Calculating the rate of occurrence of failures for continuous-time Markov chains with application to a two-component parallel system

This paper assumes that a system process is either a continuous-time Markov chain or a higher dimensional Markov process after introducing some supplementary variables. A formula for evaluating the rate of occurrence of failures is derived. As an application, a maintenance model for a two-component parallel system, in which component 1 after repair is not ‘as good as new’ but component 2 after repair is ‘as good as new’, is studied.