical variations in design parameters

DesignParameters

(X’s)X1

X2

.XN

Noise Parameters XN1 . . XNn

CTQ’s (Y’s)

Y1...

YN

Transfer FunctionY = f (X1, X2, … XN)

DFSS uses statistical design to understand and control variationMarch 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 24

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Statistical DesignWhy Prototyping Doesn’t Reveal Problems

• Prototyping does not verify product robustness• It assesses functionality of a single, often hand-selected, sample

Reality: Multiple Product CopiesPrototyping: Single Product Copy

Range of possible inputs

USLLSLX1

X2Y=f(X1,X2...)

YXnInput

variabilitynot captured,

defects masked

Selectedprototype

inputs

USLLSL

Y

Realisticdistributionof product

Y (CTQ)

Defects

X1

X2

Xn

Y=f(X1,X2...)

Statistical DesignMechanical Example: Simply Supported Box Beam

P

L1

LT

WP

F

th

w

Performance Requirements:• Applied load: 200 kg/m over 1.5 m• Overhang = LT-L1 = 4.5 m• Design margin must be positive,

i.e., yield strength > max stress• 6 quality• Low cost

Performance Requirements:• Applied load: 200 kg/m over 1.5 m• Overhang = LT-L1 = 4.5 m• Design margin must be positive,

i.e., yield strength > max stress• 6 quality• Low cost

Analysis: Transfer functionMargin = Yield strength - Max stress

= Yield strength - (Max stress from tensile load + Max stress from bending)

F 3hPWp (2LT - 2L1 - Wp)Margin = Sy - ____________ - ____________________

2ht + 2wt - 4t2 wh3 - (w - 2t) (h - 2t)3

Baseline Design

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Statistical DesignDeterministic Design of Beam

F 3hPWp (2LT - 2L1 - Wp)Analysis: Margin = Sy - ____________ - ____________________ 2ht + 2wt - 4t2 wh3 - (w - 2t) (h - 2t)3

Choose values for design parameters and applied loads:

Substituting: Margin = + 9,726 kg/m2

Design Parameter/Load ValueBeam length, LT (m) 12Support length, L1 (m) 7.5Beam height, h (m) 0.75Beam width, w (m) 0.25Section thickness, t (m) 0.05Yield strength, Sy (kg/m2) 89,600Uniform load density, P (kg/m) 200Uniform load width, Wp (m) 1.5Tensile load, F (kg) 100

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Baseline design meets positive design margin requirement,but quality level unknown

Statistical DesignSimply Supported Box Beam

Design Parameter/Load Mean Std Dev TolerancesLower Upper

Beam length, LT (m) 12 0.017 0.05 0.05Support length, L1 (m) 7.5 0.013 0.04 0.04Beam height, h (m) 0.75 0.0033 0.01 0.01Beam width, w (m) 0.25 0.0033 0.01 0.01Section thickness, t (m) 0.05 0.0025 0 0.01Yield strength, Sy (kg/m2) 89,600 3,200 7,500 0Uniform load density, P (kg/m) 200 3.3 5 5Uniform load width, Wp (m) 1.5 0.07 0.2 0.2Tensile load, F (kg) 100 1.65 5 5

Design parameters & applied loads are statistical in nature • Choose mean values and a variability measure (e.g., std deviation) • Consider tolerances

F 3hPWp (2LT - 2L1 - Wp)Analysis: Margin = Sy - ____________ - ____________________ 2ht + 2wt - 4t2 wh3 - (w - 2t) (h - 2t)3

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Statistical DesignSimply Supported Box Beam

Design margin may be positive or negative!

Do a statistical analysis (e.g., Monte Carlo), using transfer function and statistical parameter & load values

Results:• Margin mean 9,726 kg/m2

• Margin std dev 5,466 kg/m2

• Defect probability 3.8% • Design 3.3

F 3hPWp (2LT - 2L1 - Wp)Analysis: Margin = Sy - ____________ - ____________________ 2ht + 2wt - 4t2 wh3 - (w - 2t) (h - 2t)3

.000

.010

.020

.030

.040

-5,000 10,000 20,000 30,0000

Prob

abili

ty

Design Margin (kg/m2)

Mean = 9,726

Defects

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Design optimization analysis:• Use transfer function to understand the shape of the response surface and the design margin’s sensitivity to each design parameter

• Reduce defects by shifting mean values or reducing variances of the most sensitive design parameters

• Sensitivities found by partial differentiation of transfer function and evaluation at design point

Statistical DesignReaching “6”

Design Parameter/Load Mean Std Dev Sensitivity

Beam length, LT (m) 12 0.017 - 21,003Support length, L1 (m) 7.5 0.013 21,003Beam height, h (m) 0.75 0.0033 180,205Beam width, w (m) 0.25 0.0033 181,676Section thickness, t (m) 0.05 0.0025 1,158,739Yield strength, Sy (kg/m2) 89600 3200 1Uniform load density, P (kg/m) 200 3.3 - 393.8Uniform load width, Wp (m) 1.5 0.07 - 42,007Tensile load, F (kg) 100 1.65 - 11.1

