The Bayesian Assessment of System Availability: Advanced Applications and Techniques

The statistical assessment of system availability within a Bayesian framework is extended here to consider four additional areas: 1) applications to more complicated availability definitions than considered in an earlier paper; 2) applications to measures of performance other than availability; 3) the use of prior distributions on the failure and repair rates more general than the gamma form; and 4) the use of a model involving nonexponential repair intervals. Under category 1) we consider applications involving: a) a demand for system performance which occurs at a random time within an initial interval; b) a situation involving demands upon a system repeated at intervals; and c) the availability statistics of a redundant configuration. Under category 2) we develop: a) the moment and distributional statistics for the accumulated repair time in a given real-time interval when the rate parameters are uncertain; and b) additional measures of performance in a repeated demand situation. Under category 3) we treat fully the case of a prior distribution composed of a linear combination of gamma distributions; this allows multimodal priors. Under category 4) we treat the case of gamma-distributed repair intervals where both the location and shape parameters are uncertain. The results obtained under all four categories can be expressed in terms of the basic measures for the Euler distribution developed in an earlier paper [1].