Hierarchical computation of interval availability and related metrics

As the new generation high-availability commercial computer systems incorporate deferred repair service strategies, steady-state availability metrics may no longer reflect reality. Transient solution of availability models for such systems to calculate interval availability over shorter time horizon is desirable. While many solution methods for transient analysis have been proposed, how to apply these methods on hierarchical models has not been well addressed. This paper describes an approach to computing interval availability and related metrics for hierarchical Markov models. The approach divides the time interval of interest into small subintervals such that the input parameters can be treated as constants in each subinterval to make the model satisfy the homogeneous Markov property, and then pass the output interval availability metrics as constants from the sub-model to its parent model. Finally, these quantities are integrated to obtain the expected interval availability for the entire interval. The study also addresses methods of passing parameters across levels for generating multiple metrics from a hierarchical model. The approach is illustrated with an example model and has been implemented in RAScad. All computations for the example model have also been carried out using the SHARPE textual language interface.