Bathtub distributions: a review

Abstract Bathtub distributions are characterized by bathtub failure rate functions . These are possibly more realisitic models than the monotone failure rate models . A systematic account of such distributions is not available and this review aims to give such an account . We give some easily verifiable conditions to check the bathtub property of a distribution along with methods to construct such distributions . We also discuss some stochastic and reliablity mechanisms which lead to bathtub distributions. These include mixtures ( stochastic failure rate models ) , series system , stochastic differential equation models and so on. We also review inference on bathtub distributions. The paper concludes with a rather exhaustive list of bathtub distributions. Keywords: survive 1 databathtub Distributionsinfant mortalityfailure ratemixtures at distributionsseries systemsmean residual lifeabundance distributionleast squares