并行系统中故障率的性质
Failure Rate Properties of Parallel Systems
AI总结：
本文研究了并行系统中故障率的单调性和随机序性质，通过分析尾部权重迭代过程对分布的影响，证明了由指数分布寿命组件构成的并行系统的老化特性。
摘要：
我们研究随机变量的故障率单调性和广义凸变换随机序性质，关注其应用。我们特别关注尾部权重迭代过程对定义分布的影响，这相当于在给定时刻对残余寿命矩的特征化。对于单调性性质，我们主要关注与迭代过程相关的继承性质，通过反例展示继承性质是否成立或逆向推论是否不成立。对于随机序，我们引入一个新的标准，基于对合适函数符号变化的分析。该标准随后应用于证明由具有指数分布寿命的组件组成的并行系统的老化性质。
英文摘要：
We study failure rate monotonicity and generalized convex transform stochastic ordering properties of random variables, with a concern on applications. We are especially interested in the effect of a tail weight iteration procedure to define distributions, which is equivalent to the characterization of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counter-examples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterium, based on the analysis of the sign variation of a suitable function. This criterium is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes.
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