雙邊規格CNpk信賴下界複式抽樣計算方法

Abstract

製程能力指標廣泛地被用來評估製程產出產品是否符合規格的重要工具，不僅能提供品質保證，也是提供品質改善方面的一個方針。其中又以雙邊規格Cpk指標在製造業中使用最多、最廣泛的指標。但Cpk僅於製程資料服從常態分配時適用，本篇研究考慮Pearn and Chen(1997)提出之CNpk指標，能夠在製程資料為非常態分配時也能精確的評估製程良率，然而該指標估計式的抽樣分配不易求得，因此，本篇研究應用複式抽樣法建構出指標之四種信賴下界，並利用校正因子D來改善樣本分配，提出一新估計量進行求算，最後比較在不同的參數變化下四種信賴下界之涵蓋率，模擬結果顯示，bootstrap-t方法較其他方法為佳，即其涵蓋率與預先要求之信賴水準最為接近。

The process capability indices (PCIs) have been extensively used to measure whether the process meets the specifications and they provide quality assurance and guide a principal for quality improvement at the same time. Cpk is the most popular index used in the manufacturing industry. However, Cpk is only appropriate for process under normal distribution. Pearn and Chen (1997) proposed the capability index CNpk for non-normal process. However the exact sampling distribution of CNpk is mathematically intractable. Thus, in this paper, we apply bootstrap methods to construct four lower confidence bound methods of the index. We also modify the sample percentile deviation by a correction factor, called D, and we propose a new estimator to calculate process capability. Under different parameter setting, we compare the coverage rates of the four lower confidence bound methods, and the simulation results showed that bootstrap-t method outperformed the other methods since its coverage rate and pre-determined confidence level is closest.