In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more life distributions. In a previous paper on mixtures, Block, Mi and Savits (1993) showed that the failure rate behaves like the limiting behavior of the strongest component. We show a similar result here for convolutions. We also show by example that unlike a mixture population, the ultimate direction of monotonicity does not necessarily follow that of the strongest component.
"The limiting failure rate for a convolution of life distributions." J. Appl. Probab. 52 (3) 894 - 898, September 2015. https://doi.org/10.1239/jap/1445543854