Usual Stochastic and Hazar Rate Orderings of Fail-Safe Systems: A Multiple-Outlier Approach for Generalized Scaled Log-Logistic Model

Usual Stochastic and Hazar Rate Orderings of Fail-Safe Systems: A Multiple-Outlier Approach for Generalized Scaled Log-Logistic Model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Usual Stochastic and Hazar Rate Orderings of Fail-Safe Systems: A Multiple-Outlier Approach for Generalized Scaled Log-Logistic Model Marzieh Shekari, Zohreh Pakdaman, Ghobad Saadat Kia Barmalzan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9398932/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract This study provides a comprehensive analysis of fail-safe systems incorporating multiplegeneralized scaled log-logistic outlier components. In this Regard, two structural frameworksare examined: one in which system components operate independently, and another in whichdependence is introduced through an Archimedean survival copula. To establish rigorouscomparisons, we explore ordering relations with respect to the usual stochastic order andthe hazard rate order. The investigation leverages the majorization property of generalizedscaled log-logistic parameters with multiple outliers, thereby offering deeper insight into thereliability and performance assessment of fail-safe structures under both independent anddependent settings. To complement these theoretical derivations, an extensive Monte Carlosimulation study is conducted to quantify the magnitude of the reliability improvement andrigorously validate the underlying data-generating process using a suite of modern diagnostictools. AMS 2000 Subject Classification: Primary 62N05; Secondary 62F10. Fail-safe systems Usual stochastic order Hazard rate order Majorization order Multiple-outlier models Archimedean survival copula Generalized scaled loglogistic model Full Text Additional Declarations No competing interests reported. Supplementary Files Dr.Shekarifailsave.rar Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 27 Apr, 2026 Reviewers agreed at journal 25 Apr, 2026 Reviewers invited by journal 15 Apr, 2026 Editor assigned by journal 15 Apr, 2026 Submission checks completed at journal 13 Apr, 2026 First submitted to journal 13 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9398932","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626354485,"identity":"e4088331-8d85-433d-adce-eca7e2068944","order_by":0,"name":"Marzieh 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