型一混合設限方案下廣義指數分布的多重應力－強度模型之可靠度估計

Reliability Estimation in a Multicomponent Stress–Strength Model for the Generalized Exponential Distribution with a Type-I Hybrid Censoring Scheme

張雅雯(YA-WEN CHANG)

指導教授 ： 蔡宗儒

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2022年)

https://doi.org/10.6846/TKU.2022.00085

摘要

本論文研究在型一混合設限方案下考慮廣義指數分布的多重應力－強度模型之可靠度估計問題。假設模型內k 個多重元件強度承受相同的應力變數，元件強度與應力互相獨立且服從廣義指數分布時，本論文使用最大概似估計法及貝氏估計法推論多重應力－強度模型系統的可靠度，此外，我們也使用自助法及馬可夫鏈蒙地卡羅法推論多重應力－強度模型系統的可靠度的信賴區間與可靠區間，模擬結果顯示使用訊息先驗的貝氏估計法的估計效能優於最大概似估計法及、使用無訊息先驗及重要抽樣的貝氏估計法，文中使用兩個實際範例來說明如何使用我們所建議的估計方法。

關鍵字

多重應力－強度模型 ； 廣義指數分配 ； 最大概似估計 ； 貝氏估計 ； 自助法 ； 蒙地卡羅模擬

並列摘要

Assume that the stress and strength variables in a multicomponent system follow generalized exponential distributions. The maximum likelihood estimation and Bayesian methods are studied to infer the reliability of the multicomponent system in this thesis. The bootstrap method and Markov chain Monte Carlo method are used to obtain the confidence interval and credible interval of the reliability of the multicomponent system. Simulation results show that the Bayesian estimation method with an informative prior distribution outperforms the maximum likelihood estimation method and the Bayesian estimation method with important sampling. Two real examples are used for illustration.

並列關鍵字

multicomponent stress-strength model ； generalized exponential distribution ； maximum likelihood estimation ； Bayesian estimation ； Bootstrap method ； Monte Carlo simulation

參考文獻

參考文獻

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