Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system

Most of the existing studies on the two-dimensional consecutive system have focused on the non-repairable case. Nevertheless, considering the repairable case of components in engineering, it is necessary to study the reliability of the two-dimensional consecutive repairable system. Owing to the more complex spatial structure of the two-dimensional consecutive system, the analysis methods of the one-dimensional consecutive repairable system are not applicable to the two-dimensional case. In this work, we give a general method to analyze the reliability of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system. Firstly, to calculate the number of different cases of the system in a certain state, a key issue in the analysis of the consecutive repairable system, we propose the sliding window search method and inverse search method, whose computational complexities are compared and correctness is verified. Next, under the assumption that the repair time follows a general distribution, we analyze the reliability of the two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system using the supplementary variable method. Finally, we use an example of a wireless sensor network to analyze the effects of system parameters on system reliability indices, such as steady-state availability, steady-state failure frequency, and MTTFF.