Failure rate of a cold- or hot-spared component with a lognormal lifetime

Graphical and asymptotic representations are derived for the failure rates of cold-spared and hot-spared assemblies consisting of a pair of statistically independent components with identical, lognormally distributed lifetimes. Application to a laser regenerator in an undersea optical-communication cable is discussed. For the lognormal-lifetime distribution, which applies to many solid-state components with predictive screening, redundancy causes a large increase in reliability. An symptotic expansion is presented along with graphs to compute the reduction in the failure rate due to cold and hot sparing.>