Non-normal Capability Indices for the Weibull and Lognormal Distributions

Abstract

Because the normal process capability indices (PCIs) Cp, Cpu, Cpl, and Cpk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs Pp, Ppu, Ppl, and Ppk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard Cp, Cpu, Cpl, and Cpk if a short-term variance is analyzed. An application to a set of simulated data is presented. Copyright © 2015 John Wiley & Sons, Ltd.