預測市場回饋區間資料的失效率對於製造商來說是一個重要的課題，本論文主要在探討三種模型韋伯(Weibull)、Burr XII 及 Gamma-Weibull(Gamma frailty based on Weibull distributions)分配在區間設限資料的情況下，透過最大概似估計法(Maximum Likelihood Estimation)進行評估衡量。本文將採用DE(Differential Evolution)演算法來求得最大概似估計值，參數之區間估計亦可求得。市場回饋區間資料亦可用來分析及應用。由本研究案例分析結果可得知，Gamma-Weibull 在AIC值上，表現得比其他兩種模型來的出色，因此我們建議使用Gamma-Weibull模型來分析市場回饋區間資料。

Predicting failure rate from the field return data is an important task for manufacturers. In this study, we compare three models: Weibull, Burr XII and Gamma frailty based on Weibull (Gamma-Weibull) distributions and evaluate performance their through maximum likelihood estimation (MLE) via Differential Evolution (DE) with interval censored data. In addition, the confidence intervals are obtained. The field return data are used as an example to illustrate the applications. The results show that the Gamma-Weibull model outperforms the other two models in term of AIC. Thus, we recommend using Gamma-Weibull model to do analysis on field return data.

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