本文假設電火工品壽命服從韋伯分佈,電火工品為高可靠度的產品,由於成本昂貴以致於在試驗上通常樣本數不會太大,對於此類高靠度的產品必須採用加速失效試驗來加速產品失效以利分析,假設韋伯分佈中尺度參數與加速應力存在對數線性關係,我們使用最大概似與貝氏方法,探討在正常應力下電火工品的期望壽命與可靠度函數之統計推論。在貝氏分析中,本文將失效機率之先驗分佈轉換為模型中參數之先驗分佈,並分別考慮以動差和眾數來決定先驗分佈之超參數,由馬可夫鏈蒙地卡羅方法得貝氏估計。模擬結果顯示,貝氏方法所得結果優於最大概似方法。考慮在貝氏方法下,若先驗訊息較不確定時,以眾數方法所決定的先驗分佈所得結果較佳。另外我們也考慮電火工品之貝氏零失效可靠度示範實驗,以產品是否達到預期之標準,求得實驗所需之最小樣本數與最短試驗時間之組合。

Due to the high reliability and high testing cost of electro-explosive devices, we consider an accelerated failure experiment in which the lifetime following a Weibull distribution with scale parameter being related to the accelerated variable. We use the maximum likelihood and Bayesian approaches to develop statistical inference on the mean-time-to-failure (MTTF) and reliability under normal condition. In the Bayesian approach, we convert the prior information from the success probability to the prior distribution of the underlying parameters and use the moments and mode to determine hyperparameters of the prior distributions, respectively. Markov chain Monte Carlo method is applied to derive the Bayesian inference.
Simulation study shows that the Bayesian approach performs better than the ML approach, especially when there only few failures or zero failures. In Bayesian approach, using mode to determine the prior outperforms using the moments. On the other hand, a Bayesian zero-failure reliability demonstration test is also conducted to design composition of the minimum sample size and the shortest experiment time subject to certain specified reliability criterion.

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