Nil Kamal Hazra

Some results on majorization and their applications

Majorization is a key concept in studying the Schur-convex property of a function, which is very useful in the study of stochastic orders. In this paper, some results on Schur-convexity have been developed. We have studied the conditions under which a function ? defined by ? ( x ) = ? i = 1 n u i g ( x i ) will be Schur-convex. This fills some gap in the theory of majorization. The results so developed have been used in the case of generalized exponential and gamma distributions. During this, we have also developed some stochastic properties of order statistics. Some useful results on majorization are developed.This enriches the theory of majorization.As applications, some distributions have been studied.

On stochastic comparisons of maximum order statistics from the location-scale family of distributions

We consider the location-scale family of distributions, which contains many standard lifetime distributions. We give conditions under which the largest order statistic of a set of random variables with different/the same location as well as different/the same scale parameters dominates that of another set of random variables with respect to various stochastic orders. Along with general results, we consider important special cases, namely, the FellerPareto, generalized Pareto, Burr, exponentiated Weibull, Power generalized Weibull, generalized gamma, Half-normal and Frchet distributions.

Reliability study of a coherent system with single general standby component

In this paper, the properties of a coherent system equipped with a single general standby component is investigated. Here, the standby component may initially be put into cold state and is switched over to warm state after a certain time period, up to which the system certainly does not fail. Then the standby component in warm state starts to work in active state at the time of failure of a component which may cause the system failure. Here three different switch over cases regarding the state changes of the standby component are considered. Numerical examples are also provided.

General standby allocation in series and parallel systems

ABSTRACT Stochastic orders are very useful tools to compare the lifetimes of two systems. Optimum lifetime of a series (resp. parallel) system with general standby component(s) depends on the allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby components. In each model, we compare different series (resp. parallel) systems (which are formed through different allocation strategies of standby component(s)) with respect to the usual stochastic order and the stochastic precedence order. The results related to the cold as well as the hot standby models are obtained as particular cases of the results discussed in this article because the model considered here is a general one.

On optimal grouping and stochastic comparisons for heterogeneous items

In this paper, we consider series and parallel systems composed of n independent items drawn from a population consisting of m different substocks/subpopulations. We show that for a series system, the optimal (maximal) reliability is achieved by drawing all items from one substock, whereas, for a parallel system, the optimal solution results in an independent drawing of all items from the whole mixed population. We use the theory of stochastic orders and majorization orders to prove these and more general results. We also discuss possible applications and extensions.

ON STOCHASTIC COMPARISONS FOR LOAD-SHARING SERIES AND PARALLEL SYSTEMS

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning, however, the corresponding additional assumptions are not obvious, which can be seem from the proofs of our theorems