在系統可靠度的加速壽命試驗中，不同應力下的樣本數配置將會影響正常應力下，系統可靠度推論的精準性。本文考慮兩元件串聯系統之三應力加速壽命試驗的最佳樣本配置問題，其中各元件壽命具獨立指數分配。假設最佳樣本配置比例介於(0, 1/2)，且三應力為妥協設計下，理論推導D-最佳化樣本配置比例之確切解，亦討論其實務意義。此外，三應力中第二應力之兩元件平均壽命若相等，則可理論求其最佳應力水準之設定。最後，輔以實際例子說明使用最佳樣本配置，最多可提高原始設計約40%之相對效率。;In accelerated life tests of system reliability, the accuracy of the reliability inference can be affected by the sample size allocation under different stress levels. Given three stress levels of an accelerated variable, this thesis considers the problem on the optimal allocation for a series system with two independent exponential distributions of the components under accelerated life tests. For a compromise design with the assumption of all optimal allocations being in (0, 1/2), the exact D-optimal sample size allocations are analytically derived and the experimental implication is provided as well. Furthermore, the optimal stress levels are determined when the mean-time-to-failures of the two components are assumed to be equal at the median stress level. The analytic results are illustrated and verified by two real examples. The numerical results show that the relative efficiency of the three-level optimal allocation to the original design can be enhanced at most 40%.
