Estimation of a Modified Capability Index for Non-Normal Distributions

Abstract

Process capability indices (PCIs), which are very important in quality control have been one of a numerical measure index in manufacturing processes. Index C-pk is the most popular one used in the manufacturing industry. It is applied under the assumption that the processes are normally distributed. In real-world applications, non-normal processes may occur in industries, and the index C-Npk has been proposed for non-normal processes in which its exact sampling distribution is mathematically intractable. Quality practitioners commonly use the existing NCPPM (non-conformities in parts per million) table of C-pk to obtain process yields. However, the table could not be applied directly via the value of index CNpk. For the consistency of NCPPM mapping, we propose procedures to obtain the modified index C-Npk* and its approximately unbiased estimator C-Npk* for three non-normal distributions, involving Log-normal, Gamma, and Weibull distributions. The values of modified index C-Npk* could be used to inquire the existing popular NCPPM table of C-pk. In addition, four bootstrap methods were used to construct the lower confidence bounds of the index C-Npk*, which are useful to the practitioners for making reliable decisions regarding process performance based on process yield.