On the distribution of some stochastic compartmental models having time-dependent transition probabilities, with applications to reliability

Abstract

The cumulant generating functions of some multi-compartment stochastic models having time-dependent transition rates are derived. Using these, the first and second moments of the stochastic distributions are found. Under certain assumptions concerning the initial conditions the stochastic distributions are specifically identified. The models investigated are the n-compartment mixed catenary-mammillary model and the n-compartment general irreversible model. These derivations are then used to analyze some reliability systems. In particular, the catenary portion of the mixed model is used to obtain stochastic analyses of a standby redundant system. The mixed model is used for a system wherein a component is subject to competing-risks with standby components. The general model is employed to evaluate a mission reliability with a hierarchical failure structure.