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First of all, let me thank Professors Jorge Navarro and Nozer Singpurwalla for an extremely interesting and inspiring discussion of my paper. Although the topic of failure rates in heterogeneous populations is not new and the ï¬rst publications date back to the late 1950s and early 1960s, the advanced study of the shapes of mixture failure rates only really started with the papers by Block et al. [1] and Gurland and Sethuraman [2]. The former was devoted mostly to describing the general asymptotic (as t â â) behavior of these functions, whereas the latter dealt with mathematical results showing that for different speciï¬c settings the failure rate of a mixture of distributions with increasing failure rates (IFRs) can decrease, at least in certain intervals of time. As it was stated in the Introduction of my discussion paper (DP), âthis is not a complete review of the subject as we discuss our ï¬ndings and results of other authors that are aligned with our vision of this topic.â Therefore, a number of speciï¬c results (especially those of a mathematical nature) are not covered in the paper. I agree with Professor Jorge Navarro (hereafter referred to as âJNâ) that more studies
Applied Stochastic Models in Business and Industry – Wiley
Published: Nov 1, 2009
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