Stochastic ageing models : extensions of the classic renewal theory

Exact knowledge of the reliability characteristics as the time dependent unavailability coefficient for example, under influence of different ageing processes as well as under different failure types is very useful to the practitioners who have to find the optimal maintenance policy for their equipment. In this paper found models and their solutions have potential to face the optimisation task under the conflicting issues of safety and economics. Most of the solved models take into account ageing processes. An increasing tendency lately exists to include aging effects into the risk assessment models to evaluate its contribution. We developed different renewal models taking into account different ageing distributions of failures (Weibull, Erlang, log-normal): models with negligible renewal time, models with periodical preventive maintenance, alternating renewal process with lognormal distribution of failure time, and with two types of failures.