Performability studies of automated manufacturing systems with multiple part types

We consider the transient performance analysis of failure-prone manufacturing systems producing multiple part types. We decompose the exact monolithic model into: 1) a slower time scale structure state process modeling the failure and repair, and 2) a faster time scale performance model describing the part processing and the material movement. We combine the solution of these two models to show that the accumulated reward over a given time interval is a solution of a set of forward or adjoint multidimensional linear hyperbolic partial differential equations. This result generalizes the existing results on composite performance-dependability analysis of manufacturing systems. We also present efficient numerical methods for computing the distribution of the cumulative operational time, and the mean and variance of the cumulative production over a given time interval. Further, we bring out the significance of these results in the manufacturing systems context through several examples