Capability Testing Based on C_(pm) with Multiple Samples

摘要

Numerous process capability indices have been proposed in the manufacturing industry to provide unitless measures on process performance, which are effective tools for quality improvement and assurance. Most existing methods for capability testing are based on the distribution frequency approaches. Recently, Bayesian approaches have been proposed for testing capability indices C_p and C_(pm) but restricted to cases with one single sample. In this paper, we consider estimating and testing capability index C_(pm) based on multiple samples. We propose accordingly a Bayesian procedure for testing C_(pm). Based on the Bayesian procedure, we develop a simple but practical procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset capability requirement. A process is capable if all the points in the credible interval are greater than the pre-specified capability level. To make the proposed Bayesian approach practical for in-plant applications, we tabulate the minimum values of C~*(p) for which the posterior probability p reaches various desirable confidence levels.