On Stress-Strength Interval-System Reliability with Applications in Heart Conditions

The random variable X represents the stress placed on the system by the operating environment and random variable Y represents the strength of the system. A system is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability of the system is define...

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Main Author: Hoang Pham
Format: Article
Language:English
Published: International Journal of Mathematical, Engineering and Management Sciences 2020-02-01
Series:International Journal of Mathematical, Engineering and Management Sciences
Subjects:
Online Access:https://ijmems.in/volumes/volume5/number1/1-IJMEMS-19-564-51-112-2020.pdf
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spelling doaj-02e8067f2af74a7ea87570b2d64fe54d2020-11-25T01:46:31ZengInternational Journal of Mathematical, Engineering and Management SciencesInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492020-02-015111210.33889/IJMEMS.2020.5.1.001On Stress-Strength Interval-System Reliability with Applications in Heart ConditionsHoang Pham0Department of Industrial and Systems Engineering, Rutgers University, New Jersey, 08854, USAThe random variable X represents the stress placed on the system by the operating environment and random variable Y represents the strength of the system. A system is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability of the system is defined as the probability that the system is strong enough to overcome the stress. That is, R = P(Y >X). In other words, reliability is the probability that the strengths of the unit are greater than the stresses. The stress-strength model has found interests in many applications include mechanical engineering and human heart monitoring conditions. The interval-system is defined as a system with a series of chance events that occur in a given interval of time. A k-out-of-n interval-system is a system with a series of n events in a given interval of time which successes (or functions) if and only if at least k of the events succeed (function). In short, the k-out-of-n interval-system is an interval-system which successes if and only if at least k of n events succeeds. The stress-strength reliability inference of the interval-system with a series of n independent events that occurs in a given interval of time is considered. The reliability of the interval-system is the probability that at least k out of n events in a given interval of time succeed. This paper derives uniform minimum variance unbiased and maximum likelihood reliability estimates of k-out-of-n interval-system based on stress-strength inference events where X (stress) and Y (strength) are independent two-parameter exponential random variables. An application in human heart conditions to illustrate the results is discussed.https://ijmems.in/volumes/volume5/number1/1-IJMEMS-19-564-51-112-2020.pdfk-out-of-n systemsystem reliabilityheart monitoring conditionumvuestress strength interval system
collection DOAJ
language English
format Article
sources DOAJ
author Hoang Pham
spellingShingle Hoang Pham
On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
International Journal of Mathematical, Engineering and Management Sciences
k-out-of-n system
system reliability
heart monitoring condition
umvue
stress strength interval system
author_facet Hoang Pham
author_sort Hoang Pham
title On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
title_short On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
title_full On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
title_fullStr On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
title_full_unstemmed On Stress-Strength Interval-System Reliability with Applications in Heart Conditions
title_sort on stress-strength interval-system reliability with applications in heart conditions
publisher International Journal of Mathematical, Engineering and Management Sciences
series International Journal of Mathematical, Engineering and Management Sciences
issn 2455-7749
2455-7749
publishDate 2020-02-01
description The random variable X represents the stress placed on the system by the operating environment and random variable Y represents the strength of the system. A system is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability of the system is defined as the probability that the system is strong enough to overcome the stress. That is, R = P(Y >X). In other words, reliability is the probability that the strengths of the unit are greater than the stresses. The stress-strength model has found interests in many applications include mechanical engineering and human heart monitoring conditions. The interval-system is defined as a system with a series of chance events that occur in a given interval of time. A k-out-of-n interval-system is a system with a series of n events in a given interval of time which successes (or functions) if and only if at least k of the events succeed (function). In short, the k-out-of-n interval-system is an interval-system which successes if and only if at least k of n events succeeds. The stress-strength reliability inference of the interval-system with a series of n independent events that occurs in a given interval of time is considered. The reliability of the interval-system is the probability that at least k out of n events in a given interval of time succeed. This paper derives uniform minimum variance unbiased and maximum likelihood reliability estimates of k-out-of-n interval-system based on stress-strength inference events where X (stress) and Y (strength) are independent two-parameter exponential random variables. An application in human heart conditions to illustrate the results is discussed.
topic k-out-of-n system
system reliability
heart monitoring condition
umvue
stress strength interval system
url https://ijmems.in/volumes/volume5/number1/1-IJMEMS-19-564-51-112-2020.pdf
work_keys_str_mv AT hoangpham onstressstrengthintervalsystemreliabilitywithapplicationsinheartconditions
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