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題名：最佳置換策略之貝氏分析與圖解法
作者：莊木貴
作者(外文)：Juang, Muh-Guey
校院名稱：國立台灣科技大學
系所名稱：管理研究所工業管理學程
指導教授：林玉斌
學位類別：博士
出版日期：1999
主題關鍵詞：貝氏方法；小修理；置換策略；維護；可靠度；總測試時間；韋伯分配；Bayesian approach；Minimal repair；Replacement policy；Maintenance；Reliability；Total Time on Test (TTT)；Weibull distribution
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本論文旨在應用貝氏分析法和總測試時間圖解法於系統維護策略上，探討最佳之維護策略，在此條件下，本論文包括以下三項研究主題：
1. 使用貝氏分析法，推導出具有小修理年齡置換策略之最佳解．首先藉由小修理、有計劃性與非計劃性置換等策略，推導出長期與置換週期兩種情況之每單位時間期望成本數學公式，並證明在某些合理的條件下，兩種情況 皆具有最佳置換時間唯一且有限解。當失效密度函數具有不確定參數之韋伯分配時，建立貝氏分析表示法及修 正前述之不確定參數，即可導出最佳年齡置換策略。
2. 應用貝氏分析法，推導出調適性預防維護策略之最佳解。結合小修理，維護及置換等策略，推導出每單位時間 期望成本公式，並在某些合理的條件下，証明最佳維護時間與最佳置換時間有唯一及有限解。當失效密度函數 具有不確定參數之韋伯分配時，建立貝氏分析公式，並修正前述之不確定參數，即可導出最佳之維護時間及置 換時間．
3. 另外一種方法稱為總測試時間(TTT)圖解法，它的觀念已被証實為在許多可靠度之應用上是非常有用的一種工具 。因為此種方法，系統的失效分配函數可以不需要特別的指定，僅需要系統（或產品）在測試階段所獲得的完 整樣本資料即可，且求出的最佳置換策略之結果接近於理論上之最佳值。本文係利用TTT圖解法,並藉由小修理 ，有計劃性與非計劃性置換等策略，推導出有衝擊型式的k-out-of-n 系統置換策略之最佳解。
The aim of this thesis is to apply the Bayesian and Total Time on Test (TTT) graphic approach to system maintenance policy, which minimize the expected cost per unit time. The three topics of the thesis may be summarized as follows:
1. We present a Bayesian decision theoretic approach for determining optimal age replacement policy with minimal repair. By introducing costs due to minimal repairs, planned replacement and unplanned replacement we derive the expected cost per unit time for the infinite-horizon case and the one replacement cycle case, respectively. We show that, under certain conditions, there exists a finite and unique optimum policy. A Bayesian decision approach enables us to formally incorporate, express and update our uncertainty when determining optimal age replacement policy with minimal repair.
2. A Bayesian approach is developed for determining an optimal adaptive preventive maintenance policy with minimal repair. By incorporating minimal repairs, preventive maintenance, and replacement, the mathematical formulas of the expected cost per unit time are obtained. We show that there exists a unique and finite optimal maintenance interval and the replacement age under some reasonable conditions. When the failure density follows a Weibull with uncertain (scale, shape) parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal adaptive preventive maintenance policy.
3. An alternative approach is the total time on test (TTT) concept which has proved to be a very useful tool in many reliability applications. Since this method can depend on only the complete sample data obtained in testing phase for system or product, the distribution function need not be specified subjectively and the resulting estimator of optimal replacement policy will be optimal asymptotically. In this thesis we deal with the problem of incorporating minimal repair, planned replacement, and unplanned replacement into a k-out-of-n system subject to shocks for determining an optimal age replacement.
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