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On the role of dependence in residual lifetimes

机译：论依赖于残余寿命的作用

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摘要

Consider a vector (X, Y) that describes the failure times of two non-independent components of a system. Assuming that the first component has survived up to a given time t > 0, i.e., assuming X > t, one can define the corresponding residual lifetime under different assumptions on the failure of the second component, having lifetime Y. In particular, one can observe that the second component has not failed before a time s >= 0 (maybe different from t), thus the conditioned residual lifetime (X) over tilde (t) = [X - t vertical bar X > t, Y > s] can be considered, or one cannot observe Y, and in this case the conditioned residual lifetime X-t = [X - t vertical bar X > t] has to be studied. This note deals with conditions on the survival copula of (X, Y) such that (X) over tilde (t) and X-t are comparable according to the main reliability stochastic orders. Similar conditions, based on the connecting copula of (X, Y), are described also for the conditioned inactivity times (X) over tilde (t) = [t - X vertical bar X <= t, Y <= s] and X-t = [t - X vertical bar X <= t]. (C) 2019 Elsevier B.V. All rights reserved.
机译：考虑一个向量（x，y），其描述系统的两个非独立组件的故障时间。假设第一组件已经存活到给定的时间t> 0，即假设x> t，可以在第二组分的失败的不同假设下定义相应的残差寿命，特别是一个寿命。观察到在时间S> = 0之前没有发生故障（可能与T）未发生故障，从而通过线圈（t）= [x-t垂直条x> t，y> s]的条件残留寿命（x）可以考虑，或者一个人不能观察Y，在这种情况下，必须研究条件残留寿命XT = [X-T垂直条X> T]。该说明对（x，y）的生存豆荚上的条件涉及（x）在波浪上（t）和x-t的情况相当，根据主要可靠性随机订单相当。基于（x，y）的连接谱图，还针对TildE（t）= [t-x垂直条x <= t，y <= s]和xt的条件不活动时间（x）描述了类似的条件。 = [t - x垂直条x <= t]。 （c）2019年Elsevier B.V.保留所有权利。

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