Page 273 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

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258 Strategies for Experimentation under Operational Constraints
With the size of experiment (number of observations) reduced to its limit, it is still
commonplace in industry for an experimental design to be found impossible to imple-
ment because of operational constraints. Such concerns are addressed in this chapter,
with the emphasis more on the feasibility of the suggested expedient procedures than
their theoretical rigor. In the following discussions, the notation used by Box et al. 1
2
and Taguchi will be used without explanation.

17.2 HANDLING INSUFFICIENT DATA

One basic requirement in the application of design of experiments is that the experi-
mental data stipulated in the design matrix (orthogonal array) must all be available
beforeanyanalysiscanbeinitiated.Thus,inaneight-rundesign,regardlessofwhether
it is a full or fractional factorial, all eight observations are needed for any assessment
of the effects of the factors under study. Regular data analysis of an experiment may
have to be abandoned if any of the planned observations turns out to be unavailable.
Incomplete data availability could happen for various reasons. One is technical; for
example, certain combinations of factor settings may be physically difficult to arrange,
or found undesirable from a safety point of view. Another is cost and time, as certain
factor combinations may entail long setup time or total process time, or consumption
of large amounts of test material. Yet another reason could be missing experimental
data due to unexpected shortage of raw materials, equipment breakdown, mishan-
dling of samples, or inadvertent loss of records. If the textbook data requirements
cannot be fulfilled, the investigator may not be able to salvage the experimental ef-
4
fort. Some theoretical studies of such problems have been done in the past; one
related problem formulation is the inclusion, in a saturated experimental design, of
more effects to be estimated than such a design would normally be able to handle. 5−8
There is another consequence of the requirement of complete data availability. An
5
investigatorlaunchingalargeexperiment,saya2 factorial,whilehavingastatistically
superior design in terms of resolution of factor effects, may, in the face of industry
demands for interim results, progress reports, or early decision indicators, be at a
disadvantage compared to someone who uses a 2 5−2 design in the first instance,
makes some quick assessments based on the first eight data points, and goes for
another follow-up 2 5−2 experiment only when necessary. This leads to the strategy
9
of sequential experimentation, with which savings in data collection would also be
10
possible. Much is made of the effect sparsity found in industrial experiments, so that
a number of effects can be reasonably assumed zero to facilitate the analysis of small
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experiments. This is taken one step further in lean designs where, making use of part
ofanorthogonaldesignmatrix,resultsareobtainedwithincompletedatasets;thisisto
suit situations ranging from some stop-gap, preliminary round of study to desperate
damage control for an unsatisfactorily completed experiment. Against this backdrop,
several variations of experimental design procedures will now be presented.

17.3 INFEASIBLE CONDITIONS

The nature of an orthogonal experimental design matrix is such that it contains a pre-
scribed number of mandatory combinations of factor settings. Situations could arise