Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components. (English) Zbl 1458.60032

Patra, Lakshmi Kanta; Kayal, Suchandan; Nanda, Phalguni

Appl. Math., Praha 63, No. 1, 55-77 (2018).

Summary: We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different scale and shape parameters is studied when its matrix of parameters changes to another matrix in certain sense.

MSC:

60E15	Inequalities; stochastic orderings
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

stochastic order; parallel system; series system; majorization; multivariate chain majorization; Pareto type distribution; \(T\)-transform matrix