Discrete-time Markov-reward models: random rewards

Considers the discrete-time version of performability modeling, when the Markov rewards are random. The discrete-time approach is well-suited for the performance studies of automated manufacturing systems (AMS) in the presence of failures, repairs and reconfigurations. AMS exist in various configuration states and this transitional behavior is modeled using discrete-time Markov chains. In addition, the performance in each configuration state is modeled by a Markov reward structure. The random reward structure used resembles closely the behavior of actual systems than the deterministic models used in earlier literature. In this paper, the authors derive recursive expressions for the conditional densities and moments of the cumulative performance function, when the underlying Markov chain describing the evolution of the configuration states is homogenous. An example is used to illustrate the methods obtained in the paper