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In developing any successful maintenance strategy it is important to be able to estimate the rate of occurrence of maintenance events. In a previous paper the authors have argued that there are advantages to using a non-parametric or semi-parametric approach to such analysis. In this paper the authors explore the use of the approach to data from the water industry using a case study. The approach provides insight into the context revealing the impact of maintenance on the process. The effect of the maintenance strategy can be evaluated. The paper explores the practical issues of missing values and implementation of an appropriate maintenance strategy.

We consider a general repair process where the virtual age V i after the ith repair is given by V i = O(V i-1 + X i ), O(.) is a specified repair functional, and X i is the time between the (i - 1)th and ith repair. Some monotonicity and dominance properties are derived, and an equilibrium process is considered. A computational method for evaluating the expected number/density of repairs is described together with an approximation method for obtaining some parameters of the equilibrium process.

We consider a component which undergoes instantaneous general repairs on failure. Suppose that V i = Φ(V i-l + Y i ), where V i is the virtual age immediately after the ith failure, Y i is the time between the (i - 1)th and ith failures, Φ(.) is a specified repair functional, and V 0 =s. We derive integral equations for the repair density, and also for the joint density of repairs with respect to chronological age and virtual age on failure. In the asymptotic case, approximations are obtained for the mean and variance of virtual age on failure, virtual age after repair, and time between failures. Two policies are then considered. The first, an upgraded repair strategy employs minimal repairs until the component reaches a specified age, thereafter repairs restore the virtual age to that prescribed level. The second policy considered is the Kijima Type 2 model which is not amenable to the usual g-renewal analysis that is used in the Type 1 model. The repair density is obtained by numerical solution of the relevant integral equation. Finally, approximations for the asymptotic moments are found to be in close agreement with simulated results.