製程能力指標Cpmk的近似不偏估計量

Abstract

在於現今的業界之中，製程能力指標已經被廣泛地運用於評估產品是否符合規格與提供品質保證，進而達到品質改善的效果。在眾多指標當中，Cpmk常常被用來衡量製程或產品品質，但Cpmk的估計值為偏誤估計，而為了使業界更方便且精準的評估製程，因此，在本篇研究當中我們提出了一個修正係數來並利用curve fitting使Cpmk指標的估計量為近似不偏估計量。但在實際業界的製程當中，由於製程的參數μ和σ為未知，所以我們無法求得修正係數，因此，我們又利用複式模擬bootstrap方法求出參數的估計量近而計算求得ξ，並帶入修正因子得以找到Cpmk的近似不偏估計量。

In today's industry, the process capability indices (PCIs) have been extensively used to measure whether the process is in line with the specifications and they provide quality assurance, further achieve quality improvement at the same time. In the process capability indices, the index Cpmk, an useful index, is widely used to evaluate manufacturing yield and quality, but the estimator of Cpmk is biased. For the industry can evaluate manufacturing yield comfortably and precisely. Therefore, in this thesis, we propose a correction factor cf and use curve fitting by the computer program Matlab to calculate approximately unbiased estimator. However, in the real industry, the process parameters μ and σ are unknown, so that we use bootstrap method by Efron (1979, 1982) to obtain the ξ. Then, we can calculate correction factor cf to obtain the approximately unbiased estimator of Cpmk.