Quality Progress - March 2018 - 52

Statistics Spotlight
1213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262

experiment. If we run an experiment to determine
the impact of different doses on the response of
interest for our test subjects, for example, we cannot
randomly assign gender. Hence, a good design
one hard-to-change
would treat gender as a blocking factor, and assign
factor, but the analysis
factor combinations within the blocks.3
If some of these answers do not
of the experiment must
Alternatively, we might have an experiment (such
match what was anticipated,
reflect the two different
as the earlier humidity example) in which condithe opportunity exists to make
randomizations, which
tions during the test vary over time. In this case, we
some adjustments to the expereach may have different
could run a blocking design that considers different
iment to avoid wasting further
associated amounts of
portions of the day as blocks. This imposes balance
resources and maximizing the
natural variability.7
of treatment combinations in the blocks and also
information obtained.
Deciding whether this
allows qualitative exploration of potential differences
is the right type of design
between the blocks.
for your experiment balances ease of implementation, potenFigure 2 (p. 49) shows a sample of how a 24 factorial expertial reduced cost for fewer changes of the hard-to-change
iment can be run in two blocks of size eight. The blocks might
factors, and additional complexity of analysis. 8
coincide with gender or time of day. Note how in each block,
there are four runs at the high level and four runs at the low
3. Sequential experimentation: Finally, another option
level of each factor. This ensures that factor effects can be
to a completely randomized design is to run the experiestimated independently of the block effect.
ment with the goal of getting partial information about
Hence, for these types of designs, the primary goal is to
the response as the experiment is being run. For example,
take into account a factor or conditions that cannot be conconsider a definitive screening design (DSD)9,10 with three
trolled during the experiment, but are thought to potentially
three-level continuous factors and three two-level categoriaffect the response. The analysis of the experiment should
cal factors. These DSDs are supersaturated designs, but are
include a term for the blocking because differences between
capable of separately estimating all main effects, two-factor
the blocks should be removed from the estimate of the natuinteractions and quadratic terms.
ral variability.4
In many experiments, it is beneficial to obtain preliminary
information about the range of responses, as well as early
2. Split-plot designs: These designs recognize the fact
feedback about the choice of factor levels and the factor
that some factors may be time-consuming, complicated
effects on the response. By taking advantage of the notion of
or expensive to adjust, and allow for groups of runs to be
blocking, we can divide the experiment into two blocks, with
performed without resetting all of the factor levels between
the goal of building in a slight pause in the experiment after
the runs. 5,6 The requirement that each factor be reset for
the first block has been completed.
each run of the experiment is often impractical, so split-plot
At this time, we can take stock of how the experiment
designs allow for two (or more) levels of randomization.
is running: Are we getting sensible results at each of the
Figure 3 (part a), p. 50, shows a 16-run experiment in which
factor levels? Do the main effects for each factor match our
factor X1 is hard to change, and hence the experimenter
expectations? Is the range of responses what is required for
wishes to reduce the number of times that factor is reset. The
optimization or other post-experiment decisions?
experiment has four whole plots, where within each of these,
If some of these answers do not match what was anticthe level of factor X1 is set just once and then four subplot
ipated, the opportunity exists to make some adjustments
runs are performed. For each of the four runs in each whole
to the experiment to avoid wasting further resources and
plot, the levels of the easy-to-change factors X2, X3 and X4
maximizing the information obtained. If things are turning
are reset each time. In setting up the experiment, two ranout as expected, the second block of the experiment can be
domizations are performed:
completed, and only a small modification to the analysis (the
1. The order that the whole plots will be performed.
inclusion of a blocking term in the model) is required.
2. The order that the subplots are run within each whole plot.
Randomization is performed, as with any blocking
Figure 3 (part b) shows another variation of the same
experiment: The run order of experimental units in a block is
design, but with a different randomized order. Note how the
randomized. This simple strategy of creating a small number
order of the whole plots has changed, as well as the order of
of blocks-and strategically choosing to run one or more
the runs in each block.
of them first-allows for easy design construction, while
Split-plot designs can flexibly accommodate more than

