qe4 statistical concepts

8/7/2019 QE4 Statistical Concepts

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EMgt-475:Quality Engineering

Kenneth M. Ragsdell, PhD

Professor of Engineering Management

& Systems Engineering

QE04: Data & Statistical Concepts


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W'09 copyright K.M. Ragsdell 2

Why Statisti

cs?

We need to carefully examine

performance so that trends can be

observed and used for improvement.

Let the data talk!

Dont let your experience and judgment

speak louder than product performance. LET THE DATA TALK!!!!


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Metrics

Mean or average

Standard deviation

Variance

Coefficient of variation

Signal to noise ratio Loss function

Etc


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Mean or Average

Q ! y !1

ny

ii!1

n


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Variance

W2! s

2!

1n 1

(yi

i!1

n

y)2


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Standard Deviation

s! 1n 1

(yi

i!1

n

y)2


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Coefficient of Variation

cv! W

Q

! s

y


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W'09 copyright K.M. Ragsdell

9

Signal to Noise Ratio

L =cv!

y

s

S / N 0log0 (L


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0

Loss Function

(m

A0

L

y

A0=cost of corrective action

( point of intolerance

m=target value

y=quality characteristic

L=loss ($)

L(y) !A

0

(02

(y m)2


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Process Capability

c p !USL LSL

6Wc pk ! MIN(c pu ,cpl)

c pu !USL Q

3W

c pl !Q LSL

3W


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Data Analysis/Robust Design Data - types, origins and uses

Data analysis

Graphical

Quantitative

Mean

Variance Standard deviation



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Data Types Data comes in allsizes, shapes and

forms

Numeric

Integer

Real

Graphical

Ordered categorical


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Numeric

data Numbers, numbers, numbers!! 1,2,3,10

1.7965432113, 1.25

Example data set

Mean

Variance

Standard deviation



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Graphical Data Histogram

Run chart

Control chart

Pie chart

Flow diagram


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Factor Effe

ct PlotsSt d rd D vi tio

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

A

B

C

D

A 4.598 5.427 5.532

B 2.963 4.594 8.000

C 5.993 5.531 4.034

D 4.811 5.576 5.171

1 2 3

NTB Sig

l to Nois

R

tio

12.000

14.000

16.000

18.000

20.000

22.000

A

B

C

D

A 17.201 18.462 18.995

B 13.845 20.198 20.615

C 15.519 18.193 20.946

D 16.902 19.339 18.417

1 2 3


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Catapult Spreadsheet


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Crystal Ball


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9

Consider the Possibilities!


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0

Crystal Ball User-friendly

Graphically oriented

Forecasting and risk analysis decision-

making tool Monte Carlo simulation

No special statistical orcomputer

knowledge Who should use CB?

Anyone wishing to predict outcomes in thepresence of uncertainty and risk


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Linear Gap Analysis


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Run the Example using CB


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Sigma Level = 4.25

2900

DPMO


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Change Part A to Normal


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Uniform to Normal Notice the negative effects associatedwith uniform distributions!

Uniform = BAD!!!


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Summary Why do we needstatistics?

Metrics

Statistics Mean

Variance

Standard deviation

Coefficient ofvariation

S/N ratio

Loss function

Process capability

Example

Data analysis

Data types

Numeric

Graphical

Excel Crystal Ball

example


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Program Completed

qe4 statistical concepts

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