Using Laplace transforms, necessary and sufficient conditions are given for classes of life distributions which are of interest in reliability. Using these conditions, the problem of class closure under convolution is discussed. Furthermore, converses to results of A-Hameed for gamma wear processes are given.
Henry W. Block. Thomas H. Savits. "Laplace Transforms for Classes of Life Distributions." Ann. Probab. 8 (3) 465 - 474, June, 1980. https://doi.org/10.1214/aop/1176994721