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KXGX 6101: Research Methodology

If we knew what we were doing, it wouldn't be calledresearch, would it? - Albert Einstein

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Science & Statistic

Objective of statistical methods to make the process as efficient as possible!

deduction inductiondeduction induction

deduction induction

data (facts/phenomenon)

Hypothesis (conjecture/model/theory)

Hypothesis H1

deduction

Consequence

of H1

induction

data

ModifiedHypothesis H2

I f the facts do n't f i t the theory, change the facts

Alber t Einste in

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Introduction to Design of Experiment (DoE)

What is it? - DoE is efficient way to quantitatively determine hownumerous input variables (Xi) affect the outcome (Y)

DoE can be best used if: Multiple variables affect outcome

Interactions of inputs exist

Want to sort out , using data, which variables are significant

Unsure of how variables are affecting the outcome

Want to verify what you think you know Want to quantify how a process works

It is not Magic!

All life is an experiment. The more experiments you make the better

Ralph Waldo Emerso n

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DoE Factorial Strategy

All Possibilities are Considered from Main Effects to Interaction Effects

Variable 2

Variable 1

Variable 3

23

= (Two Levels)(Three Factors)

The probability of anything happening is in inverse ratio to its desirability

John W. Hazard

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DoE for Mileage Example

Speed(A)

Octane(B)

Tyre Pressure(C)

Mileage(Y)

55 (-) 87 (-) 30 (-) Y1

65 (+) 87 (-) 30 (-) Y2

55 (-) 92 (+) 30 (-) Y3

65 (+) 92 (+) 30 (-) Y4

55 (-) 87 (-) 35 (+) Y5

65 (+) 87 (-) 35 (+) Y6

55 (-) 92 (+) 35 (+) Y7

65 (+) 92 (+) 35 (+) Y8

How Many Runs? 23= 8

How Many Observations for each level? 4

Problem: Gas mileage for Car is 20 mpg

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What DoE Tools to Use

Current State of Problem Knowledge

Low High

Type of Design Screening FractionalFactorial

Factorial

Usual Number ofFactors

> 10 5-10 1-5

Purpose

Identify Most ImportantFactors- Vital Few

Some Interactions RelationshipsAmong Factors

Estimate Crude directionfor Improvement- Liner Effects

Someinterpolation

All main effectsand interactions

Golden rule of an experiment: the duration of an experiment

should not exceed the lifetime of the experimentalist

Unknown Physic ist

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Analyzing a Full Factorial Design

Step 1: Set-up Table of Contrast Example: This example relates two quantitative Input Variables (Temperature

and Concentration) and one qualitative Input (Catalyst) to Yield.

The factors and levels:

- Temperature : 160C (-1), 180C (+1)

- Concentration (%) : 20 (-1), 40 (+1)- Catalyst : Brand A (-1), Brand B (+1)

Temp Concentration Catalyst Yield

-1 -1 -1 ?

1 -1 -1 ?

-1 1 -1 ?

1 1 -1 ?

-1 -1 1 ?

1 -1 1 ?

-1 1 1 ?

1 1 1 ?

Everything should be made as simple as possible,

but not one bit simpler

Albert Einstein

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Step 2: Calculating Main Effects

We will now calculate the effects of the experiment.

First we look at Temperature. We simply add the Yields associated with (-1) and the Yields

associated with (1) and calculate the average.

Temp Concentration Catalyst Yield

-1 -1 -1 60

1 -1 -1 72

-1 1 -1 54

1 1 -1 68

-1 -1 1 52

1 -1 1 83

-1 1 1 45

1 1 1 80

Total (-) 211 267 254

Total (+) 303 247 260

Diff 92 -20 6

Mean Eff 23 -5 1.5

Temperature Effect = (72 + 68 + 83 + 80) - (60 + 54 + 52 + 45)

4 4

= 75.72 - 52.75 = 23

This can be interpreted as the Yield going up by and average of 23 points as temperaturemoves from low to high

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Step 3: Calculating Interaction Effects (cont.)

The Interaction Effects is represented by multiplying the columns to bepresented. For the 2x2 example, the Temperature x Concentration interactioncontrast is created by multiplying the Temp contrast and Concentrationcontrast.

