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，在實務上可利用壽命績效指標 來衡量產品的壽命績效，其中 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Rayleigh分配或Gompertz分配之逐步右型Ⅱ設限樣本， ，來評估壽命績效指標 ，並且利用 的最大概似估計量發展一個新的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的水準。 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 is utilized to measure lifetime performance for products with some lifetime distributions, where 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. In this thesis, we construct a maximum likelihood estimator (MLE) of based on the Progressively type Ⅱ right censored sample from the Rayleigh distribution and the Gompertz distribution. The MLE of is then utilized to develop a new hypothesis testing procedure and the confidence interval under the condition of known . 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.
