Quality Progress - March 2018 - 49

```When it is run, the assumption is that between each run,
the levels of each factor are reset. For example, for the
first run, factors X1 and X2 at their low levels, and X3
and X4 at their high levels. For the second run, X1 is set
at its high level and X2 at its low level, and so on. For
factor X1, this involves changing the setting from low to
high, while for X2, the setting stays the same level, but
should still be set again. Regardless, the assumption is
that the levels for each of the five factors will be reset
between each run.
Why is this beneficial? Suppose that factor X2 is
a temperature with levels 200° F (for the low level
denoted with -1) and 250° F (high level denoted +1),
and for the first run, the temperature was actually set
at 199° F. By resetting the temperature between each
run, the potential for systematic bias can be reduced. If
the factors were not reset after each run, then runs one,

In his mind, the "untidy run order" from randomization
seemed unorganized, unscientific and something that a
good researcher would never do. So, he and I spent the
next half hour talking about the merits of randomization, and how it was absolutely relevant and necessary
for good scientific investigation.

Merits of randomization

I'd like to recap some of these principles, as well as
provide some options when faced with constraints on
randomization when implementing an experiment. The
design shown in Figure 1 is called a completely randomized design because there were no restrictions in
determining the order of the experimental runs.
The same 16 runs are shown in Figure 1 (parts a and
b), but the run order for the latter has been permuted
from the standard order-shown in Figure 1 (part a).
FIGURE 1

FIGURE 2

24 factorial design
Pattern

Pattern

24 factorial design run
in 2 blocks of size 8

X1

X2

X3

X4

X1

X2

X3

X4

1 −−−−

−1

−1

−1

−1

1 −−++

−1

−1

1

1

2 −−−+

−1

−1

−1

1

2 +−−+

1

−1

−1

1

3 −−+−

−1

−1

1

−1

3 −−+−

−1

−1

1

−1

1 −−−−

1
1

Pattern

Block

X1

X2

X3

X4

−1

−1

−1

−1

−1

1

−1

1

4 −−++

−1

−1

1

1

4 +−++

1

−1

1

1

2 −+−+

5 −+−−

−1

1

−1

−1

5 +++−

1

1

1

−1

3 +−+−

1

1

−1

1

−1

6 −+−+

−1

1

−1

1

6 −−−+

−1

−1

−1

1

4 −−++

1

−1

−1

1

1

1

1

1

1

1

7 −++−

−1

1

1

−1

7 −+−+

−1

1

−1

1

5 ++++

8 −+++

−1

1

1

1

8 −+−−

−1

1

−1

−1

6 −++−

1

−1

1

1

−1

1

1

−1

−1

1

1

1

−1

−1

9 +−−−

1

−1

−1

−1

9 −++−

−1

1

1

−1

7 +−−+

10 +−−+

1

−1

−1

1

10 ++++

1

1

1

1

8 ++−−

1

11 +−+−

1

−1

1

−1

11 +−+−

1

−1

1

−1

9 +++−

2

1

1

1

−1

10 −−−+

2

−1

−1

−1

1

12 +−++

1

−1

1

1

12 +−−−

1

−1

−1

−1

13 ++−−

1

1

−1

−1

13 −−−−

−1

−1

−1

−1

11 −+−−

2

−1

1

−1

−1

2

1

−1

1

1

−1

−1

14 ++−+

1

1

−1

1

14 ++−−

1

1

−1

−1

12 +−++

15 +++−

1

1

1

−1

15 ++−+

1

1

−1

1

13 +−−−

2

1

−1

16 ++++

1

1

1

1

16 −+++

−1

1

1

1

14 −+++

2

−1

1

1

1

15 ++−+

2

1

1

−1

1

16 −−+−

2

−1

−1

1

−1

a
Standard order

b
Randomized order

Note: For each block, there are equal numbers
of runs at the high and low levels of each factor.

qualityprogress.com ❘ March 2018

QP 49

```
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Quality Progress - March 2018 - INTRO
Quality Progress - March 2018 - cover1
Quality Progress - March 2018 - cover2
Quality Progress - March 2018 - 1
Quality Progress - March 2018 - 2
Quality Progress - March 2018 - 3
Quality Progress - March 2018 - 4
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Quality Progress - March 2018 - My Quality Story
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Quality Progress - March 2018 - In the Right Direction
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Quality Progress - March 2018 - 21
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Quality Progress - March 2018 - 23
Quality Progress - March 2018 - A Different Kind of BBQ
Quality Progress - March 2018 - 25
Quality Progress - March 2018 - 26
Quality Progress - March 2018 - 27
Quality Progress - March 2018 - 28
Quality Progress - March 2018 - 29
Quality Progress - March 2018 - 30
Quality Progress - March 2018 - 31
Quality Progress - March 2018 - Gaining Ground
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Quality Progress - March 2018 - 34
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Quality Progress - March 2018 - 36
Quality Progress - March 2018 - Impeding Progress
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Quality Progress - March 2018 - 43
Quality Progress - March 2018 - Innovation Imperative
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Quality Progress - March 2018 - Statistics Spotlight
Quality Progress - March 2018 - 49
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Quality Progress - March 2018 - Standard Issues
Quality Progress - March 2018 - 55
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Quality Progress - March 2018 - Marketplace
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Quality Progress - March 2018 - Footnotes
Quality Progress - March 2018 - 61
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Quality Progress - March 2018 - 63
Quality Progress - March 2018 - Back to Basics
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