本文考慮具共變數韋能衰退隨機過程之貝氏可靠度分析, 其中漂移係數為共變數之線性函數。實務上同款產品的衰退特徵可能存在個別差異, 並不適合用同一模型來描述所有個體, 因此我們以三種不同的模型, 在共同的先驗分配下, 分別經由馬可夫鏈蒙地卡羅方法(MCMC) 進行貝氏可靠度推論。另一方面當主觀先驗資訊微弱或無法確認資料來源的真實模型時, 我們先經由觀測資料估計具個別差異之模型中參數的先驗分配建立經驗貝氏模型, 模擬結果驗証經驗貝氏方法可在模型不確定時取其折衷進而降低選模錯誤的風險。也就是說, 在先驗資訊不足或不確定產品間是否有差異, 經驗貝氏模型可提供較穩健的可靠度推論。

For high reliability products, the degradation test can provide more information than accelerated life test to assess the lifetime distribution. In this thesis, we consider the degradation test based on Wiener processes in which the drift coefficient is linear in the covariates. In practice, there may have unit-to-unit variantion of the products with the same type. Therefore, it may not be appropriate using the same model to fit all products. Here, we aim on the Bayesian approach with three difference models. Empirical Bayes methods are used to determine the prior parameters using all the observed data. It not only provides a compromise in the model uncertainty with the advantage of ”borrowing the strength” among the data, but also solve the situation when the prior information is vague. Further, we are interest in reliability inference under given covariates. Simulation study shows that the empirical Baysian method can reduce the risk for fitting wrong models and yield robust reliability inference.

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