Ordering results of the smallest order statistics from independent heterogeneous new modified generalized linear failure rate random variables

Abstract

This article deals with stochastic comparisons of series systems comprising a new modified generalized linear failure rate family of distributions. The results are established in three directions. First, we establish based on vector majorization the usual stochastic order and the hazard rate order of series systems. Next, multiple-outlier models are considered. When the number of components is equal, the results are obtained in terms of the likelihood ratio order. For an unequal number of components, we develop comparisons according to the usual stochastic order, and hazard rate order. Then, based on weak majorization and p-larger orders between the vector of parameters, some characterization results for comparing the lifetimes of series systems are also established. Finally, we discuss based on multivariate chain majorization the usual stochastic order of series systems. Numerical examples are considered to illustrate the results.

Keywords:

• New modified generalized linear failure rate distribution
• order statistics
• stochastic orders
• multiple-outlier model
• series systems

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 62G30
• 62D05
• 62N05

Acknowledgments

The authors thank the Editor and anonymous Referees for their helpful comments, which contributed greatly to improve this paper.