A Comprehensive Survey on Machine Repair Problems with Standby Systems

The Machine Repair Problem (MRP), also referred to as the Machine Interference Problem, is a fundamental queueing framework used to analyze manufacturing and service environments where machines or service units are prone to random failures. Such failures may lead to considerable loss of productivity, revenue, and operational efficiency, particularly in large-scale automated systems. To mitigate these disruptions, modern industries incorporate standby units, cold, warm, or hot, to enhance reliability, maintainability, and system availability. This survey provides a comprehensive chronological and thematic review of standby-supported MRPs, covering classical queueing foundations, reliability-oriented formulations, and modern optimisation and AI-driven repair strategies. A taxonomy of MRP models is proposed to categorise existing literature, followed by an annotated summary table covering the years 2021–2025. This survey also outlines major research gaps and future directions to guide scholars and practitioners interested in the modelling and analysis of repairable standby systems. The authors believe that this paper serves as a valuable reference for researchers entering the domain of machine repair systems, reliability analysis, and queueing theory applications.