Economic Analysis of Redundant System with Repair/Replacement Facility and Correlated Life Time

A cold standby system with two non-identical units with different failure rates is analyzed. The main emphasis is placed on how correlation between repair and failure times affects reliability measures. It involves examining the process of repair and replacement when a substandard unit experiences a failure. Assuming that the first unit remains operational during the repair or replacement process of the substandard unit, the system is considered to have failed when both units are in failure mode simultaneously. Various reliability measures and statistical distributions are used to assess the effectiveness of the system. An exponential distribution of the failure time, a general distribution of the time taken for repairs and Bivariate Exponentials are used for correlation. The time it takes for the entire system to fail when both units are in failure mode (MTSF), the proportion of time during which the system is operational (Availability), how often repair workers are needed to address failures, the duration in which repair workers are occupied (Busy Period Analysis), and the financial implications of the system's operation (Profit) are calculated using a Semi-Markov procedure and the Regenerative point method. The main focus is on understanding the reliability and effectiveness of a system with two non-similar units, emphasizing the correlation between repair and failure times. The analysis of this correlation can provide valuable insights into system performance and maintenance strategies. Graphs using MATLAB are prepared to present and interpret findings.