多品質特性製程的製程能力指標 CpkT 的分布和推論

Abstract

Process capability index Cpk has been popularly used in the manufacturing industry for measuring process performance based on yield (proportion of conformities). Most researches on Cpk focus on processes with single quality characteristic; but in many real applications, a process often has multiple quality characteristics. In this study, we extend Cpk to a new index CpkT for processes with multiple characteristics. We prove that the inequalities that link Cpk to the yield also hold for the new index. A natural estimator of CpkT_hat is provided and a normal approximation to its distribution is derived. With this normal approximation, standard processes for statistical inferences such as hypothesis testing and confidence interval are developed for testing whether the process is capable and providing an interval estimate on CpkT, respectively. More importantly, we can obtain a confidence lower bound for CpkT, which measures the minimum process capability and is directly linked to quality assurance of products. The accuracy of the normal approximation is studied by simulation. Finally, we demonstrate how the new index CpkT as well as the inferential procedures developed in this study can be used with a real example of a dual-fiber tip process.