A General Multivariate Bayesian Process Capability Index

Abstract

Process capability analysis is designed to estimate the proportion of parts that do not meet engineering requirements in a stable production process. In this paper, we review and criticize the capability indices that are typically used in industry for this purpose, and we propose a general multivariate Bayesian capability index which contains the conventional index as a limiting case. We further derive its analytical expression under standard assumptions, discuss numerical approximations and illustrate the theory with some examples.