- 學位論文
雙參數指數分配產品的壽命績效指標在多重型II設限下之統計檢定程序
Computational Testing Algorithmic Procedure of Assessment for Lifetime Performance Index of Products with Two-parameter Exponential Distribution Based on the Multiply Type II Censored Sample.
摘要
近年來，產品品質的評估、控管與改善變成生產廠商的一個非常重要的課題。在實務上，已經發展了很多種方法來評估產品的品質能力，製程能力指標(process capability indices, PCIs)就是其中一種方法。大部分的PCIs皆是在常態分配的假設下發展或研究的，但產品壽命往往服從非常態分配，例如指數(exponential)、伽瑪(gamma)或者是韋伯(Weibull)分配等，所以本研究考慮雙參數指數分配。而在壽命試驗中常因成本、時間、人為疏失或其他限制而導致無法取得完整的樣本資料。本文的研究目的即在多重型II設限(multiply type II censoring)下評估產品壽命在服從雙參數指數分配(two-parameter exponential distribution)的壽命績效。 本研究使用了十四個估計量包括十二個加權動差估計量(weighted moments estimators, WMEs)、近似最大概似估計量(AMLE)和最佳線性不偏估計量(BLUE)去估計尺度參數 ，代入壽命績效指標 後以估計 ，在點估計方面，我們研究了這十四種壽命績效指標估計量的偏誤(Bias)與均方差(MSE)，在最小均方差的準則下，選出最佳的估計量。而且在規格下界 為已知的情況下，我們提出一個假設檢定的演算程序，以檢定產品之壽命績效指標是否達到給定的水準。最後，我們提供了兩個數值實例，來示範如何利用多重型II設限樣本，檢定產品之壽命績效指標是否達到所要求的水準。 表單編號：ATRX-Q03-001-FM030-01
並列摘要
In recent years, it's an important issue for manufacturers to assess, monitor and improve product quality and performance. Process capability indices (PCIs) are used to evaluate whether product quality meets the required level in many industries. Since the lifetime of products may not be normal distribution and it may follow an exponential, gamma or Weibull distribution, etc. On the other hand, the experimenters may not be able to obtain the lifetime of all products which are put on test due to the limitation of cost, time or artificial difficulties in data collection. Therefore, we assess the lifetime performance index of products for a two-parameter exponential distribution base on the multiply type II censored samples. We use 14 estimators including 12 weighted moments estimators (WMEs), approximate maximum likelihood estimator (AMLE) and best linear unbiased estimator (BLUE) to estimate the scale parameter and then we can obtain 14 estimators of the process capability index . The bias and mean square error(MSE) of 14 estimators are simulated and the optimal estimator is identified in the sense of minimum MSE. We also propose a hypothesis testing algorithmic procedure for practitioners to determine whether the lifetime of products meet the required level. Finally, two real-life examples are given to demonstrate the testing algorithmic procedure. 表單編號：ATRX-Q03-001-FM031-01