Analysis of system reliability with control, dependent failures, and arbitrary repair times

This work is motivated by modelling of real information systems. Parallel and series reliability models or their combinations are usually used for these tasks. Common assumptions for such models are independent failures, exponentially distributed failures and recoveries. These assumptions simplify a system modelling significantly, but often give a very rude approximation for it. So there are a lot of restrictions for an application of these models to practical tasks. This study presents a system with more general assumptions: dependent failures, arbitrary failures and repairs, and a system with control. We apply a continuous-time semi-Markov process to evaluate the reliability and the mean time to system failure (MTTF) for a system under these assumption. The repair time of each component is assumed to have an arbitrary distribution function (e.g., Weibull, Poisson or exponential). Kolmogorov equations method and the Laplace transform are used to derive generalised expressions for system state probabilities, reliability and MTTF. A numerical example is presented in order to illustrate the performance analysis of the model.