Asymmetry and Stochastics Applied to Reliability Theory and Engineering

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 4882

Special Issue Editor


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Guest Editor
Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China
Interests: optimal (re)insurance; insurance economics; risk sharing; systemic risk; risk measure; credibility theory; stochastic orders; dependent risk models
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Special Issue Information

Dear Colleagues,

Symmetry is a common feature in many branches of applied mathematics, such as reliability theory and engineering. More specifically, for redundancy allocation problems in reliability theory, researchers usually pay attention to seeking optimal allocation policies for reliability systems with symmetrical structures such as the series, parallel, fail-safe, and k-out-of-n systems.

However, phenomena of asymmetry and stochastics have not only occurred increasingly but also played an increasingly important role in the fields of reliability theory and engineering. For example, reliability systems often have asymmetrical structures in many practical engineering problems, and thus, components may have a different and stochastic/random contribution to the systems’ performances. Therefore, modeling various structures of asymmetry and stochastics and analyzing and comparing effects induced by them become especially important in solving interested problems arising from reliability engineering.

This Special Issue is addressed to scientific researchers working in the fields of reliability theory and engineering. The main aim of this Special Issue is providing a platform for the discussion of the major research challenges and achievements related to asymmetry and stochastics applied in various research areas arising from these two research areas. Research articles as well as review articles are welcome.

The topics include but are not limited to:

  • Reliability analysis of complex systems with asymmetrical structure;
  • Asymmetrical dependence modeling in components lifetimes;
  • Statistical inference on component lifetimes for reliability systems with symmetry/asymmetry structure;
  • Redundancies allocation problem in reliability systems with symmetry/asymmetry structure;
  • Stochastic orders/comparisons on interested variables with symmetry/asymmetry dependent structure;
  • Stochastic behaviors of order statistics.

Dr. Yiying Zhang
Guest Editor

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Keywords

  • asymmetry in reliability analysis of complex systems
  • asymmetrical dependence in components lifetimes
  • statistical inference on component lifetimes
  • systemic risk
  • redundancy allocation problem (RAP)
  • order statistics
  • stochastic orders
  • stochastic comparisons

Published Papers (3 papers)

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Research

16 pages, 402 KiB  
Article
Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method
by Ebrahem A. Algehyne, Farman Ullah Khan, Sami Ullah Khan, Wasim Jamshed and El Sayed M. Tag El Din
Symmetry 2022, 14(10), 2137; https://doi.org/10.3390/sym14102137 - 13 Oct 2022
Cited by 8 | Viewed by 1144
Abstract
The Zika virus model (ZIKV) is mathematically modeled to create the perfect control strategies. The main characteristics of the model without control strategies, in particular reproduction number, are specified. Based on the basic reproduction number, if R0<0, then ZIKV [...] Read more.
The Zika virus model (ZIKV) is mathematically modeled to create the perfect control strategies. The main characteristics of the model without control strategies, in particular reproduction number, are specified. Based on the basic reproduction number, if R0<0, then ZIKV satisfies the disease-free equilibrium. If R0>1, then ZIKV satisfies the endemic equilibrium. We use the maximum principle from Pontryagin’s. This describes the critical conditions for optimal control of ZIKV. Notwithstanding, due to the prevention and treatment of mosquito populations without spraying, people infected with the disease have decreased dramatically. Be that as it may, there has been no critical decline in mosquitoes contaminated with the disease. The usage of preventive treatments and insecticide procedures to mitigate the spread of the proposed virus showed a more noticeable centrality in the decrease in contaminated people and mosquitoes. The application of preventive measures including treatment and insecticides has emerged as the most ideal way to reduce the spread of ZIKV. Best of all, to decrease the spread of ZIKV is to use avoidance, treatment and bug spraying simultaneously as control methods. Moreover, for the numerical solution of such stochastic models, we apply the spectral technique. The stochastic or random phenomenons are more realistic and make the model more informative with the additive information. Throughout this paper, the additive term is assumed as additive white noise. The Legendre polynomials and applications are implemented to transform the proposed system into a nonlinear algebraic system. Full article
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20 pages, 396 KiB  
Article
Copulas Arisen from Degradation-Based Time-to-Failure Models
by Lolwa Alshagrawi and Mohamed Kayid
Symmetry 2022, 14(4), 785; https://doi.org/10.3390/sym14040785 - 9 Apr 2022
Viewed by 1138
Abstract
There are a variety of degradation models in the literature, each with a certain effect of random variation around the mean degradation path on the time-to-failure of the device being degraded. To assess the dependence that the random variation around the mean degradation [...] Read more.
There are a variety of degradation models in the literature, each with a certain effect of random variation around the mean degradation path on the time-to-failure of the device being degraded. To assess the dependence that the random variation around the mean degradation path exerts on the resulting time-to-failure, this paper presents copula functions for time-to-failure-based degradation models with respect to two well-known degradation models, namely, the multiplicative degradation model and the additive degradation model. The implied copula functions for the case of the multiplicative degradation model have explicit forms. The implied copula functions are proved to be symmetric in the case of deterministic effect of degradation on failure, but the copulas obtained when failure is affected uncertainly by degradation are asymmetric. Necessary and sufficient conditions for the implicit copula functions to be symmetric are given. Full article
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27 pages, 711 KiB  
Article
Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks
by Liang Jiao and Rongfang Yan
Symmetry 2021, 13(12), 2248; https://doi.org/10.3390/sym13122248 - 25 Nov 2021
Cited by 2 | Viewed by 1398
Abstract
To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of [...] Read more.
To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods. Full article
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