Simultaneous optimisation of test and maintenance intervals of given components using non-homogeneous semi-Markov models

A model was developed for simultaneous optimisation of test and maintenance intervals of components, where failures are not self-annunciated but observable only by tests or true demands. Costs caused by maintenance, tests and repairs constitute a complicated objective function for optimisation. An average non-availability, which must not be exceeded for safety reasons, is given as the main condition. In order to compute the objective function, a suitable non-homogeneous semi-Markov process was taken as the mathematical model and the descriptive integral equations were solved numerically. This was possible by using frequency densities hrj(t) rather than transition probabilities pij(t) as a base for calculation. Hence, for a process with N states, a formulation as an initial value problem with N dependent integral equations can be developed as opposed to N² equations, which normally are required. Applicability has been shown with a practical example (emergency diesel generators).