Ordering results for series and parallel systems comprising heterogeneous exponentiated Weibull components

ABSTRACT

In this paper, we discuss the usual stochastic and reversed hazard rate orders between the series and parallel systems from two sets of independent heterogeneous exponentiated Weibull components. We also obtain the results concerning the convex transform orders between parallel systems and obtain necessary and sufficient conditions under which the dispersive and usual stochastic orders, and the right spread and increasing convex orders between the lifetimes of the two systems are equivalent. Finally, in the multiple-outlier exponentiated Weibull models, based on weak majorization and p-larger orders between the vectors of scale and shape parameters, some characterization results for comparing the lifetimes of parallel and series systems are also established, respectively. The results of this paper can be used in practical situations to find various bounds for the important aging characteristics of these systems.

KEYWORDS:

• Exponentiated Weibull distribution
• Multiple-outlier model
• Order statistics
• p-larger order
• Stochastic orders
• Weak majorization order

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 90B25