52 QP

March 2018 ❘ qualityprogress.com


http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - March 2018

Seen and Heard
Expert Answers
Progress Report
Mr. Pareto Head
Career Coach
My Quality Story
In the Right Direction
A Different Kind of BBQ
Gaining Ground
Impeding Progress
Innovation Imperative
Statistics Spotlight
Standard Issues
Marketplace
Footnotes
Back to Basics
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
Quality Progress - March 2018 - 5
Quality Progress - March 2018 - Seen and Heard
Quality Progress - March 2018 - 7
Quality Progress - March 2018 - Expert Answers
Quality Progress - March 2018 - 9
Quality Progress - March 2018 - Progress Report
Quality Progress - March 2018 - 11
Quality Progress - March 2018 - 12
Quality Progress - March 2018 - Mr. Pareto Head
Quality Progress - March 2018 - Career Coach
Quality Progress - March 2018 - 15
Quality Progress - March 2018 - My Quality Story
Quality Progress - March 2018 - 17
Quality Progress - March 2018 - In the Right Direction
Quality Progress - March 2018 - 19
Quality Progress - March 2018 - 20
Quality Progress - March 2018 - 21
Quality Progress - March 2018 - 22
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
Quality Progress - March 2018 - 33
Quality Progress - March 2018 - 34
Quality Progress - March 2018 - 35
Quality Progress - March 2018 - 36
Quality Progress - March 2018 - Impeding Progress
Quality Progress - March 2018 - 38
Quality Progress - March 2018 - 39
Quality Progress - March 2018 - 40
Quality Progress - March 2018 - 41
Quality Progress - March 2018 - 42
Quality Progress - March 2018 - 43
Quality Progress - March 2018 - Innovation Imperative
Quality Progress - March 2018 - 45
Quality Progress - March 2018 - 46
Quality Progress - March 2018 - 47
Quality Progress - March 2018 - Statistics Spotlight
Quality Progress - March 2018 - 49
Quality Progress - March 2018 - 50
Quality Progress - March 2018 - 51
Quality Progress - March 2018 - 52
Quality Progress - March 2018 - 53
Quality Progress - March 2018 - Standard Issues
Quality Progress - March 2018 - 55
Quality Progress - March 2018 - 56
Quality Progress - March 2018 - 57
Quality Progress - March 2018 - Marketplace
Quality Progress - March 2018 - 59
Quality Progress - March 2018 - Footnotes
Quality Progress - March 2018 - 61
Quality Progress - March 2018 - 62
Quality Progress - March 2018 - 63
Quality Progress - March 2018 - Back to Basics
Quality Progress - March 2018 - cover3
Quality Progress - March 2018 - cover4
https://www.nxtbook.com/naylor/ASQM/ASQM0719
https://www.nxtbook.com/naylor/ASQM/ASQM0619
https://www.nxtbook.com/naylor/ASQM/ASQM0519
https://www.nxtbook.com/naylor/ASQM/ASQM0419
https://www.nxtbook.com/naylor/ASQM/ASQM0319
https://www.nxtbook.com/naylor/ASQM/ASQM0219
https://www.nxtbook.com/naylor/ASQM/ASQM0119
https://www.nxtbook.com/naylor/ASQM/ASQM1218
https://www.nxtbook.com/naylor/ASQM/ASQM1118
https://www.nxtbook.com/naylor/ASQM/ASQM1018
https://www.nxtbook.com/naylor/ASQM/ASQM0918
https://www.nxtbook.com/naylor/ASQM/ASQM0818
https://www.nxtbook.com/naylor/ASQM/ASQM0718
https://www.nxtbook.com/naylor/ASQM/ASQM0618
https://www.nxtbook.com/naylor/ASQM/ASQM0518
