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9

Computing Process Capability

Indices for Nonnormal Data: A

Review and Comparative Study

L. C. Tang, S. E. Than and B. W. Ang

When the distribution of a process characteristic is nonnormal, the indices C p and C pk ,
calculated using conventional methods, often lead to erroneous interpretation of the
process’s capability. Though various methods have been proposed for computing sur-
rogate process capability indices (PCIs) under nonnormality, there is a lack of literature
offering a comprehensive evaluation and comparison of these methods. In particular,
under mild and severe departures from normality, do these surrogate PCIs adequately
capture process capability, and what is the best method for reflecting the true capa-
bility under each of these circumstances? In this chapter we review seven methods
that are chosen for performance comparison in their ability to handle nonnormality
in PCIs. For illustration purposes the comparison is carried out by simulating Weibull
and lognormal data, and the results are presented using box plots. Simulation results
show that the performance of a method is dependent on its capability to capture the
tail behavior of the underlying distributions. Finally, we give a practitioner’s guide
that suggests applicable methods for each defined range of skewness and kurtosis
under mild and severe departures from normality.

9.1 INTRODUCTION

Process capability indices (PCIs) are widely used to determine whether a process is
capable of producing items within a specific tolerance. The most common indices, C p

This chapter is based on the article by L. C. Tang and S. E. Than, ‘Computing process capability indices for
non-normal data: a review and comparative study’, Quality and Reliability Engineering International, 15(5),
1999, pp. 339--353, and is reproduced by the permission of the publisher, John Wiley & Sons, Ltd
Six Sigma: Advanced Tools for Black Belts and Master Black Belts L. C. Tang, T. N. Goh, H. S. Yam and T. Yoap
C 2006 John Wiley & Sons, Ltd
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