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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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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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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
Coefficient of variation
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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
Coefficient of variation
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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
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