Calculating the expected failure rate of complex equipment subject to hazardous repair

In hazardous repair of a repairable system, there is a strong probability of further failure during a period immediately following the repair. To model failures of such systems under failure-based maintenance, a class of point process models is proposed in which the failure intensity is a function only of equipment age and of time since most recent repair. Cost modelling requires the computation of the expected number of failures by age t as a function of equipment age. This expected number is shown to satisfy a Volterra (integral) equation of the second kind that generalises the renewal equation. A solution algorithm is given. A simple (four-parameter) model from this class is introduced, and the methodology is exemplified using a database of failures of non-maintained medical equipment.