Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA
Developing analytical availability models for <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula>: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. Using the performance evaluation process algebra (PEPA) as an intermediary, this paper gives a new modeling approach for availability evaluation of such systems with <inline-formula> <tex-math notation="LaTeX">${r}$ </tex-math></inline-formula> repair facilities. The components of the system are classified into <inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> different groups that consist of statistically identical components following exponential time-to-failure and repair time distributions. A library of PEPA components and their actions are defined for system component groups, repair facilities, repair queue, and system dynamics. To capture the dependency of system states on components, a signaling mechanism is realized by actions with suitably high rates. A compilation tool is provided to automatically generate the PEPA model from a brief specification of the system, using the library components. This provides input for the PEPA analysis tool and is amenable to availability analysis. Examples are used to illustrate the proposed modeling method. Modeling with PEPA provides an efficient way to deal with availability evaluation of systems considered with many groups of repairable components.