Mean residual life and failure rate functions are ubiquitously employed in reliabilityanalysis. The term of useful period of lifetime distributions of bathtub-shaped failurerate functions is referred to the flat rigion of this function and has attracted authorsand researchers in reliability, actuary, and survival analysis. In recent years,considering the change points of mean residual life and failure rate functions has beenextensively utelized in determining the optimum burn-in time. In this paper we investigatethe difference between the change points of failure rate and mean residual life functionsof some generalized gamma type distributions due to the capability of these distributionsin modeling various bathtub-shaped failure rate functions.

Recently Bassan and Spizzichino (1999) have given some new concepts of multivariate ageing for exchangeable random variables, such as a special type of bivariate IFR, by comparing distributions of residual lifetimes of dependent components of different ages. In the same vein, we further study some properties of these concepts of IFR in the bivariate case. Then we introduce certain concepts of bivariate DMRL ageing and we develop a treatment that parallels those developed for bivariate IFR. For both the IFR and DMRL concepts, we analyse a weak and a strong version, and discuss some of the differences between them.

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.