Assessing the Proportion of Conformance of a Process from a Bayesian Perspective

Abstract

The question of assessing the capability of a process to produce according to some specifications connected with a measurable characteristic (X) of the items produced through it is of great importance in statistical process control. These specifications consist of the lower specification limit (L), which is the minimum acceptable process value; the upper specification limit (U), which is the maximum acceptable process value; and the target value (T), which coincides with the most desirable process value. Process capability indices constitute the most commonly used tool for measuring process capability. Every process capability index combines the values of process specifications, with those of the parameters of the process, that is, the mean (μ) and the standard deviation (σ), takes non-negative values, and its large values provide evidence of a capable process. The development and the estimation of a process capability index simplify substantially when the studied process is assumed to be normally distributed and most of the work that has appeared in the literature on this issue has been based on this assumption. For more details on various aspects of process capability indices, such as properties, estimation techniques, and interrelations, the reader