Investigating the Reliability of A Five-Component System with A Standby Unit Using Markov Modeling and Statistical Tools

Objectives This study aims to assess the reliability of a system comprising five primary components and one standby unit. The research seeks to identify critical components in process industries and support the development of effective management strategies to enhance the performance of large-scale and complex systems. Materials and Methods A Markov model is developed to describe the system behavior, and the governing differential equations are solved using the Laplace Transform technique. Python programming is employed to compute system reliability over time, with results presented in graphical and tabular forms. Additionally, statistical analyses, including correlation and regression techniques, are performed using SPSS software to examine the relationship between operational time and system reliability. Results The computational analysis illustrates the reliability trend of the system over time and highlights the influence of operational duration on performance degradation. The statistical results confirm a significant relationship between operational time and system reliability, providing quantitative support for the reliability model. Conclusion By integrating the Laplace Transform method, computational modeling, and statistical evaluation, this study offers a comprehensive framework for reliability assessment. The findings contribute to improved decision-making and strategic planning for optimizing reliability and performance in process industries.