Discrete-time Markov reward models of automated manufacturing systems with multiple part types and random rewards

We consider the discrete-time version of performability modeling of automated manufacturing systems (AMSs) capable of producing multiple part types, when the Markov rewards are random. The discrete-time approach is well suited for the performance studies of AMSs in the presence of failures, repairs, and reconfigurations, AMSs 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 models the behavior of real systems more accurately than the deterministic models used in the earlier literature. We derive recursive expressions for the conditional densities and moments of the cumulative performance function and study their asymptotic properties, when the underlying Markov chain describing the evolution of the configuration states is homogenous. Recursions are also derived for the computation of the cross correlation of the productivity of different part types. Examples are provided to illustrate the methods obtained in the paper