The aim of this publication is to present a new probability distribution which for particular parameter values has a bimodal density function and a bathtub hazard rate function. All the main reliability properties of such distribution will be described in details in this paper. Such a distribution can constitute a very good mathematical model that would enable the description of the lifetime of technical devices. It can successfully be implemented in the planning of a burn-in procedure and a preventive maintenance of non-repairable devices.
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This paper shows how the renewal process in which the sums of independent random variables of the modified Makeham distribution appear can be approximated by the surrogate distribution.