4. Analytical study The purpose here is to determine the dates of inspections allowing the optimisation of the total average cost per unit of time. In view of the unavailability of real-time data of the equipment and its environment, a stochastic approach is recommended.
4.1 Mathematical development We denote by Pc(D) the probability that the cycle will finish with a breakdown, the equipment has a breakdown before the planned preventive maintenance date, and by Pp(D) the probability that the cycle will finish with a preventive maintenance. We therefore have