Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776283 | Journal of Computational and Applied Mathematics | 2017 | 21 Pages |
Abstract
As a measure of maximum dispersion from the mean, upper bounds on variance have applications in all areas of theoretical and applied mathematical sciences. In this paper, we obtain an upper bound for the variance of a function of the residual life random variable Xt. Since one of the most important types of system structures is the parallel structure, we give an upper bound for the variance of a function of this system consisting of n identical and independent components, under the condition that, at time t, nâr+1, r=1,â¦,n of its components are still working. Here we characterize the Pareto distribution through Cauchy's functional equation for mean residual life. It is shown that the underlying distribution function F can be recovered from the proposed mean and variance residual life function of the system for r=1. Moreover, we see that the variance residual lifetime of the components of the system is not necessarily a decreasing function of r and increasing of n for r=1, unlike their mean residual lifetime. As an application, the variance of XFâ1(p0) for all p0â[0,1) is investigated and also a real data analysis is presented.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
F. Goodarzi, M. Amini, G.R. Mohtashami Borzadaran,