On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems

In this paper, first- and second-order discrete-time semi-Markov systems are considered with their finite state space divided into three subsets as perfect functioning states, imperfect functioning states and failure states, respectively. The counting processes for one-step increasing transitions, one-step equivalent transitions and one-step decreasing transitions in working/failure periods are defined and investigated in detail. Formulas for …