Composite performance-dependability analysis of manufacturing systems producing multiple part types using Markov reward models

The notion of performability is formulated for automated manufacturing systems producing multiple part types using Markov reward models. It is shown that the distribution of accumulated performance over a given interval of time is the solution of a set of forward or adjoint linear hyberbolic partial differential equations. The performability analysis presented allows the computation of probability of meeting a target mix production, the probability that the manufacturing lead time of a part type is less than a given limit. Analyses are conducted using variance and cross-covariance functions to evaluate the volume-variety tradeoff