\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We propose optimal preventive maintenance strategies for $n$-component coherent systems. We assume that in the early time of the system operation all failed components are repaired, such that the state of a failed component gets back to a working state, worse than that of prior to failure. To modeling this repair action, we utilize a counting process on the interval $(0,\tau]$, known as generalized Polya process (which subsumes the non-homogeneous Poisson process as special case). Two generalized Polya process-based repair strategies are proposed. The criteria that will be optimized are the cost function formulated based on the repair costs of the components/system, and the system availability, to get the optimal time of preventive maintenance of the system. To illustrate the theoretical results, two coherent systems are studied for which the optimal preventive maintenance times are explored under different conditions.
\end{document}