Process capability indices for non-normal data

Abstract

When probability distribution of a process characteristic is non-normal, Cp and Cpk indices calculated using conventional methods often lead to erroneous interpretation of process capability. Various methods have been proposed for surrogate process capability indices (PCIs) under non-normality but few literature sources offer their comprehensive evaluation and comparison, in particular whether they adequately capture process capability under mild and severe departures from normality, and what is the best method to compute true capability under each of these circumstances. We overview 9 methods as to their performance when handling PCI non-normality. The comparison is carried out by simulating log-normal and data and the results presented using box plots. We show performance to be dependent on the ability to capture tail behavior of the underlying distribution.