Time-dependent reliability computation of system with multistate components

System reliability analysis in discrete phase-type (DPH) distributions requires longer computation time as the matrix order increases with the number of components and the complexity of the system structure. This paper presents a method to reduce the computation time by performing a similarity transformation on the DPH distribution model of the component lifetimes. Similarity transformation produces a matrix-geometric (MG) distribution whose generator matrix is in Jordan canonical form with fewer non-zero elements, so the computation time is faster. We modified the algorithms for system reliability in DPH distributions to make them applicable to MG distributions. Our experiments using several Jordan canonical forms show significant reductions in computation times.