Time-Dependent Reliability and Sensitivity Analyses of Multi-Performance Multi-State Weighted Star Configuration System Incorporating Maintenance

The multi-performance multi-state (MPMS) weighted star configuration system introduces an advanced reliability model that considers multiple states and performance levels rather than just operational or failed states. This approach reflects real-world scenarios where components degrade over time instead of failing abruptly. The star configuration system comprises a central hub connected to multiple radial subsystems, each contributing differently to overall system performance. Using the Lz-transform method, a comprehensive analytical framework is developed to evaluate the dynamic reliability measures while incorporating maintenance and inspection strategies. Failed components are managed through an (M|M|1):(∞|FCFS) queuing model, where repair or replacement is decided based on inspection outcomes and preventive or corrective maintenance procedures. Minor, semi-minor and semi-major failures are repaired using Erlang distributions, while major failures necessitate replacements governed by Weibull distributions. These distribution sensure accurate estimation of failure probabilities, support better maintenance planning and enhance cost analysis by incorporating realistic failure patterns. Key reliability measures including reliability, availability, sensitivity, instantaneous mean expected performance and cost analysis are examined. A practical example involving a star-shaped gear system demonstrates the applicability and effectiveness of the proposed methodology, highlighting its potential for enhancing system reliability and cost management.