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298 3:6 Economical Experimentation via ‘Lean Design’
into account prior technical knowledge as well as possible confounding of effects
in data analysis), size of experiments (basic number of observations together with
replications), and execution plans (a single complex design, or several simpler designs
conducted sequentially).
Against the above backdrop, this chapter presents a practical experimental design
approach, referred to as lean design, which has economy of data collection as its prime
objective and can address a number of problems arising from constrained resources
in industrial experimentation. The procedures, based on the provisional use of in-
complete orthogonal matrices, are shown to be useful for damage control in the event
of inadvertent incomplete experimentation. The working of lean design is also illus-
trated by a numerical example based on a well-known case study in the seminal work
on applied experimental design by Box et al. 6

19.2 TWO ESTABLISHED APPROACHES

The strategies for lean design are developed with reference to some of the most no-
table features of design of experiments as advocated by the Taguchi school and by
mainstream statisticians. For example, while a Taguchi design tends to be a one-shot
experimental effort, mainstream statisticians would prefer using simpler designs con-
6
ducted in a sequential manner -- the ‘fold-over’design used by Box et al. being a well
known example. With sequential experimentation, interim results can be obtained to
provide insights into the behavior of the subject of study and help focus experimen-
tal efforts: for example, two suitably designed 2 7−4 experiments in tandem would be
preferable to one 2 7−3 experiment comprising the same physical experimental runs,
since the investigator using the 2 7−3 design would have no inkling of the likely re-
sults of the experiment before all 16 observations are available. This principle will be
brought up again in later discussions.
In Taguchi methods, an experiment is designed with the assumption that interac-
tion effects among experimental factors can generally be ignored, except for those
already known to be present by virtue of the technical knowledge on the part of the
investigator. For this reason most designs are saturated fractional factorials, but the
resulting confounding of effects in data analysis is, rightly or wrongly, not of partic-
ular concern -- a subsequent ‘confirmation experiment’ will serve to guard against
erroneous results.
Although the wisdom of ignoring interactions has often been questioned, Taguchi
designs have attracted a considerable following, mainly because they make it possible
to use experiments with fewer experimental runs. If such an approach is accepted and
exploited in the thought processes of experimental design, then there are opportuni-
ties to reduce experimental runs in a given investigation to their bare minimum. The
discussion below therefore covers situations where Taguchi’s no-interaction assump-
tion is not categorically rejected.

19.3 RATIONALE OF LEAN DESIGN

The basic principles, explained in terms of common notation used in the literature,
are as follows. In an orthogonal experiment, the maximum number of independent