Temp Concentration TxC

-1 -1 1

1 -1 -1

-1 1 -11 1 1

It is always better to be approximately right than precisely wrong

Unknown Engineer

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Step 3: Calculating Interaction Effects

Calculate the interaction effects for the entire matrix

Temp (T) Conc (C) Cat (K) T*C T*K C*K T*C*K Yield-1 -1 -1 1 1 1 -1 60

1 -1 -1 -1 -1 1 1 72

-1 1 -1 -1 1 -1 1 54

1 1 -1 1 -1 -1 -1 68

-1 -1 1 1 -1 -1 1 52

1 -1 1 -1 1 -1 -1 83

-1 1 1 -1 -1 1 -1 45

1 1 1 1 1 1 1 80

Total (-) 211 267 254254 237 257 256

Total (+) 303 247 260 260 277 257 258

Diff 92 -20 6 6 40 0 2

Mean Eff 23 -5 1.5 1.5 10 0 0.5

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Step 4: Graph Main Effects Plot

-1 1 -1 1 -1 1

75 _

70 _

65 _

60 _

50 _

Temp Conc Cat

Average Yield at

(-1) Level

Average Yield at

(+1) Level

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Step 5: Graph Interaction Plot

Mean

Catalyst

80 _

70 _

60 _

50 _

-1 1

Interaction Plots (T*K)

Mean

Concentration

80 _

70 _

60 _

50 _

-1 1

Interaction Plots (T*C)

Average Yield at(+1) Cat and (+1) Temp

Average Yield at

(-1) Cat and (-1) Temp

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2520151050-5

USLLSL

Process Capability Analysis for C1

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 (Wi thin)

Sample N

Mean

LSL

Target

USL

687520.13

554607.20

132912.93

673422.73

559030.23

114392.51

900000.00

750000.00

150000.00

-0.05

0.37

-0.05

0.16

*

-0.05

0.40

-0.05

0.18

5.12602

4.73941

20

10.7039

5.0000

*

10.0000

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capabil ity

Potential (Within) Capability

Process Data

Within

Overall

Distribution Plot

Cpk = X - LSL

3

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Importance of Statistics in Industry

Organizations around the world are constantlysearching for more effective methodology toachieve improvement (breakthroughimprovement)

Financial Performance

Customer Satisfaction The improvement methodology evolved from

common sense, PDCA, Kaizen, Just-in-Time,Lean, SPC, TQM, Business Process Re-engineering to Six Sigmanow.

I f your result needs a statist ician then you s hou ld design a better

experiment."Ernest Rutherford

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Six sigma commonly refers to a statistically derived performance

target of 3.4 defects for every 1 million opportunities (3.4 DPMO).

Six Sigma (with 1.5 sigma mean shifts)

Statistical Definition of Six Sigma

-6s -5s -4s -3s -2s -1s 0 1s 2s 3s 4s 5s 6s

99.99966% or 3.4 DPMO

Short -term

LSL USL

Short-term

99.9999998% or 0.002 DPMO

1.5s

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Practical Meaning of Six Sigma

54,000 lost articles of mail per year

Five short or long landings at most

major airports/day More than 40,500 newborn babies

dropped by doctors/nurses each year

Unsafe drinking water about two hours

each month

20,000 Lost bags per Day (Baggage

Handling System

Houston Airport )

35 lost articles of mail per year

One short or long landings at most

major airports/10 year Three newborn babies dropped by

doctors/nurses in 100 years

Unsafe drinking water 1 second

every 16 years

< 5 Lost bags per day

99% Good

3-Sigma

99.99% Good

6-Sigma

Why 99% Good is often not Good Enough

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Six Sigma DMAIC Approach

There are five major steps involved in applying Six Sigma Approach toachieve breakthrough quality and performance.

Define, Measure,Analyze, Improve, & Control. (D-M-A-I-C).

D M A I C

Be thankful for problems. If they were less difficult,

someone with less ability might have your job

Reliabil i ty Engineer

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DMAIC - Systematic Problem Solving Tool

In Define phase, the team :

Defines the Project

Defines Problem & Goal Statement

Defines Project Benefits (Financial Analysis)

Defines Project Charter & Project Scope

Obtains support from Management

Classic American and Russian

approach for a problem during

space mission!

D M A I C

A SMART Goal statement

Specific

Measurable

Attainable

Relevant

Time Bound

"Stat ist ic s: The only scienc e that enables different experts using the

same figures to draw different conclusions. - A frustrated Statist ician

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Measure Phase cont.

