In this paper we introduce a variation on Glaser's method for determining the shape of the failure rate function of a mixture. It has often been seen that the shape of the failure rate depends on the mixing parameter q. Our method provides an explanation for this phenomenon. We then illustrate our technique with the mixture of an exponential and a gamma density for all possible cases.
"A Glaser twist: focus on the mixture parameters." J. Appl. Probab. 49 (4) 1144 - 1155, December 2012. https://doi.org/10.1239/jap/1354716663