淡江大學機構典藏:Item 987654321/33885
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    题名: Gompertz分配產品之壽命績效的評估
    其它题名: Assessing the lifetime performance for the products with Gompertz distribution
    作者: 吳亭潔;Wu, Ting-chieh
    贡献者: 淡江大學統計學系碩士班
    吳錦全;Wu, Chin-chuan
    关键词: Gompertz 分配;雙參數指數分配;右型Ⅱ設限樣本;壽命績效指標;最大概似估計量;蒙地卡羅模擬;Gompertz distribution;Two-parameter exponential distribution;Type Ⅱ censored sample;Lifetime performance index;Maximum Likelihood Estimator;Monte Carlo Simulation
    日期: 2009
    上传时间: 2010-01-11 04:38:02 (UTC+8)
    摘要: 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.
    显示于类别:[統計學系暨研究所] 學位論文

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