Assessment of a capability index sensitive to skewness

For many quality characteristics, such as circularity, cylindricity, straig htness and flatness, positive skewness in the inspection data is the norm, and, in fact, is desirable. Summarizing the process performance using such data in conjunction with capability indices has recently received a conside rable amount of attention, with new indices being proposed and compared for usefulness and accuracy. This paper is intended to contribute to this grow ing discussion, and to add a unique focus. In particular, this investigatio n concentrates on one form of a neoclassical index, the C-S index, original ly proposed to be sensitive to skewness and to decrease in value as the ske wness increased in the underlying distribution of the data. In other words, 'skewness is badness'. Looking at this index from an altered perspective, the possibility that this index could serve a useful purpose in summarizing process performance for such non-normal processes by merely changing its i nterpretation or slightly changing its form is considered. Hence, actual da ta from circularity measurements are used to identify a relevant group of d istributions, and then the accuracy of C-S is investigated along with its m odified version for this group of distributions. In particular, this invest igation includes several Rayleigh and gamma distributions for various sampl e sizes and reports on the bias of the proposed estimators. These findings indicate that such a modified index has some useful attributes in reflectin g process performance, with respect to the percentage of non-conformance an d the accuracy for relatively large samples. Copyright (C) 2001 John Wiley & Sons, Ltd.