Bathtub-shaped failure rate functions

The failure rate function is an important quantity characterizing life phenomena. Ideally, one would expect this function to exhibit a bathtub shape. In this paper, a comprehensive review of the known distributions that exhibit this shape is provided. Over 17 such distributions are identified. This review is especially important because almost all of the commonly known distributions in statistics do not exhibit the bathtub shape. Furthermore, it could serve as an important reference and encourage developments of further distributions that exhibit a bathtub shape.