Analysis of Redundant System with Facility for Repair/Replacement of Substandard Unit

This paper analyses a system with two non-identical units, one of higher quality than the other. The inferior-quality unit can be repaired or replaced with a similar one. These systems occur in the electronics industry, hospitals, and other settings. A general time distribution is used for repair times. A technician for repair/replacement is consistently available with the system. This analysis evaluates the systems reliability through various measures. Practical examples include assessing system performance, analysing its effectiveness, and understanding its behaviour under different circumstances. Reliability measures are calculated to evaluate the systems performance. An exponential time distribution is used for failure; for other time distributions, reliability measures that assess system effectiveness are obtained. The average time the system operates before experiencing a failure, the time the system is operational and available for use, how often the repairman needs to visit the system for maintenance actions, the period when the repairman is busy due to maintenance tasks, and the profit generated by the system are calculated using mathematical techniques that model the systems behaviour, using the Semi-Markov procedure and the method of regenerative points. MATLAB is used for numerical and graphical analysis. By combining mathematical models, statistical distributions, and computational tools like MATLAB, this analysis provides insights into the systems behaviour and effectiveness.