Optimum replacement intervals with random time horizon Available to Purchase

An optimization problem to obtain the optimal replacement interval is studied. The system is minimally repaired at failure and is replaced by a new one at age T. The model assumes that the time horizon associated with the number of replacements is random. The total expected cost is calculated, and the optimal replacement interval minimizing the cost is found. A numerical example is used to compare the costs associated with an infinite time line and a random time line, which this model used.