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References 221
Table 14.5 Sensitivity analysis of Q when p is changed.
p/p Q/Q p/p Q/Q
10 % 26 % −10 % −24 %
20 % 32 % −20 % −49 %
30 % 115 % −30 % −62 %
40 % 199 % −40 % −88 %
50 % 217 % −50 % −122 %
60 % 296 % −60 % −153 %

14.6 DISCUSSION

In this chapter the problem of nonnormality for geometrically distributed quality
characteristics is discussed and some transformation techniques that can be used to
transform a geometrically distributed quality characteristic to normal are studied.
With the transformed data, standard statistical process control software which com-
putes control limits based on 3σ can be used. Furthermore, procedures based on other
process control techniques such as EWMA or CUSUM can be used. It seems that the
Anscombe or log transformation, although it is reasonably simple and can be used
for raw observations, is not appropriate for a geometric distribution.
5
The Q transformation of Quesenberry might perform better, but assumes that the
model parameter is known or estimated and is sensitive to the error of the estimated
parameter. AsensitivityanalysishasbeenconductedontheQtransformation. Itseems
that the Q transformation is sensitive to changes in p. The double square root transfor-
mation has been shown to be appropriate and the procedure is easily implemented.

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