Estimation of differences between process capability indices Cpm or Cpmk for two processes

In this article, the estimation of the difference between the values of process capability indices C-pm or C-pmk for two processes is considered. Point estimators of such types of differences are defined, separately for each of the two indices, and their distributional properties are investigated. Formulae for the moments, the expected value, and the variance of these estimators are derived as well. Moreover, the assessment of confidence intervals for the true values of the differences of either C-pm or C-pmk is described using three alternative bootstrap techniques. The performance of these intervals seems to be rather satisfactory, as shown via simulation. It should be noted that the assessment of such confidence intervals has real practical value, since it can be implemented to several problems arising in real-world applications, such as the selection of the superior between two candidate suppliers of an industry.