Probabilistic Evaluation of Industrial Systems under Daily Operational Cycles with Constraints on Maximum Repair Time

Probabilistic Evaluation of Industrial Systems under Daily Operational Cycles with Constraints on Maximum Repair Time | 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 Probabilistic Evaluation of Industrial Systems under Daily Operational Cycles with Constraints on Maximum Repair Time Mohamed ElSherbeny This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7514819/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This article focuses on the performance of a single-active-unit repairable industrial system with three different states of unit: active unit (N), partial failure unit (P), and complete failure unit (F). The system operates continuously, 24 hours a day, without interruption, except for two cases: a complete failure of the active unit or maintenance at partial failure (P). The system always has one service available, which is kept for maintenance and repair. In the case of complete failure, the faulty unit is replaced with a new one if the repair duration exceeds the maximum allowed time predefined. However, the nighttime replacement operations have a lot of challenges that may include limited availability of spare part suppliers or replacement must be performed at a higher cost since options are limited. In this paper, it is assumed that all the times in the system are negative exponentially distributed. The supplementary variable technique and Markov process theory have been employed to evaluate the reliability of the system. Further sensitivity and relative sensitivity analyses are performed on some system parameters in order to study the effect of these parameters on the proposed system. These results are presented with numerical examples that provide useful insights contributing to the enhancement of the systems efficiency and operational reliability. Single-unit System Reliability analysis Sensitivity analysis Maximum repair times Day and night hours Supplementary variable technique Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-7514819","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":516031805,"identity":"2f174fcb-22d1-40f3-b8d3-c038a6e3c6fd","order_by":0,"name":"Mohamed ElSherbeny","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYHACxgMMDEAkAWJXMDAYEKMHScsZkrUwthGhRbeB+cABhj935MxnNx97zDvvsLw5e/MBhh8V23BqMTvAlnCAse2ZscydY+nGvNsOG+7sOZbA2HPmNh4tPAYHGBsOJ86QyDGTBmph3HAjx4CZsQ2fFv4PQIcdrp8hkf9NmnfOYXsitPAA/c52OEFCIodNmhdoHRFa2IAOaztsOEPmmJnknGPpyRvOHEs4iN8vzA8fAB0mLyHd/EziTY217YbjzQcf/KjArYVB/gED8x8om4mHoRnMOIBbPRpg/MFQR7TiUTAKRsEoGDkAAEXIXv7dJdbQAAAAAElFTkSuQmCC","orcid":"","institution":"Jeddah International College (JIC)","correspondingAuthor":true,"prefix":"","firstName":"Mohamed","middleName":"","lastName":"ElSherbeny","suffix":""}],"badges":[],"createdAt":"2025-09-02 07:53:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7514819/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7514819/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91605088,"identity":"c9dd7e93-a3e0-4ef0-937b-bdba11318f06","added_by":"auto","created_at":"2025-09-18 09:11:54","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":852954,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript..pdf","url":"https://assets-eu.researchsquare.com/files/rs-7514819/v1_covered_f240967f-e5e2-45f0-8aa0-fb10923146e7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Probabilistic Evaluation of Industrial Systems under Daily Operational Cycles with Constraints on Maximum Repair Time","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Single-unit System, Reliability analysis, Sensitivity analysis, Maximum repair times, Day and night hours, Supplementary variable technique","lastPublishedDoi":"10.21203/rs.3.rs-7514819/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7514819/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article focuses on the performance of a single-active-unit repairable industrial system with three different states of unit: active unit (N), partial failure unit (P), and complete failure unit (F). 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