Superposition of renewal processes for modelling imperfect maintenance

In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements and that systems or objects are therefore brought back into an as-good-as-new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption can not be made. The quintessential problem with imperfect maintenance is how to model it. In many cases it is very difficult to assess by how much a partial repair will improve the condition of a system or object and it is equally difficult to assess how such a repair influences the rate of deterioration. In this paper, a superposition of renewal processes is used to model the effect of imperfect maintenance. It constitutes a different modelling approach than the more common use of a virtual age process.