On the multiattempt minimal repair and the corresponding counting process

Minimally repaired items are considered. In practice, minimal repair can be unsuccessful, and in this case, it should be repeated. The Polya-Aeppli process, which is a generalization of the Poisson process is used in the article for the corresponding modeling. Some properties, useful for optimal maintenance, are derived. An important generalization to the case when the probability of the unsuccessful attempt is time-dependent is described. An application of the derived results to obtaining the optimal time of replacement for a system with multiattempt minimal repairs is discussed. The study is illustrated by detailed numerical examples.