A Monte Carlo comparison of capability indices when processes are non‐normally distributed

Abstract

AbstractProcess capability indices are widely used to quantify the ability of a process to produce results on target and within specification limits. The most commonly seen capability indices assume that measurements are taken from normally distributed populations. However, such normality‐based capability indices are very sensitive to departures from normality. Therefore, another non‐normality‐based indices based on the weighted variance method have been developed to deal with non‐normal processes in this paper. Also, a comparison among the Clements, the Johnson–Kotz–Pearn, and the weighted variance methods has been conducted by considering the Johnson family of distributions to generate non‐normal distributions systematically. The results show that the Clements method becomes misleading when the underlying distribution is skewed. On the other hand, the performance of the Johnson–Kotz–Pearn method is far from the nominal values except for the log–normal cases with smaller values of kurtosis. On the other hand, the weighted variance method is the best estimator to estimate the nominal values in unbounded and log–normal cases for different combinations of skewness and kurtosis. It is concluded that the weighted variance method is the best among the three estimators, especially when the underlying distribution belongs to the log–normal and unbounded distributions of the Johnson family. Copyright © 2001 John Wiley & Sons, Ltd.