Measurement System Analysis: Four characteristics to examine in a gaugesystem

1) Sensitivity

The gauge should be sensitive enough to detect differences in measurement asslight as one-tenth of the total tolerance specification.

e.g: 200 0.1 mmtool should be able to measure at 0.01mm accuracy.

2) Reproducibility

The reliability of the gauge system to reproduce measurements. Customarilychecked by comparing the results of different operators taken at different time.

This affects both accuracy and precision.

D M A I C

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Measure Phase cont.

3) Accuracy

An unbiased true value

Normally reported as difference between the average of a number of measurementsand the true value.

e.g: checking a micrometer with a gauge block

4) Repeatability/Precision

The ability to repeat the same measurement by the same operator at the sametime.

To improve the accuracy and precision of a measurement process, it must have adefined test method and must be statistically stable.

D M A I C

Precise but not

accurate

Accurate but

not precise

Accurate and

precise

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D M A I C

Measurement Error

Repeatability & Reproducibility

- Analysis of variance (ANOVA) is the most accurate method for quantifyingrepeatability and reproducibility.

- It considers error by appraiser and the system

How to do ANOVA Test:

1) Calculate variance between system/appraiser

2) Calculate variance within system/appraiser

3) Calculate F ratio

4) If F ratio is greater than the Fcritical value accept or reject your hypothesis

Any equation longer than three inches is most likely wrong

Unknown Physic ist

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Example : A Complex DoE Model (using JMP)

0

0.5

1

1.5

2

2.5

3

3.5

%

StressActual

.0 .5 1.0 1.5 2.0 2.5 3.0 3.5

% Stress Predicted P

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InAnalyze phase:

Brainstorm potential root causes

Use the data collected to determine root causes

and opportunitiesfor improvement

Verifies the hypothesisestablished Establishes the priority for action regarding theXs

2 common techniques:

i) Fish bone diagram

ii) Why-why analysis

Analyze Phase

Separate what we think is happening from what is really happening !!

Avoids solutions that dont solve the real problem !

D M A I C

Well done is better than well said

Benjamin Frankl in

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Cause-And-Effect Diagrams (Fish Bone)

D M A I C

Problem

Material

Method

Machine Man

Mother Nature

(Effect )(Causes )

Measurement

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Why-Why Analysis

It is a technique to determine root causes to a phenomenon by

repeatedly asking Why

It is a variant of the 5 Why Analysis used at Toyota Motor

company for discovering true causes by repeating the question

Why five times.

Why?...Why?...Why?...Why?...Why? Stop!

D M A I C

It is easy to see, it is hard to foresee

Benjamin Franklin , Am erican Scientist and Statesman

h

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After invested much time in the Define-Measure-Analyzephases, the team needs to change gear from being detailed

minded (in process analysis and data analysis) to creativeand innovative in developing solutions and changeprocesses.

Piloting whenever possible, before the fullimplementation.

Improve Phase

D M A I C

If you bet on a horse, thats gambling.

If you bet you can make three spades, thats entertainment.

If you bet the device will survive for twenty years, thats engineering.

See the difference?

Unknown Engineer

C t l Ph

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Control Phase

D M A I C

This is the last phase in the DMAIC

improvement process. Without control efforts, the improved process

may revert to itsprevious state.

Be more careful is not effective

The old way of dealing with human error was to scold

people, retrain them, and tell them to be more careful

We cantdo much to change human nature, and peopleare going to make mistakes (often the same mistakes

too). If we canttolerate them ... we should remove the

opportunitiesfor error.

What Abo ut Human Error ???

To err is hum an, to forgive is divine, but to inc lude errors in

your design is statistical

Lesl ie Kisch

P k Y k E P fi

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Poka-Yoke Error Proofing

Beep !!Beep !

D M A I C

Reliability it is when the customer comes back, not the product,

Unkno wn Reliabil i ty Manager

Key Take Away

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Key Take Away

Cpk = X - LSL

3

1. Plan DoE matrix using 23= (Two Levels) (Three Factors)You should have at least 8 runs for your simple DoE matrix

2. Calculate Mean, Std Deviation (sigma ) and Cpk

MsoftExcel application can be easily used for this

Calculate Cpk using below formula:

3. Plot interaction chart to understand the interaction of various input

factors and identify the most significant factor(s)

4. Plot distribution curve for better visualization of your data if needed

5. Consider measurement errors in your data

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Thanks for your attention

Statist ics is like mod ern art, the more com plicated it is

the higher the value

Unknown Engineer