本論文對壽命績效指標的估計提出改良方法,傳統的壽命績效指標設計立基於常態分布的假設,假設產品的壽命服從韋伯分布,以型一混合設限方案收集樣本以節省測試時間與成本,我們提出一個以中位數取代平均數的改良型壽命績效指標,並使用最大概似估計法、及分別運用訊息性與無訊息性的先驗分布的貝氏估計法,針對模型參數與新壽命績效指標進行統計推論,並以自助法及使用馬可夫鏈蒙地卡羅法來求得新壽命績效指標的信賴區間與可靠度區間。經使用蒙地卡羅模擬法評估所提出的估計方法後,我們發現兩種貝氏估計法在相對偏誤、相對均方誤差與參數覆蓋率的表現皆比傳統的最大概似估計法佳。考量現實的操作條件,對參數的先驗分布可能缺乏認知,建議可以採用本論文建議的運用無訊息先驗分布之貝氏估計法進行參數推論,我們使用兩個實際範例來說明如何應用所提出的三種估計方法。
In this thesis, a new life performance index for the Weibull lifetime data is proposed. The type-I hybrid censoring scheme is used to collect lifetime samples. Moreover, the maximum likelihood estimation method and the Bayesian estimation methods with using informative and noninformative prior distributions are used to infer the model parameters and new proposed life performance index. From simulation results, we find that two Bayesian estimation methods outperform the maximum likelihood estimation method in terms of the relative bias, relative mean square error and coverage probability. The Bayesian estimation method with using a noninformative prior distribution is suggested when we do not have knowledge about the model parameters. Two examples are used for illustration.