Systems in parallel with different types of rate risk: analysis of periods and cost of inspection

Let us consider two or more parallel systems with different hazard rates whose state of effective or non-effective functioning is only detected by perfect inspections. Considering different costs for each inspection and for unit of time of non-effective functioning, we analyse, following in the steps of previous works, the optimal inspection period and the respective expected total cost per cycle of the resulting global system which presents greater reliability, taking as reference one of the initial parallel systems.