Kernel estimation based method for the optimization of the system age preventive replacement policy

This paper investigates the preventive age replacement policy for a system subject to random failures. According to such a policy the system is replaced by a new one, either at failure or at given age T, whichever occurs first. The system is assumed having experienced its mission under a given operating environment and then conducted to fulfill its mission under a new operating condition. This later could be more or less severe that the first and does impacts the system lifetimes distribution. In this paper unlike of the most existing approaches, the system lifetimes distribution is assumed unknown but rather estimated from lifetime data. To estimate the reliability of the system, the Kernel methods is exploited. Such a method offers the advantage of non-parametric estimation methods and in addition to be easy to implement. First, we show that the smoothing parameter of the Kernel estimator has no effect on the estimated values of the system reliability. Second, a mathematical cost model is derived on the basis of Kernel estimator so as to evaluate the optimal preventive age replacement of the system under the new operating environment. The impact of the variability of Kernel smoothing parameter on the cost model is studied, and conditions under which an optimal preventive maintenance age exists, are provided. A numerical example is given to illustrate the proposed work.