雙邊規格多品質特性製程能力指標CpkT的信賴下界

Abstract

製程能力指標經常被用來衡量製程製造產品符合規格的能力，不僅是提供品質保證的工具，也是提供品質改善方面的一個方針。尤其指標Cpk是目前製造業中使用最多、最廣泛的指標。現今高科技製程具有多品質特性，但Cpk僅適用於製程只有單一產品品質特性的時候。為了能更精確的得到多品質特性製程的良率Pearn (2011) 等學者由Cpk推廣出新指標CpkT。本文中我們考慮CpkT的常態近似分配，用模擬方法檢測其誤差，再根據誤差大小決定適當的樣本數。接著我們在適當的樣本數的情況下，使用四種Bootstrap方法模擬出信賴下界，然後根據覆蓋率與平均數，與近似分配產生的信賴下界做比較。

Process capability indices (PCIs) have been proposed in the manufacturing industry to provide yield measures on process capability, which are effective tools for quality assurance and guidance for process improvement. In particular, the index Cpk is the most popular capability index widely used in the manufacturing industry. Nowadays, high-technology processes have a variety of quality characteristics; however, the index Cpk is only investigated the process with single characteristic. In order to obtain accurate yield assessment for processes with multiple characteristics, a new capability index CpkT, which is a generalization of the index Cpk, has been proposed. In this thesis, we consider a normal approximation distribution of CpkT, and conduct a simulation method to detect the distribution. For the purpose of measuring the accuracy of the approximate distribution of CpkT, a nonparametric but computer intensive method called the bootstrap is used to obtain a lower confidence bound. Also a comparison between the bootstrap and approximate distribution based on coverage rate and mean of lower confidence bound are executed.