Reliability of a 2-Dimensional $k$-Within-Consecutive- $r\times s$-out-of- $m\times n$:F System Using Finite Markov Chains

In this article, we propose efficient methods, based on the use of a 2-dimensional scan statistic, and a Markov chain approach, to evaluate the reliability of a 2-dimensional (rectangular or cylindrical) -within-consecutive--out-of-:F system. Our results are established under three different assumptions that the components of the system are: (i) -independent and identically distributed, (ii) -independent but non-identically distributed, and (iii) first-order homogeneous Markov dependent. Numerical results are provided for illustrative purposes.