Margin most sensitive to t,

with w and h next

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Design margin results:Beam width, w 0.25 0.30 0.35

• Mean 9,726 17,879 24,518• Std deviation 5,466 5,124 4,853• Defect prob, % 3.8 0.024 0.00002• Design 3.3 5.0 6.5

Statistical DesignReaching “6”

Improving the design margin:• In general, design can be improved by shifting means of the most

sensitive parameters or reducing their variabilities• Although t is the most sensitive parameter, we elect to shift the mean of w

(next most sensitive) because box beams come in only a few standard thicknesses (the next thicker beam would be too costly and heavy)

.000

.010

.020

.030

.040

-5,000 10,000 20,000 30,0000

Prob

abili

ty

Design Margin (kg/m2)

w = 0.25

w = 0.30

w = 0.35

Defects

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Problem Solving or Problem Prevention

• Discussion and Questions ??

Statistical DesignElectronics Example: Switching Power Supply

Baseline Design• Isolated switching converter/ feedback section

• Baseline design combines power MOSFET & control circuit in a 3-pin package

Input Filter Isolated Switching Converter

Feedback

Vo = 5 Vdc, +/-5%Vin = 85 - 275 Vac

Performance Requirements• Output voltage, Vo: 5 V, +/-5% • Input voltage, Vin: 85 - 275 V• 6 quality• Low cost

R2

R1CTRL

Vo

PWM IC

OPTO

VrefIb

••

R1

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 33

Statistical DesignDeterministic Design of Power Supply

Baseline design meets 5V, +/- 5% performance requirement,but quality level unknown

Analysis: Transfer function

Choose values for design parameters:

Substituting: Output voltage = 5.04 volts

Design Parameter ValueLM 431I ref voltage, Vref (volts) 2.495 R1 (ohms) 10,000R2 (ohms) 10,000Bias current, Ib (amps) 5.0E-06

VrefVo = Vref + R2 ____ + Ib

R1

( )

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 34

Statistical DesignSwitching Power Supply

Design Parameter Mean Std Dev TolerancesLower

UpperLM 431I Vref (volts) 2.495 0.0283 0.085 0.085R1 (ohms) 10,000 33.33 1% 1%R2 (ohms) 10,000 33.33 1% 1%Bias current, Ib (amps) 5.0E-06 1.15E-06 2.00E-06 2.00E-06

Analysis: Transfer function(unchanged)

• Design parameters are statistical in nature. Choose mean values and a variabilitymeasure (e.g., std deviation):

Baseline design meets 5V, +/- 5% performance requirement, but quality level is not 6

• Do a statistical analysis(e.g., Monte Carlo), using the transfer function and the statistical parameter values

Results:• Vo mean 5.04 volts• Vo std dev 0.059 volts• Defects/million 188 (5.06)

Vref Vo = Vref + R2 ____ + Ib

R1

( )

4.75 4.875 5.00 5.125 5.25Volts

.000

.009

.017

.026

.035Pr

obab

ility

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Design optimization analysis:• Use transfer function to understand the shape of the response surface and the output voltage’s sensitivity to each design parameter

• Reduce defect rate by shifting mean values or reducing variances of design parameters

Statistical DesignReaching “6”

Design Parameter Mean Std Dev SensitivityLM 431I Vref (volts) 2.495 0.0283 2R1 (ohms) 10,000 33.33 -0.0002495R2 (ohms) 10,000 33.33 0.0002545Bias current, Ib (amps) 5.0E-06 1.15E-06 10,000

Design Mod 1: Center distribution by increasing R1 to 10,160 ohms

Results:• Vo mean 5.00 volts• Vo std dev 0.058 volts• Defects/million 20 (5.61)

4.75 4.875 5.00 5.125 5.25Volts

Prob

abili

tyBase Centered

.000

.009

.019

.028

.038

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Statistical Design Reaching “6” (cont’d)

Summary

Statistical design enables performance, quality & cost prediction during the design process

Design Mod 3: Mod 2 plus LM 431AI MOSFET to reduce Vref variance

Base 0.1% ResistorsMOSFET Upgrade

.000

.012

.025

.037

.050

4.75 4.875 5.00 5.125 5.25Volts

Prob

abili

ty

Design Mod 2: Mod 1 plus 0.1% resistors to reduce resistor variance

Centered 0.1% Resistors

.000

.009

.019

.028

.038

4.75 4.875 5.00 5.125 5.25Volts

Prob

abili

ty

Mean Std Dev DPMO ZST CostBaseline Design 5.04 0.059 189 5.06 100%

Mod 1: Centered via R1 5.00 0.058 20 5.61 100%Mod 2: 0.1% Resistors 5.00 0.057 13 5.7 101%Mod 3: LM 431AI 5.00 0.041 ~0 7.58 105%

March 2014 Confidential and Proprietary to Fiat Chrysler Automobiles 37