本論文以逐步型二設限在韋伯壽命分配下，引用貝氏決策理論建立允收抽樣計畫。假設韋伯分配的形狀參數已知，但尺度參數是隨機的且依照一個已知的先驗分配逐批變動，本論文使用一個包含抽樣成本、檢驗成本以及決策損失的損失函數來描述貝氏風險。此外，本文也提出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，並根據此程序對批量大小、設限計畫表和先驗分配的參數做敏感度分析，進而衡量其影響。

The thesis employs Bayesian decision theory to establish acceptance sampling plans for the Weibull lifetime distribution based upon progressively Type-II censored data. Assume that the shape parameter of the lifetime distribution is known, but the scale parameter is random and varies from lot to lot according to a predetermined prior distribution. A loss function involving sampling cost, test cost and decision loss is proposed to describe the Bayes risk. Moreover, an algorithm is suggested to determine the optimal sampling plans which minimize the expected average cost per lot. A sensitivity analysis study is conducted to evaluate the influences of the lot size, the censoring scheme and the parameter of the prior distribution on the proposed sampling plans.

1. Introduction                                     -1-
2. Acceptance Sampling Plans with Progressive Type-II Censoring                                           -6-
3. Numerical Study and Sensitivity Analysis         -15-
4. Conclusions                                      -27-
Bibliography                                        -30-

list of figures
2.1 Flowchart of finding the optional sampling plans 14
3.1 The ECPI for different lot sizes with the Schemes I,II
and III for B=0.8, a=4.0,b=1.8                       24
3.2 The ECPI v.s. the Schemes I, II and III for different values of a when N=800, B=0.8 and b=1.8              25
3.3 The ECPI v.s. the Schemes I, II and III for different values of b when N=800, B=0.8 and a=4                26

list of tables
3.1 Optional sampling plans for B=0.8, a=4.0, b=1.8, r=0.7, cs=0.7, and ct=8                                     21
3.2 Sensitivity analysis for the sampling plan as the prior
parameter a changes                                  22
3.3 Sensitivity analysis for the sampling plan as the prior
parameter b changes                                  23

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