Let (\bar{F}{n}) be an estimator of an IFRA survival function (F) and let (A) be such that (0<\bar{F}(A)<1). The main result constructs an IFRA estimator by splicing the smallest increasing failure rate on the average majorant and greatest increasing failure rate on the average minorant of the restrictions of (\bar{F}{n}) to the intervals ([0, A]) and ([A, \infty)), respectively. The resulting etimator (\hat{\bar{F}}{n}) has the property that (\sup {x}\left|\hat{\bar{F}}{n}-\bar{F}\right| \leqslant k \sup {\mathrm{r}}\left|\bar{F}{n}-\bar{F}\right|), where (k \geqslant 2), and (k=2) if and only if (A) is the median of (F). As a consequence, if (\bar{F}{n}) represents the empirical survival function, or the Kaplan-Meier estimator, the estimator (\hat{\bar{F}}{n}) inherits the strong and uniform convergence properties, as well as the optimal rates of convergence of the empirical survival function and Kaplan-Meier estimator respectively. Simulations show a substantial improvement in mean-squared error when comparing (\hat{\hat{F}}{n}) to those IFRA estimators available in the literature. Under suitable conditions, asymptotic confidence intervals for (\bar{F}\left(t_{0}\right)) are also provided. 1994 Academic Press, Inc.