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References 129
though more tedious, seem to provide estimates of C pu that truly reflect the capa-
bility of the process. In particular, for the lognormal distribution, which has a heavy
tail, other methods severely overestimate C pu . This can easily be explained by the fact
that, under the normality assumption, C p and C pk jointly determine the proportion of
nonconforming items, p. If the process distribution is not normal, this relation is no
longer valid. Thus, unless a proposed method is able to provide a PCI that captures
such a relation, the surrogate PCI value will not give an objective view of the real
capability of the process in terms of p. The simulation results have supported this, as
the performance of a method depends on its capability to capture the behaviour of
the tail of the distribution. A method that performs well for a particular distribution
may give erroneous results for another distribution with a different tail behavior. The
effect of the tail area is quite dramatic (see case studies in Chapter 10), especially for
more capable processes.
Though computer-intensive, the Box--Cox transformation method yields highly
ˆ
consistent and accurate C pu values for all the distributions investigated with reason-
able sample size (n ≥ 100). This is evident from the simulation results. Today, most
process capability studies and analyses are carried out using computers. Therefore the
computer-intensive nature of the Box--Cox transformation is no longer a hindrance
to practitioners. The accuracy of the Box--Cox transformation method is also robust
to departures from normal. Therefore this avoids the trouble of having to search for
a suitable method for each distribution encountered in practice. The PCIs calculated
using the Box--Cox transformation method will definitely give practitioners a more ac-
curate picture of a process’s capability, especially in terms of p. Nevertheless, for each
reference under various applications a practitioners’guide is proposed that shows the
methods applicable for each defined range of skewness and kurtosis.

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