Sequential interval estimation of the limiting interval availability for a bivariate stationary dependent sequence

In this paper, we consider the sequential confidence interval estimation of the limiting interval availability of a repairable system when the sequences of failure and repair times are generated by a bivariate stationary dependent sequence. The confidence interval and the proposed stopping rule are shown to be asymptotically consistent and efficient as the width of the interval approaches zero. In particular, we consider the sequential interval estimation of the limiting interval availability for a first-order bivariate exponential autoregressive process. A simulation study is also conducted to asses the performance of the proposed confidence interval.