On the comparison of reliability experiments based on the convolution order

• 成果类型: Article
• 署名作者: Shaked, M; Suarez-Llorens, A
• 署名单位: University of Arizona; Universidad de Cadiz
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503000000602
• 发表日期: 2003
• 页码: 693-702
• 关键词: information; statistics; systems; models

摘要

In this article we study the comparison of experiments in system reliability theory when the component lifetimes are independent and identically distributed random variables that have a common two-parameter exponential distribution with a location parameter theta. For this purpose, we define a new stochastic order, which we call the convolution order, and study some basic properties of it. We then focus our attention on the family of distribution functions that are mixtures of distributions of partial sums of independent exponential random variables, and derive results that identify several conditions under which members of this family are ordered in the convolution stochastic order. We apply the results to order lifetimes of coherent systems, and as a consequence we obtain information inequalities among various lifetimes of coherent systems. We find situations wherein high reliability decreases statistical information.