Optimal age replacement time for coherent systems under Geometric Point Process

Abstract

In spatial context, the understanding of event dynamics and point distributions is a fundamental requirement. This study addresses a critical need by introducing the Geometric Point Process (GPP) and explaining its potential impact on optimizing the determination of optimal replacement ages for coherent systems. Our paper has three overarching aims: firstly, to bridge the gap by presenting the novel GPP model that effectively captures the geometric distribution of points, filling a void in point process theory. Secondly, we calculate the optimal replacement age for the coherent system based on the principles of GPP. This involves employing the Infinitesimal-Look Ahead stopping rule within the framework of Smooth Semi-Martingale (SSM) decomposition. A comprehensive comparative analysis is conducted to assess the distinct features and advantages of the GPP in relation to other point processes, offering valuable insights into its applicability and performance. Lastly, we extend the practical application of GPP by examining optimal replacement strategies for components in coherent systems, offering a bridge between theory and real-world practices, especially in the context of aircraft and wind turbine component deterioration. Additionally, we conduct reliability and sensitivity analyses, providing management suggestions, and present Monte Carlo simulations as an alternative method for validating optimal solutions. This research invites the industrial community to utilize the proposed replacement policy, paving the way for exploring geometric characteristics in stochastic processes. The timeliness and significance of this work are underscored by the relatively unexplored field of smooth semi-martingales, with the most recent publication dating back to 2015 by Bueno.