Matrix-Geometric Analysis of a Reboot-Based Multi-Component Machining System with Imperfect Coverage

This study presents a reliability and availability analysis of a multi-component machining system subject to service interruptions, imperfect coverage, and a reboot mechanism. The system comprises multiple identical components, each susceptible to random failures. A single repair server addresses these failures under a first-come-first-served policy. Upon a failure, there is a probability that the fault is detected and covered; otherwise, an uncovered failure leads to service interruption and triggers a system reboot. The model employs a Continuous-Time Markov Chain (CTMC) framework, utilizing matrix-geometric methods to derive steady-state probabilities. Performance measures such as system availability, expected number of failed components, server utilization, and reliability function are computed. Numerical illustrations highlight the sensitivity of system reliability to variations in failure rate, repair rate, coverage probability, and reboot rate. Additionally, a cost function incorporating failure, repair, and downtime costs is formulated and optimized through sensitivity analysis. The findings provide significant insights for designing and managing robust machining systems with high operational reliability.