The independence assumption would lead to poor estimation of the availability and even misleading conclusions when dependence actually exists. In this paper, we provide the estimation of the limiting availability of a repairable series system when the failure times and repair times are two independent sequences of stationary dependent random variables. Furthermore, consistency and asymptotic normality of the estimator of the limiting availability are derived under some regular conditions. Finally, we investigate the limiting availability for a first-order exponential moving average (EMA1) process and a first-order exponential autoregressive (EAR(1)) process. Simulations are presented to study the impact of dependence on the estimation of the limiting availability.

独立性假设会导致对可用性的估计不佳，甚至在实际存在依赖性时会产生误导性结论。在本文中，我们提供了当故障时间和修复时间是平稳相关随机变量的两个独立序列时可修复系列系统的极限可用性的估计。此外，有限可用性估计量的一致性和渐近正态性是在一些规则条件下导出的。最后，我们研究了一阶指数移动平均 (EMA1) 过程和一阶指数自回归 (EAR(1)) 过程的极限可用性。提出了模拟来研究依赖对有限可用性估计的影响。