Bathtub-type curves in reliability and beyond

Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub-type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.