產品可靠度 (reliability) 是決定消費者挑選產品之重要影響因素，因此如何從眾多供應商中，建構適當的擇優挑選法則 (selection rule) 來挑選出具有能生產高可靠度產品能力之最佳供應商是生產者經常面臨之重要決策問題。 本研究在假設供應商之產品衰變路徑服從逆高斯衰變模型，探討如何建構適當之擇優法則及規畫衰變試驗之最適實驗配置 (包括測試樣本、觀測頻率及終止時間) 之決定。 具體而言，在確保可正確挑選出最佳供應商之機率達到給定的 P^* 及做錯誤決策機率要小於 α^* 下，決定可使得實驗總成本極小化之最適配置。 最後並舉例說明如何使用本文所建構之挑選法則；與傳統的挑選法則相比較，可發現本研究所建構的挑選法則之最大優點是可以有效地降低實驗所需的樣本數及總實驗時間。

At the research and development (R & D) stage, the manufacturers may wish to select the most reliable product (supplier) from among several competing products (suppliers). In this study, assuming the degradation paths of product’s quality characteristics come from an inverse Gaussian degradation process, we first apply locally optimal (LO) criterion to construct a suitable selection rule. Furthermore, with a minimum guarantee of probability of correct selection (CS) of the proposed rule, we deal with the optimal design of a degradation experiment (which includes the determinations of the sample size, sampling frequency and the termination time) in such a way that the total experimental cost can be minimized. Finally, we use an example to demonstrate the proposed procedure. From the results, it shows that our proposed procedure has the ability of substantially reducing the sample size and termination time, which are needed to conduct a degradation experiment.

第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 研究架構 3
第二章 文獻探討與問題描述 4
2.1 衰變模型簡介 4
2.2 動機例子 8
2.3 衰變模型之擇優問題簡介 10
2.4 局部最佳擇優法則 11
2.5 問題描述 13
第三章 逆高斯衰變試驗擇優之最佳設計 15
3.1 形狀參數相等且已知下之擇優問題 15
3.1.1 模型參數估計 15
3.1.2 LO挑選法則 17
3.1.3 最佳化衰變試驗設計 19
3.1.4 實例分析 21
3.1.5 敏感度分析 (sensitivity analysis) 26
3.2 形狀參數相等但未知下之擇優問題 29
3.3 形狀參數未知下之擇優問題 32
第四章 結論與後續研究 34
4.1 結論 34
4.2 後續研究 34
附錄 36
附錄一 引理3.1證明 36
附錄二 定理3.1證明 37
附錄三 定理3.2證明 37
附錄四 (4.1) 證明 39
參考文獻 41

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