GENERALIZATION OF THE PAIRWISE STOCHASTIC PRECEDENCE ORDER TO THE SEQUENCE OF RANDOM VARIABLES

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

RESIDUAL STOCHASTIC PRECEDENCE ORDER

The aim of this paper is to introduce a new stochastic order based on the residual lifetimes of two nonnegative dependent random variables and the stochastic precedence order. We develop some characterizations and preservation properties of this stochastic order. In addition, we study some of its reliability properties and its relation with other existing stochastic orders. One of the possible applications in reliability theory has also been discussed.

On optimal operational sequence of components in a warm standby system

We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

RELATIONS BETWEEN STOCHASTIC ORDERINGS AND GENERALIZED STOCHASTIC PRECEDENCE

The concept of stochastic precedence between two real-valued random variables has often emerged in different applied frameworks. In this paper, we analyze several aspects of a more general, and completely natural, concept of stochastic precedence that also had appeared in the literature. In particular, we study the relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular, we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between “Prospects” and “Targets”. Our analysis concerns the case of stochastic dependence.

ACTIVE REDUNDANCY ALLOCATIONS IN SERIES SYSTEMS

We consider the problem of optimally allocating one/two active spares in series systems. Lifetimes of different configurations are compared with respect to the reversed failure rate order, the failure rate order, the increasing concave order, and the stochastic precedence order.

Standby Redundancy Allocations in Series and Parallel Systems

To enhance the performance of a system, a common practice employed by reliability engineers is to use redundant components in the system. In this paper we compare lifetimes of series (parallel) systems arising out of different allocations of one or two standby redundancies. These comparisons are made with respect to the increasing concave (convex) order, the hazard rate order, and the stochastic precedence order. The main results extend some related conclusions in the literature.

Standby Redundancy Allocations in Series and Parallel Systems

To enhance the performance of a system, a common practice employed by reliability engineers is to use redundant components in the system. In this paper we compare lifetimes of series (parallel) systems arising out of different allocations of one or two standby redundancies. These comparisons are made with respect to the increasing concave (convex) order, the hazard rate order, and the stochastic precedence order. The main results extend some related conclusions in the literature.