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A new class of life distributions, namely new better than used in the total time on test transform ordering (NBUT ) is introduced. The relations of this class to other classes of life distributions, closure properties under some reliability operations are discussed as well. We provide a simple argument based on stochastic orders that the family of the NBUT(More)
In this paper we introduce and study a family of new better than used ageing notions parameterized by a function h. The new better than used (NBU), the new better than used of a specified age t0 (NBU-t0) and the new better than used in total time on test transform order (NBUT), are special cases of this new family. We study some properties of the new(More)
Abstract The concept of reversed hazard rate of a random life is defined as the ratio between the life probability density to its distribution function. This concept plays a role in analyzing censored data and is applicable in such areas as Forensic Sciences. In this investigation, we address the question of testing the reversed hazard rate where the null(More)
Based on the comparison of a certain function ofmean inactivity times of two nonnegative random variables, we introduce and study a new stochastic order. Several elementary and then basic preservation properties of the new stochastic order under reliability operations of convolution, mixture, and shock models are discussed. We also derive characterizations(More)
The concept of mean inactivity time plays an important role in reliability and life testing. In this investigation, based on the comparison of mean inactivity times of a certain function of two lifetime random variables, we introduce and study a new stochastic order. This new order lies between the reversed hazard rate and the mean inactivity time orders.(More)
The purpose of this paper is to provide further study of the Marshall-Olkin log-logistic model that was first described by Gui (Appl Math Sci 7:3947-3961, 2013). This model is both useful and practical in areas such as reliability and life testing. Some statistical and reliability properties of this model are presented including moments, reversed hazard(More)