Publication Date: 2000
Statistics and Probability Letters (01677152)49(3)pp. 263-269
A direct approach to measure uncertainty in the residual life time distribution has been initiated by Ebrahimi (1996, Sankhya Ser. A 58, 48-57) and explored further by Ebrahimi and Pellerey (1995) and Ebrahimi and Kirmani (1996). In this paper, some new properties of the proposed measure in connection to order statistics and record values are derived. The generalized Pareto distribution has been widely used in the literature. We have also given several characterizations of this distribution in terms of the proposed measure.
Publication Date: 2001
Handbook of Statistics (01697161)20pp. 199-214
Asadi, M.,
Ebrahimi, N.,
Hamedani, G.,
Soofi, E.S. Publication Date: 2004
Journal of Applied Probability (00219002)41(2)pp. 379-390
A formal approach to produce a model for the data-generating distribution based on partial knowledge is the well-known maximum entropy method. In this approach, partial knowledge about the data-generating distribution is formulated in terms of some information constraints and the model is obtained by maximizing the Shannon entropy under these constraints. Frequently, in reliability analysis the problem of interest is the lifetime beyond an age t. In such cases, the distribution of interest for computing uncertainty and information is the residual distribution. The information functions involving a residual life distribution depend on t, and hence are dynamic. The maximum dynamic entropy (MDE) model is the distribution with the density that maximizes the dynamic entropy for all t. We provide a result that relates the orderings of dynamic entropy and the hazard function for distributions with monotone densities. Applications include dynamic entropy ordering within some parametric families of distributions, orderings of distributions of lifetimes of systems and their components connected in series and parallel, record values, and formulation of constraints for the MDE model in terms of the evolution paths of the hazard function and mean residual lifetime function. In particular, we identify classes of distributions in which some well-known distributions, including the mixture of two exponential distributions and the mixture of two Pareto distributions, are the MDE models.
Publication Date: 2005
Communications in Statistics - Theory and Methods (1532415X)34(2)pp. 475-484
One of the most important types of system structures is the parallel structure. In the present article, we propose a definition for the mean residual life function of a parallel system and obtain some of its properties. The proposed definition measures the mean residual life function of a parallel system consisting of n identical and independent components wider the condition that n -i, i = 0, 2,..., n -1, components of the system are working and other components of the system have already failed. It is shown that, for the case where the components of the system have increasing hazard rate, the mean residual life function of the system is a nonincreasing function of time. Finally, we will obtain an upper bound for the proposed mean residual life function. Copyright © Taylor & Francis, Inc.
