Replacement and inspection policies for products with random life cycle

In this paper, we consider maintenance policies for products in which the economical life cycle of products is a random variable. First, we study a periodic replacement policy with minimal repair. The system is minimally repaired at failure and is replaced by new one at age T (periodic replacement policy with minimal repair of Barlow and Hunter). The expected present value of total maintenance cost of products with random life cycle is obtained and the optimal replacement interval minimizing the cost is found. Second, we consider an inspection policy for products with random life cycle to detect the system failure. The expected total cost is obtained and the optimal inspection interval is found. Numerical examples are also included.