scholarly journals Stochastic Comparisons of Parallel and Series Systems Comprising Multiple-Outlier Scale Components

2022 ◽  
Vol 15 (2) ◽  
pp. 341-362
Author(s):  
Ebrahim Amini Seresht ◽  
Ghobad Barmalzan ◽  
◽  
Keyword(s):  
Stochastic Comparisons ◽  
Series Systems

scholarly journals Stochastic Comparisons of Symmetric Supermodular Functions of Heterogeneous Random Vectors

2013 ◽  
Vol 50 (02) ◽  
pp. 464-474
Author(s):  
Antonio Di Crescenzo ◽  
Esther Frostig ◽  
Franco Pellerey
Keyword(s):  
Queueing Theory ◽  
Queueing Networks ◽  
Random Variables ◽  
Random Vectors ◽  
Convex Order ◽  
Stochastic Comparisons ◽  
Increasing Convex Order ◽  
Supermodular Functions ◽  
Stop Loss ◽  
Series Systems

Consider random vectors formed by a finite number of independent groups of independent and identically distributed random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batches.

A note on stochastic comparisons of excess lifetimes of renewal processes

2001 ◽  
Vol 38 (03) ◽  
pp. 747-753 ◽  
Author(s):  
Félix Belzunce ◽  
Eva M. Ortega ◽  
José M. Ruiz
Keyword(s):  
Laplace Transform ◽  
Renewal Process ◽  
Renewal Processes ◽  
Stochastic Comparisons ◽  
The Laplace Transform ◽  
Interarrival Times ◽  
Laplace Transform Order ◽  
Series Systems ◽  
New Better Than Used ◽  
Better Than

In this paper we provide new results about stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to several ageing classes. We also provide a preservation result for the new better than used in the Laplace transform order ageing class for series systems.

COMPARISONS OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

2013 ◽  
Vol 28 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Weiyong Ding ◽  
Gaofeng Da ◽  
Xiaohu Li
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Parallel Systems ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Series Systems

This paper carries out stochastic comparisons of series and parallel systems with independent and heterogeneous components in the sense of the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. The main results extend and strengthen the corresponding ones by Misra and Misra [18] and by Ding, Zhang, and Zhao [8]. Meanwhile, the results on the hazard rate order of parallel systems and the reversed hazard order of series systems serve as nice supplements to Theorem 16.B.1 of Boland and Proschan [4] and Theorem 3.2 of Nanda and Shaked [20], respectively.

scholarly journals Preservation properties of stochastic orders by transformation to Harris family

2018 ◽  
Vol 38 (2) ◽  
pp. 441-458
Author(s):  
Somayeh Abbasi ◽  
Mohammad Hossein Alamatsaz
Keyword(s):  
Random Number ◽  
Stochastic Orders ◽  
Stochastic Comparisons ◽  
Number Of Components ◽  
Lifetime Analysis ◽  
Reliability Systems ◽  
Series Systems

Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.

A note on stochastic comparisons of excess lifetimes of renewal processes

2001 ◽  
Vol 38 (3) ◽  
pp. 747-753 ◽  
Author(s):  
Félix Belzunce ◽  
Eva M. Ortega ◽  
José M. Ruiz
Keyword(s):  
Laplace Transform ◽  
Renewal Process ◽  
Renewal Processes ◽  
Stochastic Comparisons ◽  
The Laplace Transform ◽  
Interarrival Times ◽  
Laplace Transform Order ◽  
Series Systems ◽  
New Better Than Used ◽  
Better Than

In this paper we provide new results about stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to several ageing classes. We also provide a preservation result for the new better than used in the Laplace transform order ageing class for series systems.

Stochastic comparisons of parallel and series systems with heterogeneous resilience-scaled components

Statistics ◽  
2018 ◽  
Vol 53 (1) ◽  
pp. 126-147 ◽  
Author(s):  
Yiying Zhang ◽  
Xiong Cai ◽  
Peng Zhao ◽  
Hairu Wang
Keyword(s):  
Stochastic Comparisons ◽  
Series Systems
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