Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Polya Censored Shock Model

A fresh censored delta shock model is investigated. The arrival of random shocks follows a generalized Polya process, and the failure mechanism of the system occurs based on the censored delta shock model. The generalized Polya process is used for modeling because the generalized Polya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Polya process. Thus far, the lifetime properties of the censored delta shock model under the generalized Polya process have not been studied. Therefore, for the established generalized Polya censored delta shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N* by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.