衰變試驗被廣泛應用於評估高可靠度產品的壽命資訊。在可容許的變異水準下，制定具成本效益的試驗計畫，對製造商而言能大幅提升經濟效益。本研究以常見隨機過程之衰變模型為基礎，在精確度限制下，理論推導最低成本試驗計畫中各決策變數包含樣本數、測量間隔時間及測量次數之存在且唯一之充分必要條件。此外，本研究進一步推導各決策變數對總成本之影響變化率，以排序其重要性，並分析實驗成本、模型參數及精確度對決策變數重要性排序之影響。最後，藉由實例驗證理論結果，呈現精確度限制之變動與總成本變化間的關係，為決策者制定試驗計畫提供具體參考。本文提出以最低試驗成本為目標之最佳試驗計畫，大幅降低數值搜尋法的計算時間，提供更具實務需求的應用價值。;Degradation tests are widely used to evaluate lifetime information for highly reliable products. Under an allowable level of variability， developing a cost-effective experimental plan can substantially improve economic benefits for manufacturers. Based on degradation models derived from commonly used stochastic processes， this study theoretically derives the necessary and sufficient conditions for the existence and uniqueness of the minimum-cost test plan under precision constraint. The decision variables include the sample size， measurement period， and number of measurements. Furthermore， the rates of change in total cost with respect to each decision variable are discussed to rank their relative importance， while the effect of experimental costs， model parameters， and precision requirements on the importance rankings are also investigated. Finally， two numerical examples are provided to verify theoretical results and illustrate the relationship between the precision constraints and total cost changes， providing references for decision-makers. By minimizing testing costs， the proposed optimal test plan drastically reduces the computational time of numerical searches， offering greater practical applicability.
