Discrete time dynamic reliability modeling for systems with multistate components

•Exact matrix-analytic method for discrete time dynamic system reliability analysis•The systems/networks may have any combinations of basic structures including bridge•The components have multistate and their lifetimes have DPH distributions•Use only matrix algebra to generate reliability measure functions and statistics This study proposes modeling techniques for the exact dynamic reliability analyses of systems with the lifetimes of all components following independent and nonidentical discrete phase-type (DPH) distributions. The systems may have series, parallel, standby, K-out-of-N, and bridge structures with any combinations of them. The models produce numerical formulas and algorithms for generating system reliability and hazard functions; thus, they are applicable to the dynamic reliability analysis of systems, including networks. The approach is by showing that the system lifetime follows a DPH distribution. For network reliability analysis, the DPH distribution is generalized into a matrix-geometric (MG) distribution. The use of the DPH distribution makes the models suitable for systems with multistate components and simplifies the calculations of the system reliability measures. Its effectiveness is illustrated using results from complex structure systems.