Journal of Engineering Mathematics & Statistics

Authors: Sanjay Patel, Kavisha Jain

Abstract: The application of stochastic processes in the reliability analysis of mechanical systems provides a powerful framework for modeling uncertainties and predicting the performance of systems under random conditions. Mechanical systems often face operational uncertainties, such as material degradation, environmental factors, and failure events, which require a robust mathematical approach for performance analysis and reliability evaluation. This paper explores the use of stochastic processes, including Poisson processes, Markov processes, and Wiener processes, to model the failure rates, system degradation, and maintenance strategies in mechanical engineering. Through the analysis of various reliability models, this study demonstrates how stochastic processes contribute to a more accurate prediction of system behavior and help optimize maintenance schedules, improve system design, and reduce unexpected failures. The paper discusses the application of these methods in different mechanical systems, such as manufacturing equipment, transportation systems, and structural components, while highlighting the challenges and advantages of using stochastic models in real-world applications.

Keywords: Reliability analysis, stochastic processes, mechanical systems, failure modeling, maintenance optimization, Markov processes, Poisson processes, Wiener processes, system degradation, uncertainty quantification.