STOCHASTIC COMPARISONS OF SYSTEMS BASED ON SEQUENTIAL ORDER STATISTICS VIA PROPERTIES OF DISTORTED DISTRIBUTIONS

Abstract

We consider systems based on sequential order statistics (SOS) with underlying distributions possessing proportional hazard rates (PHRs). In that case, the lifetime distribution of the system can be expressed as a distorted distribution. Motivated by the distribution structure in the case of pairwise different model parameters, a particular class of distorted distributions, the generalized PHR model, is introduced and characterizations of stochastic comparisons for several stochastic orders are obtained. Moreover, results on the asymptotic behavior of some aging characteristics, for example, the hazard rate and the mean residual life function, of general distorted distributions as well as related bounds are given. The results are supplemented with limiting properties of the systems in the case of possibly equal model parameters. Some examples are presented in order to illustrate the application of the findings to systems based on SOS and also to systems with independent heterogeneous components.