Reliability of a 3-unit cold redundant system with Weibull failure

Redundancy technique is applied to increase the reliability of a system where maintenance or repair is either not possible or is too costly. Reliability of a cold redundant system is always higher than a hot one. Moreover the increase in reliability due to adding of a unit in sequence can always be exactly determined.Literature is full of derivation of reliability expressions of a cold redundant system whose units obey exponential failure density. Due to extreme difficulty in evaluation of integrals involving Weibull density function, few attempts on derivation of reliability of redundant systems have been made. We have here derived reliability of a simple case of a 3-unit cold standby system whose units obey Weibull failure density.