On innovative stochastic renewal process models for exact unavailability quantification of highly reliable systems

In previous research, we developed original methodology for high-performance computing which enables exact unavailability quantification of a real maintained highly reliable system containing highly reliable components with both preventive and corrective maintenance. Whereas the original methodology was developed for systems containing components with exponential lifetime distribution, the main objective of this article is generalization of the methodology by applying stochastic alternating renewal process models, so as to be used for unavailability quantification of systems containing arbitrary components without any restrictions on the form of the probability distribution assigned to time to failure and repair duration, that is, aging components will be allowed. For this purpose, a recurrent linear integral equation for point unavailability is derived and proved. This innovative equation is particularly eligible for numerical implementation because it does not contain any renewal density, that is, it is more effective for unavailability calculation than the corresponding equation resulting from the traditional alternating renewal process theory, which contains renewal density. The new equation undergoes the process of discretization which results in numeric formula to quantify desired unavailability function. The numerical process is elaborated for all previously intended stochastic component models. Found component unavailability functions are used to quantify unavailability of a complex maintained system. System is represented by the use of directed acyclic graph, which proved to be very effective system representation to quantify reliability of highly reliable systems.