New survival distributions that quantify the gain from eliminating flawed components

Highlights: • Integration by parts can be used to create many new survival distributions. • A subset of these allow potential reliability growth to be quantified. • Some Weibull-like distributions are fitted to data to exemplify the idea. • There is great scope for further research in this area. -- Abstract: 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. One model 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 and lognormal distributions. The methodology is illustrated by fitting some well-travelled datasets.