https://www.nxtbook.com/naylor/ASQM/ASQM0418
https://www.nxtbook.com/naylor/ASQM/ASQM0318
https://www.nxtbook.com/naylor/ASQM/ASQM0218
https://www.nxtbook.com/naylor/ASQM/ASQM0118
https://www.nxtbook.com/naylor/ASQM/ASQM1217
https://www.nxtbook.com/naylor/ASQM/ASQM1117
https://www.nxtbook.com/naylor/ASQM/ASQM1017
https://www.nxtbook.com/naylor/ASQM/ASQM0917
https://www.nxtbook.com/naylor/ASQM/ASQM0817
https://www.nxtbook.com/naylor/ASQM/ASQM0717
https://www.nxtbook.com/naylor/ASQM/ASQM0617
https://www.nxtbook.com/naylor/ASQM/ASQM0517
https://www.nxtbook.com/naylor/ASQM/ASQM0417
https://www.nxtbook.com/naylor/ASQM/ASQC12518
https://www.nxtbook.com/naylor/ASQM/ASQM0317
https://www.nxtbook.com/naylor/ASQM/ASQM0217
https://www.nxtbook.com/naylor/ASQM/ASQM0117
https://www.nxtbook.com/naylor/ASQM/ASQM1216
https://www.nxtbook.com/naylor/ASQM/ASQM1116
https://www.nxtbook.com/naylor/ASQM/ASQM1016
https://www.nxtbook.com/naylor/ASQM/ASAC0016
https://www.nxtbook.com/naylor/ASQM/ASQM0916
https://www.nxtbook.com/naylor/ASQM/ASQA0016
https://www.nxtbook.com/naylor/ASQM/ASQM0816
https://www.nxtbook.com/naylor/ASQM/ASQM0716
https://www.nxtbook.com/naylor/ASQM/ASQM0616
https://www.nxtbook.com/naylor/ASQM/ASQM0516
https://www.nxtbook.com/naylor/ASQM/ASQM0416
https://www.nxtbook.com/naylor/ASQM/ASQM0316
https://www.nxtbook.com/naylor/ASQM/ASQM0216
https://www.nxtbook.com/naylor/ASQM/ASQM0116
https://www.nxtbook.com/naylor/ASQM/ASQM1215
https://www.nxtbook.com/naylor/ASQM/ASQM1115
https://www.nxtbook.com/naylor/ASQM/ASQM1015
https://www.nxtbook.com/naylor/ASQM/ASQM0915
https://www.nxtbook.com/naylor/ASQM/ASQM0815
https://www.nxtbook.com/naylor/ASQM/ASQM0715
https://www.nxtbook.com/naylor/ASQM/ASQM0615
https://www.nxtbook.com/naylor/ASQM/ASQM0515
https://www.nxtbook.com/naylor/ASQM/ASQM0315
https://www.nxtbook.com/naylor/ASQM/ASQM0215
https://www.nxtbook.com/naylor/ASQM/ASQM0115
https://www.nxtbook.com/naylor/ASQM/ASQM1214
https://www.nxtbook.com/naylor/ASQM/ASQM1114
https://www.nxtbook.com/naylor/ASQM/ASQM1014
https://www.nxtbook.com/naylor/ASQM/ASQM0914
https://www.nxtbook.com/naylor/ASQM/ASQM0814
https://www.nxtbook.com/naylor/ASQM/ASQM0714
https://www.nxtbook.com/naylor/ASQM/ASQM0614
https://www.nxtbook.com/naylor/ASQM/ASQM0514
https://www.nxtbook.com/naylor/ASQM/ASQM0414
https://www.nxtbook.com/naylor/ASQM/ASQM0314
https://www.nxtbook.com/naylor/ASQM/ASQM0214
https://www.nxtbook.com/naylor/ASQM/ASQM0114
https://www.nxtbook.com/naylor/ASQM/ASQM1213
https://www.nxtbook.com/naylor/ASQM/ASQM1113
https://www.nxtbook.com/naylor/ASQM/ASQM1013
https://www.nxtbook.com/naylor/ASQM/ASQM0913
https://www.nxtbook.com/naylor/ASQM/ASQM0813
https://www.nxtbook.com/naylor/ASQM/ASQM0713
https://www.nxtbook.com/naylor/ASQM/ASQM0613
https://www.nxtbook.com/naylor/ASQM/ASQM0513
https://www.nxtbook.com/naylor/ASQM/ASQM0413
https://www.nxtbook.com/naylor/ASQM/ASQM0313
https://www.nxtbook.com/nxtbooks/naylor/ASQM0213
https://www.nxtbook.com/nxtbooks/naylor/ASQM0113
https://www.nxtbook.com/nxtbooks/naylor/ASQM1212
https://www.nxtbook.com/nxtbooks/naylor/ASQM1112
https://www.nxtbook.com/nxtbooks/naylor/ASQM1012
https://www.nxtbook.com/nxtbooks/naylor/ASQM0912
https://www.nxtbookmedia.com