On some comparisons of lifetimes for reliability analysis

Ordering of non-negative random variables (lifetimes) has been intensively studied in the literature. When comparing lifetimes in different applications such as reliability and risk analysis, it is often of interest to analyze also the distances between these lifetimes. In this paper, we define and discuss the stress–strength ordering and distance on the basis of the well-known stress–strength model that describes, e.g., the probability that the strength of a structure is larger than the external stress. We also compare this probability with the distance based on the difference between the means of random variables of interest and discuss several examples. The results can be useful, e.g., for analyzing reliability and safety requirements at the design stage for various engineering objects.