Preventive maintenance optimization for a stochastically degrading system with a random initial age

This paper investigates the optimal age replacement policy for used systems, such as second-hand products, which start their second life-cycle in a more severe environment with an initial age that is uncertain. This uncertain age is modelled as a random variable following continuous probability distributions. A mathematical model is developed to minimize the total expected cost per unit of time for these systems on an infinite time horizon. Optimality and existence conditions for a unique optimal solution are derived and used in a numerical procedure to solve the problem. Numerical experiments are provided to demonstrate the added value and the impacts of the random initial age on the optimal replacement policy.