Understanding the shape of the mixture failure rate' by Maxim Finkelstein : Discussion 1

Nozer D. Singpurwalla critically examines the thesis done by Maxim Finkelstein of pulling together the existing literature on mixtures of failure rates and their manifestations. The driving thesis of this paper appears to be the modeling of heterogeneity through mixtures of distributions. The motivation is the non-monotonic behavior of empirical failure rate functions under various scenarios. It seems that selecting a failure model based on the empirically observed failure rate defeats the virtue of the notion of a failure rate. The critic suggests to choose a failure model based on the failure data itself, because it is easier to estimate a probability density than the failure rate. He also recommends Barlow's paper on the same subject which offered an intuitive and believable explanation for the mixtures of constant failure rate functions result.