Evaluation of average maintenance cost for imperfect-repair model

The imperfect-repair model considers units which are either perfectly-repaired or minimally-repaired, with known, fixed probabilities. Minimal repair is defined, roughly, as returning the item to the population's average state at the failure time. The average cost of maintaining the unit under this model is studied by assuming fixed amounts of cost for perfect and minimal repairs when failed. The authors' measure of such maintenance cost is an average cost per unit-time over an infinite time span. To obtain this average cost, they use the expressions for average numbers of perfect and minimal repairs under this model. They prove the few theorems necessary to derive the formulae for the average cost per unit-time. The results are applied to some examples.