Applications of Mathematics, Vol. 63, No. 1, pp. 55-77, 2018
Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components
Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda
Received April 20, 2017. First published January 17, 2018.
Abstract: 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.
Keywords: stochastic order; parallel system; series system; majorization; multivariate chain majorization; Pareto type distribution; $T$-transform matrix
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Affiliations: Lakshmi Kanta Patra, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India; Suchandan Kayal (corresponding author), Phalguni Nanda, Department of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, India, e-mails: suchandan.kayal@gmail.com, kayals@nitrkl.ac.in
