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

In this paper, we consider the discrete-time version of performability mode ling of automated manufacturing systems (AMSs) capable of producing multipl e part types, when the Markov rewards are random. The discrete-time approac h is well suited for the performance studies of AMSs in the presence of fai lures, repairs, and reconfigurations. AMSs exist in various configuration s tates 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 behav ior of real systems more accurately than the deterministic models used in t he earlier literature. We derive recursive expressions for the conditional densities and moments of the cumulative performance function and study thei r asymptotic properties, when the underlying Markov chain describing the ev olution of the configuration states is homogenous, Recursions are also deri ved for the computation of the cross correlation of the productivity of dif ferent part types. Examples are provided to illustrate the methods obtained in the paper.