本篇論文研究隨機失效產品的最佳檢驗策略，考慮產品在使用期只執行唯一一次檢驗。在檢驗執行後，此產品不是進行矯正性置換就是進行預防性置換。此外，為了探討成本的時間價值對最佳單次檢驗策略的影響，在檢驗與置換的執行時間不可忽略的情形下，本論文建立了兩個檢驗模型。第一個模型忽略成本的時間價值，換言之，模型的建立排除了貼現因子。第二個模型則包含了貼現因子以將成本的時間價值納入考量。針對這兩個檢驗模型，除了對最佳檢驗時間的求算進行詳盡的探討外，同時建立了兩套演算法，藉以尋求這兩個模型的最佳單次檢驗策略。最後，在產品服從失效率遞增的韋伯分配下，藉由敏感度分析進一步觀察成本參數與貼現因子的變化對這兩個模型的最佳單次檢驗策略所造成的影響。

This thesis investigates the optimal inspection policies for a stochastically failing item with a single inspection during its lifetime. Following the inspection, the item must be replaced either correctively or preventively. Furthermore, to perceive the effects of the time value of cost on the optimal single-inspection policies, two inspection models are built, in which the time required for the inspection and replacement is non-negligible. The time value of cost in the first model is overlooked, that is, the discount factor is excluded from this model. The second model incorporates the discount factor to take the time value of cost into account. For both inspection models, the derivation of the optimal time epoch for inspection is discussed in detail and two algorithms are established to find their respective optimal single-inspection policies with ease. Finally, a sensitivity analysis is conducted to observe the effects of varying cost parameters and discount factor on the optimal single-inspection policies corresponding to these two models while the item follows the Weibull distribution with an increasing failure rate.

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