Quality Progress - December 2016 - 54


0 20 40 60 80 100

Hydrogen
embrittlement
Fixed

174.98085

1

0.75

0.5

Yes

0.25

No

8.5

0

5

2.75

Yes

140
150
160
170
180
190
200
210
8
9
10
11
12
13
14
15
16

4.5

Yes

4

3

No

3.5

0.977049

0 0.25 0.5 0.75 1

Estimated SS TTF X

89.49694
[74.4649,
104.529]

Desirability

Regression model predictions used to maximize
time-to-failure response / FIGURE 2

Simulate

No

pH
(chem. process B)

Temperature
(chem. process A)

Concentration
(chem. process A)

Random

Random

Random

Hot water
rinse

Desirability

Fixed

Yes

No

Normal
Mean
SD

2.75
0.1

Normal

Normal

Mean 174.981
2
SD

Mean
SD

Penalized regression methods, such as the lasso

8.5
0.25

Chem. = chemical
SD = standard deviation
SS TTF X = salt-spray time to failure,
transformed

with nonstandard response data.10

and the elastic net (a method that combines the pen-

Those familiar with reliability and survival data

alties of the lasso and ridge regression) can be highly

analysis might notice that the response here is inter-

effective at variable selection.8, 9 They excel in model

val censored time-to-failure data, for which a para-

fitting situations in which there are a large number of

metric survival analysis11 would be the more appro-

potential variables and relatively few rows of data.

priate modeling method.

In this experiment, the model selected using for-

In this case, the team was able to use a response

ward stepwise regression was in reasonable agree-

data transformation so it wasn't violating assumptions

ment with the elastic net selected regression model.

for use of least squares regression. This allowed the

It benefits an analyst to seek model parsimo-

team to use stepwise regression for convenience and

ny, which means fitting the most variation in the

reanalyze the data along the way with various com-

data with the simplest explanatory model. Using

binations of candidate model terms using parametric

least-squares regression enables the use of many

survival analysis to confirm the regression model pre-

straightforward tools such as stepwise regression

dictions and follow-on numerical optimization.

and intuitive diagnostics-which are often not
available when using other modeling techniques

Validation

such as generalized linear models, including meth-

After the team obtained an empirical model with a

ods such as logistic regression, Poisson regression

strong predictive capability, the crucial next step

or negative binomial regression, which can deal

was validation of the optimal settings. Several addi-

54 QP * www.qualityprogress.com


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Table of Contents for the Digital Edition of Quality Progress - December 2016

Quality Progress - December 2016 - cover1
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Quality Progress - December 2016 - 1
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Quality Progress - December 2016 - cover3
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