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1 行政院國家科學委員會專題研究計畫完整報告 衰變率服從 reciprocal Weibull 分配之加速衰變試驗、 部份因子實驗設計和最佳計樣式挑選問題的最 佳化設計 (1/2~2/2) 計畫編號： NSC 94-2213-E-150-013 執行期限： 94 8 1 日至 96 7 31 主持人：于鴻福 虎尾科技大學工業管理學系 ※第一年部份： 一、中文摘要 由於現今高可靠度產品的壽命很 長，所以如何改善與提升其產品可靠度， 已成為製造商的一大挑戰。針對衰變率服 從對數常態分配之解析度 III 的篩選實 驗， Yu & Chiao (2002) 曾探討如何決定各 (run) 試驗下，樣本數、量測頻率和終 止時間的最佳組合問題。惟在實際應用 上， lognormal 分配與 Weibull 分配極為 相似，在資料分析時常造成工程人員的混 淆與誤判。此二種分配的錯誤判定，將會 導致可靠度資訊估計的嚴重偏差 (bias) 本 計 畫 將 探 討 衰 變 率 服 從 reciprocal Weibull 分配之解析度 III 之篩選實驗的最 佳化設計問題。首先我們將提出一具直觀 優點的判別準則，其次在給定此一準則之 正確挑選的最小機率與不正確挑選的最 大機率的限制下，決定各次試驗下之樣本 數、量測頻率和終止時間的最佳組合，以 最小化實驗的總費用。 關鍵詞：解析度 III 、衰變率、量測頻率、 試驗終止時間、 reciprocal Weibull 分配 Nowadays, due to the long lifetime, how to improve the reliability of highly reliable products is a great challenge to the manufacturers. With respect to a resolution III experiment with a linearized degradation model where the degradation rate follows a lognormal distribution, Yu & Chiao (2002) addressed the problem of how to determine the optimal settings of decision variables such as the inspection frequency, the sample size, and the termination time for each run, which are influential to the precision of identifying significant factors and the experimental cost. In practical applications, Weibull and lognormal distributions are much alike. They may fit the lifetime data well. However, their predictions may lead to a significant difference. This project deals with the optimal design of a resolution III experiment with a linearized degradation model where the degradation rates follow reciprocal Weibull distributions. First, an intuitively appealing identification rule is proposed. Next, under the constraints of a minimum probability of correct decision and a maximum probability of incorrect decision of the proposed identification rule, the optimal test plan is derived by using the criterion of minimizing the total cost of experiment.

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