近年來，製程能力指標被製造業廣泛的應用在品質監控方面，以評估製程 能力是否合乎水準。大多數的製程能力指標都是假設產品的品質特性在常態分 配下；然而，產品壽命往往是服從非常態分配，例如：指數分配、柏拉圖分配、 韋伯分配等等。對於產品壽命之相關分配，在實務上會利用壽命績效指標L C 來 衡量產品的壽命績效，其中L 是規格下界。在壽命試驗中常因時間限制以及人 力和成本的考量而無法取得完整的樣本資料，使得必須使用設限樣本資料。 本文主要目的是利用產品壽命具有Gompertz 分配之右型Ⅱ設限樣本， (1) (2) ( ) , , , k X X X ，來評估壽命績效指標L C ，並且利用L C 的最大概似估計量發展 一個新的檢定程序與信賴區間。此外，也利用產品壽命來自一個具有雙參數指 數分配之右型Ⅱ設限樣本，建構出壽命績效指標L C 的信賴區間。利用此檢定程 序與信賴區間，可以提供廠商評估產品壽命是否達到要求水準。 In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs assume that the quality characteristic has a normal distribution. However, the lifetime of products frequently possesses an exponential distribution, a Pareto or Weibull distribution etc.. In practice, the lifetime performance index L C is utilized to measure lifetime performance for products with some lifetime distributions, where L is the lower specification limit. In lifetime testing experiments, we may not be able to obtain a complete sample due to time limitation or other restrictions. Therefore, censored samples arise in practice. This research constructs a maximum likelihood estimator (MLE) of L C based on the right type Ⅱ censored sample from the Gompertz distribution. The MLE of L C is then utilized to develop a new hypothesis testing procedure and the confidence interval in the condition of known L . In addition, the confidence interval of L C is also constructed for the two-parameter exponential distribution with the right type Ⅱ censored sample. The purchasers can then employ the new hypothesis and the confidence interval to determine whether the lifetime performance of products adhere to the required level.
