Optimization Design of the Shock Model for Repairable Retrial Systems with $$N$$ -policy and Imperfect Coverage

Jian Liu, Linmin Hu (), Yaling Qin and Qi Shao
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Jian Liu: Yanshan University
Linmin Hu: Yanshan University
Yaling Qin: Yanshan University
Qi Shao: College of Humanities and Information Changchun University of Technology

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-29

Abstract: Abstract Based on the intelligent power supply system for offshore monitoring platforms, this paper develops a shock model and a optimal design scheme for a repairable retrial system with N-policy, warm standby and imperfect coverage. Component failure is caused by a combination of intrinsic stochastic defects and external shocks, and failed components are characterized by imperfect coverage. When the repair device is dormant, it is activated only when the number of failed components in the retrial space reaches a threshold. We use Markov process theory to construct system state probability equations. The transient probability and steady-state probability of each system state are calculated by using the Runge-Kutta method and Crammer’s rule, respectively, and the effects of different parameters on the performance metrics are analyzed by numerical examples. We construct a single objective optimization model with the goal of maximum profit, and use the Pattern search algorithm (PSA) and Simulated annealing algorithm (SA) to find the optimal parameter combination. A bi-objective optimization model is proposed to maximize both system availability and profit, and is optimally designed based on the Non-dominated sorting genetic algorithm (NSGA-II) to obtain its optimal Pareto front.

Keywords: N-policy; Imperfect coverage; Retrial system; Shock model; Optimization; 62N05; 62E15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10198-y

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