Reliability analysis of recovery blocks with nested clusters of failure points

A Markov model is developed to obtain first and second moments of the number of successfully processed input-points for recovery blocks with a primary module and two alternate modules. A nested structure of clusters of failure points is assumed. When in a failure cluster of the primary module, the input sequence encounters clusters of failure points belonging to the first alternate module, in which case the second alternate is invoked. Some special cases are discussed in detail. A Markov chain model for one of the well-documented fault-tolerant software techniques, the recovery block, is analyzed. The model is intended to study recovery block reliability when the sequence of input values traverses nested clusters of failure points in the input domain. The method of solution exploited the specific structure of the state-transition diagram, which is two-dimensional. Moments of the number of successfully processed input points were obtained by recursively solving infinite systems of linear equations