ABSTRACT

This paper deals with the problem of maximum likelihood and Bayesian estimation of stress–strength reliability involving paired observation with ties using bivariate exponentiated half-logistic distribution. This problem is of importance because in some real applications the strength of the component is highly dependent on the stress experienced by it. A bivariate extension of exponentiated half-logistic is discussed and an expression for the stress–strength reliability is obtained. This model is also useful to analyse data having the unusual feature of having a number of pairs with tied scores, even when the scores are continuous. The maximum likelihood estimate and interval estimate of the stress–strength reliability has been developed. The Bayes estimates of the stress–strength reliability under squared error loss function are obtained using importance sampling technique. Simulation studies are conducted to evaluate the performance of maximum likelihood and Bayes estimates. Two real-life data sets are analysed to numerically illustrate the usefulness of the developed method.

摘要

本文处理了应力-强度可靠性的最大似然和贝叶斯估计问题，涉及使用双变量指数半逻辑分布的带关系的配对观察。这个问题很重要，因为在某些实际应用中，组件的强度高度依赖于它所承受的应力。讨论了指数半逻辑的双变量扩展，并获得了应力-强度可靠性的表达式。即使分数是连续的，该模型也可用于分析具有多个具有相同分数的对的不寻常特征的数据。应力强度可靠性的最大似然估计和区间估计已经被开发出来。使用重要性抽样技术获得平方误差损失函数下应力强度可靠性的贝叶斯估计。进行模拟研究以评估最大似然和贝叶斯估计的性能。分析了两个现实生活中的数据集，以数值方式说明所开发方法的有用性。