Abstract

Proportional reversed hazard model and exponentiated distributions have received considerable attention in the statistical literature due to its flexibility. In this paper, we develop the tools for statistical inference of the lifetime distribution of components in a n-component coherent system while the system lifetimes are observed, the system structure is known and the component lifetime follows the proportional reversed hazard model. Different point and interval estimation procedures based on frequentist and Bayesian approaches are developed. The existence and uniqueness of the maximum likelihood estimator are discussed. In addition, two statistical testing procedures, a pivotal quantity approach and a likelihood ratio test, to test whether the exponentiated parameter equals to a particular value are proposed. A numerical example is used to illustrate the methodologies developed in this paper and a Monte Carlo simulation study is employed to evaluate the performance of the statistical inferential procedures.

摘要

由于其灵活性，比例反转风险模型和指数分布在统计文献中受到了相当大的关注。在本文中，我们开发了用于统计推断n中组件寿命分布的工具。-组件相干系统在观察系统寿命的同时，系统结构是已知的，组件寿命遵循比例反向风险模型。开发了基于频率论和贝叶斯方法的不同点和区间估计程序。讨论了最大似然估计量的存在性和唯一性。此外，还提出了两个统计检验程序，即关键量法和似然比检验，以检验指数参数是否等于特定值。一个数值例子用于说明本文开发的方法，并采用蒙特卡罗模拟研究来评估统计推断程序的性能。