在本篇論文中，我們在形狀參數己知的韋伯壽命分配之下，根據不同的貨批大小去檢驗貝氏單次抽樣計畫。我們更進一步的假設尺度參數是隨機的，它是根據每批不同的先驗分配而有所變動。若產品是在保證政策下出售， 而且檢驗設備的個數受限時，考慮成本函數的模型包含檢驗成本， 接受成本和拒絕成本，本論文提出了一個能找出最小化每單位平均成本的最佳貝氏允收抽樣計畫程序，並且根據此程序對產品壽命和先驗分配的參數做敏感度分析。

In this thesis, we examine a Bayesian single sampling plan for lot by lot sampling under Weibull lifetime istribution with　known shape parameter; moreover it is assumed that the scale parameter is random and varies from lot to lot according to a　predetermined prior distribution. If products are sold under a warranty policy and the size of test equipments is limited. A cost model is established which involves test cost, accept cost, and reject cost. An algorithm of finding the optimal sampling plans with minimizing the expected average cost per lot is provided, and sensitivity analyses for the parameters of the lifetime and prior distributions are conducted.

Contents
1 Introduction 1
2 The Sampling Plan 6
3 Numerical Study and Sensitivity Analysis 16
4 Conclusions 27
Bibliography 28
List of Figures
1 Flowchart of finding the optimal sampling plans. . . . . . . . . . . . . . 15
2 Percentage errors in using incorrect values of β, a, and b when true
values are β = 0.8, a = 3, b=875 . . . . . . . . . . . . . . . . . . . . . 25
3 Percentage errors for different values of β, when true values are β = 0.6,
1.0, and 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
List of Tables
1 Optimal Sampling Plan for β = 0.8, a = 3.0, b = 875, w1 = 180,
cs = 2.8, ct = 0.8, cp = 2.5 and ca = 9.5. . . . . . . . . . . . . . . . . . 19
2 Searching Procedures for the proposed sampling plan with β = 0.8,
a = 3.0, b = 875, w1 = 180, w2 = 360, cs = 2.8, ct = 0.8, cp = 2.5 and
ca = 9.5 under nL =70. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Optimal Sampling Plan for selected combinations of parameters β, a
and b under nL = 70 when N = 600. . . . . . . . . . . . . . . . . . . . 24

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