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A Criterion for Burn-in That Balances Mean Residual Life and Residual Variance

Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life with residual variance. To study this quantity, we develop a general result concerning the preservation ofbathtub distributions. Using this result, we give a condition so that the residual coefficient of variation is bathtub-shaped. Furthermore, we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value, but not necessarily before the change point of the failure rate function.