Volume 20, Issue 8 p. 787-805
Research Article

A Method of Estimating the Process Capability Index from the First Four Moments of Non‐normal Data

Jianmin Ding

Corresponding Author

Agere Systems, 555 Union Boulevard, Allentown, PA 18109, U.S.A.

Agere Systems, 555 Union Boulevard, Allentown, PA 18109, U.S.A.===Search for more papers by this author
First published: 25 October 2004
Citations: 15

Abstract

A method is presented to estimate the process capability index (PCI) for a set of non‐normal data from its first four moments. It is assumed that these four moments, i.e. mean, standard deviation, skewness, and kurtosis, are suitable to approximately characterize the data distribution properties. The probability density function of non‐normal data is expressed in Chebyshev–Hermite polynomials up to tenth order from the first four moments. An effective range, defined as the value for which a pre‐determined percentage of data falls within the range, is solved numerically from the derived cumulative distribution function. The PCI with a specified limit is hence obtained from the effective range. Compared with some other existing methods, the present method gives a more accurate PCI estimation and shows less sensitivity to sample size. A simple algebraic equation for the effective range, derived from the least‐square fitting to the numerically solved results, is also proposed for PCI estimation. Copyright © 2004 John Wiley & Sons, Ltd.

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