Evaluating the Capability Index of a Process Integrating Sampling Plan and the Measurement System Number of Distinct Categories NDC

Abstract

To assess the capability of a process, the collected data are influenced by the errors of the used measurement system. This study aims to integrate these errors in determining the acceptance threshold value of the capability index \( C_{p} \) that is referred as in this work. An expression of that depends on the Number of Distinct Categories (NDC), type I and type II errors, the index of the capability process corresponding to both rejectable and acceptable quality levels (CpRQL) and (CpAQL), respectively, was developed. These parameters effects and their existing interactions on the variability in the defective parts per million ppm (Δppm) were examined using a response surface experimental design with a total of 81 runs. Analysis of the results of this experimental design showed that it is possible to propose a technique for overcoming the inaccuracy of the used measurement system by targeting higher CpAQL values as the same value of can be obtained by several combinations of CpAQL and NDC.