Cpk index estimation using data transformation

Process capability indices (PCIs) are used in industry to assess percentages of nonconforming parts. An underlying assumption is that the output process measurements are distributed as normal random variables. When normal distributions are assumed, but different distributions are present - such as skew, heavy-tailed, and short-tailed distributions - the percentages of nonconforming parts are significantly different than the computed PCIs indicate. Data arising from nonnormal distributions can sometimes be transformed to conform to the normality assumption and the PCI's computed for the transformed data. In this paper, the effect of the transformation on the estimate of nonconforming parts is examined for three examples of nonnormal distributions - gamma, lognormal, and Weibull. The results of this experimental analysis suggest that data transformation can be useful for estimating an interval for C_pk values and the number of nonconforming parts.