過去在建構加速壽命試驗(Accelerated Life Tests) 的試驗計畫時，主要考量模型參數的設定如何更接近真實參數的數值，以獲得最佳的試驗計畫。一項優良的試驗計畫將使所收集到的觀測值，能有效率的估算壽命分配的描述性統計，例如壽命之百分位數。文獻中提及運用依序貝氏程序，即依序決定物件實驗應力的水準以及利用貝氏估計逐步更新參數訊息的作法，能相較於傳統方法獲得更有效率的試驗計畫。
為了在相同時間之內能更有效率地獲得更精確的估計結果，本研究在依序貝氏的框架下，加入對初始設計規劃的探討，以了解不同初始設計對後續實驗所產生的最佳試驗計畫之影響。主要在一因子與二因子加速壽命模型下進行不同初始設計的規劃，一因子主要考量歷史資料集的樣本數量、設限狀態與應力水準的設定；而由於二因子的加速壽命試驗較為複雜，因此主要關注在設定不同應力水準的組合，包含以傳統的22、32 因子設計、降維計畫與非降維計畫。結果顯示在初始設計應力水準的設定上，影響收集資料有效性的關鍵因素與觀測值的設限機率有關，並且一因子初始設計的規劃應以「低水準」、「平均分配」與「無設限」的歷史資料為主；而二因子則顯示將初始設計規劃在邊界等較低設限機率之處，相對於平均分散在實驗範圍內要來的更有效率。

Before implementing an accelerated life tests (ALT), the main problem is how to set the model parameters closer to the true values to obtain the optimal test plan. In the literature, the sequential Bayesian strategy was proposed and it is thought to be more robust and efficient than the traditional methods. In order to obtain more accurate values of parameter estimation for a limited time, our study proposes the discussion for initial designs. The main objective is to set the initial designs for sequential Bayesian procedure to increase the efficiency of collecting informative data. We plan different initial designs to construct optimum designs for one-factor and two-factor accelerated life tests, respectively. In terms of one-factor ALT, the results show that the stress level settings of historical data should be at the low-stress level or equally balanced levels. For a two-factor ALT, our results show that put observations on experimental boundary where the design points have lower censored probability is more efficient, as compared to equally balanced design on the experimental region.

[1] Annis, J., Miller, B., & Palmeri, T. (2016). Bayesian inference with stan: A tutorial on adding custom distributions. Behavior Research Methods, 49, 863–886.
[2] Elsawah, A. M. (2019). Constructing optimal router bit life sequential experimental designs: New results with a case study. Communications in Statistics Simulation and Computation, 48(3), 723-752.
[3] Escobar, L. A., & Meeker, W. Q. (1995). Planning accelerated life tests with two or more experimental factors. Technometrics, 37(4), 411-427.
[4] Hong, Y., Ma, H., & Meeker, W. Q. (2010). A tool for evaluating time-varying-stress accelerated life test plans with log-location-scale distributions. IEEE Transactions on Reliability, 59(4), 620-627.
[5] King, C. B., Hong, Y., Dehart, S. P., Defeo, P. A., & Pan, R. (2016). Planning fatigue tests for polymer composites. Journal of Quality Technology, 48(3), 227-245.
[6] Lee, I.C., Hong, Y., Tseng, S.T., & Dasgupta, T. (2018). Sequential bayesian design for accelerated life tests. Technometrics, 60(4), 472-483.
[7] Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. New York : Wiley.
[8] Nelson, W. B. (1990). Accelerated testing: Statistical models, test plans, and data analysis. New York : Wiley.
[9] Weaver, B. P., Williams, B. J., AndersonCook, C. M., & Higdon, D. M. (2016). Computational enhancements to bayesian design of experiments using gaussian processes. Bayesian Anal., 11(1), 191-213.
[10] Zhang, Y., & Meeker, W. Q. (2006). Bayesian methods for planning accelerated life tests. Technometrics, 48(1), 49-60.