Bounded-set approach to the evaluation of the reliability of fault-tolerant systems. Part 1: Methodology, powered spares

In the paper, we present a new method for fault-tolerant reliability calculations. This method is developed to analyse closed non-Markov systems, i.e. systems containing modules having arbitrary failure-time distributions. Such systems arise for a number of reasons, such as when redundancy is employed at various levels, or when considering the effect of transient faults. The analysis of such systems by conventional techniques will be very difficult. As the bounded-set approach is new to the area of reliability modelling, a step-by-step development of the approach is presented in the paper. The model described is suitable for closed Markov systems with powered spares. Such systems can also be modelled using the more established Markov state transition approach. Comparisons of the results obtained using the bounded-set approach with those obtained using the Markov state transition approach are given. In the companion paper, further extensions of the bounded-set approach are given to enable the modelling of closed Markov systems with unpowered spares, non-Markov systems and systems whose components cannot be readily aggregated into independent sub systems.