Availability Modeling of Generalized k-out-of-n: G Warm Standby Systems with PEPA

Developing analytical availability model for k-out-of-n:G warm standby repairable systems with many nonidentical components is tedious and error-prone, requiring specification of the generator matrix of a high dimensional Markov chain. By using performance evaluation process algebra (PEPA), this paper gives a new modeling approach for availability evaluation of such systems with r repair facilities. The components of system are classified into n different groups that consist of statistically identical components following exponential time-to-failure and repair distributions. The PEPA components and their actions are defined for system component groups, repair facilities, repair queue and system dynamics. To describe the dependency of system states on components, a signaling mechanism is realised by actions with sufficiently large rates. A compilation tool is provided to automatically generate the PEPA model input file for the PEPA analysis tool, from a brief specification of the system, and this is amenable to availability analysis. An example is used to verify the proposed modeling method. Modeling with PEPA provides a efficient way to deal with availability evaluation of such systems with many groups and components.