INTEGRATED MODELING OF COLD STANDBY, MAINTENANCE STRATEGY, AND REPAIR DELAY IN MACHINING SYSTEMS
By
Gaurav Sharma and Atar Singh
Department of Mathematics, Agra College, Agra, Uttar Pradesh, India–282002 Affiliated to Dr. B.R. Ambedkar University, Agra
Email: panditgaurav439@gmail.com; atarsingh1968@gmail.com
(Received: August 01, 2025, Revised: April 04, 2026, Accepted: April 07, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.561P-6
Abstract
This paper presents a comprehensive mathematical framework for analyzing the performance of machining systems incorporating cold standby units, preventive maintenance (PM ), and repair delays. The model captures the real-world complexity of manufacturing environments, where machines may fail unpredictably, repairs are subject to resource limitations and delays, and preventive interventions are scheduled to minimize unexpected downtimes. Using a Markovian approach with state-space representation, the system is modeled through balance equations that account for various operational states, including delay queues and active maintenance. Key performance indicators such as system availability, expected number of operational machines, and server utilization are derived to quantify system efficiency under different failure, repair, and maintenance regimes. A cost function integrating repair, delay, maintenance, and unavailability penalties is formulated and optimized under system constraints. Numerical illustrations and MATLAB-based optimization reveal that strategic tuning of preventive maintenance frequency and repair responsiveness can significantly reduce operational costs and improve system reliability. Graphical results further demonstrate the impact of failure rate and maintenance parameters on performance metrics. This study provides valuable insights for decision-makers aiming to enhance productivity, reduce downtime, and optimize maintenance policies in complex industrial systems.
2020 Mathematical Sciences Classification: Primary: 62N05; Secondary: 90B25, 60K10, 60K05
Keywords and Phrases: Cold standby machining system, Preventive maintenance, Repair delay, System availability, System performance analysis, Optimization of repair policy.