基于串联系统的条件间隔的随机性质
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摘要: 在本文中, 我们考虑了串联系统在某时刻未失效时, 存活元件构成的条件间隔的随机性质. 首先, 我们得到了当元件寿命分布是任意连续性随机变量时, 条件间隔的边际生存函数, 基于此建立了条件间隔的随机比较, 并且得到标准条件间隔的联合密度函数是ISO^*的一个充分条件; 其次, 我们得到条件间隔是MTP_2以及其联合密度函数是成对RR_2; 最后, 我们考虑了当元件寿命是独立指数分布时条件间隔的生存函数及其随机性质, 以及它们的一些统计性质.Abstract: In this paper, we consider the random properties of conditional spacings composed of surviving elements based on an unfailed series system. First, we obtain the marginal survival function of conditional spacings when the component lifetime distribution is an arbitrary continuous random variable. Based on this, we establish a random comparison of conditional spacings, and obtain a sufficient condition is given for the joint density function of conditional spacings is ISO^*. Then, the MTP_2 dependence of the conditional spacings and the RR_2 in pairs of the joint survival function are also obtained. In the end, the case of conditional spacings when the component lifetimes are independent Exponential is investigated, and some statistical properties of conditional spacings are naturally investigated.