Bounds for increasing multi-state consecutive \(k\)-out-of-\(r\)-from-\(n\): \(F\) system with equal components probabilities

DOI10.1016/j.apm.2010.11.059zbMath1217.90088OpenAlexW2058610999MaRDI QIDQ554719

Taha Radwan, R. Alseedy, A. Elsherbeny, Aziz Habib

Publication date: 21 July 2011

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2010.11.059

zbMATH Keywords

upper boundinclusion exclusion formulalower boundmulti-state consecutive \(k\)-out-of-\(r\)-from-\(n\): F system

Mathematics Subject Classification ID

Reliability, availability, maintenance, inspection in operations research (90B25) Applications of renewal theory (reliability, demand theory, etc.) (60K10)

Related Items (7)

New bounds for the probability that at least \(k\)-out-of-\(n\) events occur with unimodal distributions ⋮ ALGEBRAIC RELIABILITY OF MULTI-STATE k-OUT-OF-n SYSTEMS ⋮ Unnamed Item ⋮ Consecutive k and Related Models—A Survey ⋮ Computing tolerance limits for the lifetime of a \(k\)-out-of-\(n\):\(F\) system based on prior information and censored data ⋮ An improved algorithm for finding all upper boundary points in a stochastic-flow network ⋮ The value of shape constraints in discrete moment problems: a review and extension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bonferroni inequalities
• Reliability evaluation of multi-state consecutive \(k\)-out-of-\(r\)-from-\(n:G\) system
• A consecutive-k-out-of-n:G system: the mirror image of a consecutive-k-out-of-n:F system
• A rearrangement inequality for the longest run, with an application to network reliability
• Boole-Bonferroni Inequalities and Linear Programming
• A weibull limit for the reliability of a consecutive k-within-m-out-of-n system
• Closed Form Two-Sided Bounds for Probabilities that At Least r and Exactly r Out of n Events Occur
• An improved Bonferroni inequality and applications
• Optimal-arrangement and importance of the components in a consecutive-k-out-of-r-from-n:F system
• Reliability of a consecutive k-out-of-r-from-n:F system
• Bounds on the probability of the union and intersection of m events
• An upper bound for the probability of a union
• Most Stringent Bounds on Aggregated Probabilities of Partially Specified Dependent Probability Systems
• Bounds for reliability of consecutive k-within-m-out-of-n:F systems
• Methods for Proving Bonferroni Type Inequalities
• Best Possible Inequalities for the Probability of a Logical Function of Events
• An Inequality for Probabilities
• Multistate reliability models

This page was built for publication: Bounds for increasing multi-state consecutive \(k\)-out-of-\(r\)-from-\(n\): \(F\) system with equal components probabilities