本研究採用大中取小準則應用於產品可靠度之加速壽命模型並使用粒子群最佳化演算法(particle swarm optimization, PSO) 實現。在過去的研究中，使用巢狀粒子群最佳化(nested PSO) 計算大中取小試驗(minimax design) 會耗費大量的時間，且其隨機撒點的機制可能導致無法收斂到最佳解，因此本研究以提升速率與準確率為目標針對此演算法進行修正。我們的研究主要針對加速壽命試驗常使用的失效模型Lognormal 分配與Weibull 分配進行討論，我們發現加速壽命試驗模型中將原始參數τ = (β0, β1, σ) 轉為參數θ = (pU, pH, σ) 後，在pU, pH 固定下，σ 的變動不會影響我們的目標函數，因此參數搜尋時能將三個參數修改為兩個參數搜尋以提升速率。粒子群最佳化演算法雖然能在沒有太多資訊的情況下，在問題空間內做出有效的搜尋並找出候選解，但其收斂方式無法保證找到的最佳解為全域的最佳解。在我們的研究中也發現使用巢狀粒子群最佳化搜尋參數時，經常會受到局部最佳解影響導致收斂方向錯誤進而得到錯誤的最佳解，並且在多次大中取小試驗中發現其參數的最佳解大部分會落在參數空間的邊界。因此我們根據粒子群最佳化演算法設計一個混合型演算法解決此問題，研究結果表明此演算法能有效找到正確的參數，並且在速率上也有顯著的提升。另一方面，我們在固定的參數範圍下比較兩個設計點與三個設計點在大中取小試驗下的結果，結果表明根據大中取小原則下所找到的最佳設計點，無論在Lognormal 分配與Weibull 分配皆呈現三個設計點的實驗配置為最佳，且Weibull 分配在低應力的佈點會比Lognormal 下低應力的佈點高。此外，我們也將minimax 的結果與過去的研究結果做比較，結果表明minimax 的表現在不同設計參數(planning value) 下皆有不錯的穩健性。

An efficient experiment planning depends on parameters and failure models. However,the true parameters are unknown before the experiment. Setting wrong planning parameters may obtain unreliable lifetime information. Thus, we use minimax design to solve this problem. In this study, we adopt particle swarm optimization (PSO) techniques to find a minimax design for accelerated life test (ALT). Therefore, the purpose of our study is to improve the rate and accuracy of this algorithm. We found that the parameter θ = (pU, pH, σ) used in the accelerated life test model, when pU, pH are fixed, the change of σ does not affect the result of the objective function. Thus, unknown parameters (pU, pH, σ) can be modified into (pU, pH) during parameter search. In many minimax experiments, it is found that most of the optimal solutions of the parameters will fall on the boundary of the parameter space. In the past research, it took a lot of time to calculate the minimax design using nested PSO. Which is often affected by the local optimal solution, resulting in the wrong direction of convergence and get the wrong optimal solution. We design a hybrid algorithm based on the particle swarm optimization algorithm to solve these problems. The results show that this algorithm can effectively find the correct parameters, and the speed is also significantly improved.In the study, we adopt hybrid algorithms to find the minimax designs under Weibull and lognormal models respectively. Comparing the results of two design points with three design points under a minimax experiment with a fixed parameter range, the results show 3-level plan is minimax either for lognormal or Weibull model.

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