Resumen de The reversed hazard rate and mean inactivity time in mixtures of distributions

F.G. Badía, María Dolores Berrade Ursúa

• Aging concepts constitute by far one of the most challenging issues in relia- bility theory. The role of the reversed hazard rate (RHR) de ned as the ratio of the density to the distribution function shows an increasing importance in this eld. Its connection with the mean inactivity time (MIT) which describes the elapsed time since failure, also stands out. Both measures are of interest in di erent applications such as actuarial science and survival analysis. Moreover, the RHR and MIT orderings that aim at comparing two random variables in stochastic sense can be stated.

  In this work we provide some insight about both the RHR and MIT in mix- tures of distributions that usually emerge when assessing reliability in systems that operate under random environments. We also focus on the speci c case of mixtures that follow the proportional reversed hazard model. This can be used for modeling the e ect of tougher or slighter conditions than a baseline state.