Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution

This research paper presents practical stochastic models for designing and analyzing the time-dependent reliability of nonrepairable systems. The models are formulated for nonrepairable systems with heterogeneous components having phase-type time-to-failure distributions by a structured continuous time Markov chain (CTMC). The versatility of the phase-type distributions enhances the flexibility and practicality of the systems. By virtue of these benefits, studies in reliability engineering can be more advanced than the previous studies. This study attempts to solve a redundancy allocation problem (RAP) by using these new models. The implications of mixing components, redundancy levels, and redundancy strategies are simultaneously considered to maximize the reliability of a system. An imperfect switching case in a standby redundant system is also considered. Furthermore, the experimental results for a well-known RAP benchmark problem are presented to demonstrate the approximating error of the previous reliability function for a standby redundant system and the usefulness of the current research. •Phase-type time-to-failure distribution is used for components.•Reliability model for nonrepairable system is developed using Markov chain.•System is composed of heterogeneous components.•Model provides the real value of standby system reliability not an approximation.•Redundancy allocation problem is used to show usefulness of this model.