Estimation of the limiting availability of a repairable series system with stationary dependent sequences

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.