Quality Progress - December 2016 - 53


DESIGN OF EXPERIMENTS

It can be challenging to design a small
experiment for nine process variables and
still obtain statistically meaningful
results to support decision making.
effects while minimizing statistical risk-that is,

It can be challenging to design a small experiment

the risk of making incorrect decisions based on the

for nine process variables and still obtain statistically

data-and stays within the test budget.

meaningful results to support decision making. For

When executing a DoE, the run order and con-

this experiment, the team leveraged the efficiencies

trolled test environment are important to getting the

of a cutting-edge test design technique called a defini-

most accurate information from an experiment and

tive screening design.7

reducing unnecessary variation in the data. While it

This design does double-duty: It allows experi-

requires more time and discipline, the chemists were

menters to screen out less important factors to a

able to fully randomize the order in which the process

process and selects the settings of those factors

was varied, and their team's lab in Rock Island Arse-

that were significant to optimize the response. It

nal was carefully controlled to ensure highly accurate

can be described as a screening design and central-

test results.

composite design packed into a single minimally

4

sized test.

The right design

In this example, a 22-run experiment was used to

There is a wide variety of DoEs from which to

drive discovery and breakthroughs in this complex

choose.5 Test objectives, in-depth test planning and

chemical process with nine factors, leading to deci-

experience practicing DoE helps in determine the ap-

sive predictions that enabled the team to avoid testing

propriate design to meet challenges that are unique to

the more than 8,000 unique treatment combinations

a specific project.

mentioned earlier. The team used the information

To optimize chemical formulations, DoE practitio-

gathered in this 22-sample experiment (along with

ners typically use mixture designs, such as sensitiv-

validation testing) to maximize the time-to-failure

ity testing, for experiments in which the performance

response predictions using numerical optimization

measure is binary (pass-fail). Design and analysis of

techniques that solve for the optimal combinations of

computer experiments is a family of DoE techniques

factor-level settings (see Figure 2, p. 54).

used to optimize computational models and simula-

In analyzing the results from a designed experi-

tions through the use of space-filling designs and ad-

ment with a large number of factors, a common chal-

vanced interpolation techniques.6

lenge encountered is variable reduction and model

Conjoint analysis is a type of DoE that aims to

selection. In this 22-run experiment with nine factors,

quantify user requirements and characterize user

for example, the team was interested in fitting up to

needs, in terms of product performance requirements,

a second-order model, which equates to 53 possible

and their trade-space, through analysis of systemati-

model terms.

cally designed questionnaires. Screening designs are

Even though the factor sparsity principle states a re-

typically used to test a large set of potential factors

gression model of this size is most likely unnecessary

to identify which ones most significantly affect the

to describe the behavior of the process, the inherent

response, and central composite designs are used for

model-fitting difficulty should be apparent. A frequent-

response optimization if nonlinear relationships are

ly used tool is forward stepwise regression, which is an

suspected between some variables and the response

automated model-selection algorithm used in conjunc-

(see Figure 1).

tion with stopping criteria such as a p-value threshold.

December 2016 * QP 53



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

Quality Progress - December 2016 - cover1
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