Performance Analysis and Reliability Prediction of Multi-State Service Systems With Multiple Failure Modes of Unreliable Server: An Engineering Perspective

The long-term reliability of a machining system is essential for ensuring the uninterrupted operation of an automated manufacturing process. For maintaining optimal system performance, it is essential to model and analyze the system's reliability and availability. The current study introduces a unique framework established through evolutionary advancements of the fundamental models, incorporating impatience characteristics of individuals, the notion of unreliable servers, and enhancing its practical significance by considering the working breakdown of the server/repairman. A comparative investigation of the developed model with conventional models is carried out to analyze the overall impact on the reliability and availability characteristics of the machining system through a queueing-theoretic approach. Further, the differential-difference equations are implemented to construct the mathematical model, and the Laplace transformation is applied to demonstrate the state probability distribution. Several critical system performance measures, such as mean-time-to-failure (MTTF), machining systems' reliability, and steady-state availability, are thoroughly investigated to evaluate machining system stability and efficiency. The results demonstrate that the developed model significantly increases system reliability and availability, presenting a notable increase in reliability compared to conventional models under certain service interruption circumstances. To validate the model's applicability in real-world scenarios, multiple combinations of system parameters are taken into consideration. For straightforward visualization of the impacts of multiple parameters on system reliability and availability, the results are provided, consisting of extensive tables and graphical representations. The proposed research contributes to the queueing literature by addressing the research gaps between theoretical modeling and real-life applications, highlighting the insights that are essential for system designers, decision-makers, and researchers aiming to optimize the reliability and availability of complex machining systems.