Two new classes of life distributions, namely the class of new better than its equilibrium life in convex ordering (NBBLC), and its dual class, the class of new worse than its equilibrium life in convex ordering (NWEL...Two new classes of life distributions, namely the class of new better than its equilibrium life in convex ordering (NBBLC), and its dual class, the class of new worse than its equilibrium life in convex ordering (NWELC), are introduced. Their relations to other classes of life distributlons, closure properties under the three reliability operations, and inheritance properties under shock models and Laplace-Stieltjes transforms are discussed.展开更多
In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some...In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some reliability indices of a system are less (or larger) than the corresponding indices of another system; and then, we obtain the bounds of the main reliability indices of a general system.展开更多
Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL ...Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.展开更多
In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumpti...In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumptions of X and Y. Under the assumption that Y has decreasing reverse hazard rate (DAHR), we show that if X is in any one of the classes IFR, DFR, DMRL or IMRL then XY is in the same class as X. We also obtain some useful bounds for the distribution and the moment of XY. Because the idle time in classical GI/G/1 queuing system can be regarded as the residual life at random time, the results obtained in this paper have applications in the study of such system.展开更多
文摘Two new classes of life distributions, namely the class of new better than its equilibrium life in convex ordering (NBBLC), and its dual class, the class of new worse than its equilibrium life in convex ordering (NWELC), are introduced. Their relations to other classes of life distributlons, closure properties under the three reliability operations, and inheritance properties under shock models and Laplace-Stieltjes transforms are discussed.
文摘In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some reliability indices of a system are less (or larger) than the corresponding indices of another system; and then, we obtain the bounds of the main reliability indices of a general system.
文摘Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.
基金the National Natural Science Foundation of China.
文摘In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumptions of X and Y. Under the assumption that Y has decreasing reverse hazard rate (DAHR), we show that if X is in any one of the classes IFR, DFR, DMRL or IMRL then XY is in the same class as X. We also obtain some useful bounds for the distribution and the moment of XY. Because the idle time in classical GI/G/1 queuing system can be regarded as the residual life at random time, the results obtained in this paper have applications in the study of such system.
