Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments

• A stochastically deteriorating system under different operating environments is considered.
• Probability and statistical maintenance optimization models are proposed.
• Theoretical maintenance optimality conditions are derived.
• The assumption according to which time to failure distribution is known is relaxed.
• Two kernel estimators are implemented. Results demonstrate the accuracy of the approach.

This paper investigates the preventive age replacement policy (ARP) for a system subject to random failures. Unlike most maintenance models in the literature, our model considers a system that is exploited under different operating environments each characterized by its own degree of severity. The system lifetimes follow a different distribution depending on the environment it is operating under. Furthermore, the system lifetimes distribution is assumed unknown and therefore estimated from field reliability data. The reliability of the system is calculated using two kernel estimators. This method offers the advantage of non-parametric estimation methods and completely determined by two parameters, namely the smoothing parameter and the kernel function. First, a probability maintenance cost model is derived and conditions under which an optimal preventive maintenance age exists are provided. Then, a statistical maintenance cost model is developed using two kernel estimators. The impact of the variability of the kernel smoothing parameter on the cost model is also investigated. Numerical experiments are provided to illustrate the proposed approach. Results obtained demonstrate the accuracy of the proposed statistical maintenance cost model.