Reliability Metrics of ReduNdant Systems With Log-Normal Repair Times

The data usually available related to equipment failure and repair are the MTTF (mean time to failure) and MTTR (mean time to repair), with the underlying distributions assumed exponential. The analysis of repairable redundant systems can then proceed by means of integration of Markhov transition equations. It has been found that although the exponential distribution may represent adequately the failure probability, in some cases the log-normal distribution better represents the repair probability, but this distribution leads to non-Markhovian systems. The reliability of redundant systems is affected by the distribution used to model the repair time. This paper presents a comparison of the reliability metrics for redundant systems with exponential failure distribution and two cases of repair time distributions, i.e., exponential and log-normal. The exponential failure distribution is analyzed by integration of the Markhov transition equations, and the log-normal distribution by Monte Carlo simulation. The results obtained show that the use of exponential repair distributions when the data follows the log-normal distribution overestimates the reliability of the system. Nevertheless for values of the MTTR relatively small compared to the MTTF, 10% or lower, the results obtained by using exponential failure distributions are acceptable for engineering applications.