New survival distributions that quantify the gain from eliminating flawed components

A general method for deriving new survival distributions from old is presented. This yields a class of useful mixture distributions. Fitting such distributions to failure-time data allows estimation of the improvement in reliability that could be gained from eliminating ‘frail’ components. Onemodel parameter is the proportional increase of expected survival time that could be achieved. Some 2 and 3 parameter distributions in this class are described, which are extensions of the Weibull, exponential, gamma andlognormal distributions. The methodology is illustrated by fitting some well travelled datasets. Keywords: Weibull distribution, gamma distribution, mixture distribution,hazard function, partial integration, frailty mode