Assessment of a capability index sensitive to skewness

• Published in: Quality and reliability engineering international Vol. 17; no. 4; pp. 233 - 241
• Main Authors: Nahar, P. C., Hubele, N. F., Zimmer, L. S.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.07.2001
• Subjects: bias; form tolerance; gamma distribution; process capability index; Rayleigh distribution; skewed distributions; Wright's capability index
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.395

For many quality characteristics, such as circularity, cylindricity, straightness 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 considerable amount of attention, with new indices being proposed and compared for usefulness and accuracy. This paper is intended to contribute to this growing discussion, and to add a unique focus. In particular, this investigation concentrates on one form of a neoclassical index, the Cs index, originally proposed to be sensitive to skewness and to decrease in value as the skewness 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 interpretation or slightly changing its form is considered. Hence, actual data from circularity measurements are used to identify a relevant group of distributions, and then the accuracy of Cs is investigated along with its modified version for this group of distributions. In particular, this investigation includes several Rayleigh and gamma distributions for various sample sizes and reports on the bias of the proposed estimators. These findings indicate that such a modified index has some useful attributes in reflecting process performance, with respect to the percentage of non‐conformance and the accuracy for relatively large samples. Copyright © 2001 John Wiley & Sons, Ltd.