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New Bounds for the k-out-of-n Type P...

Binmahfoudh, Ahmed M.

New Bounds for the k-out-of-n Type Probabilities and Their Applications.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	New Bounds for the k-out-of-n Type Probabilities and Their Applications./
Author:	Binmahfoudh, Ahmed M.
Description:	1 online resource (128 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Operations research. -
Online resource:	click for full text (PQDT)
ISBN:	9780355200522

New Bounds for the k-out-of-n Type Probabilities and Their Applications.
Binmahfoudh, Ahmed M.

New Bounds for the k-out-of-n Type Probabilities and Their Applications. - 1 online resource (128 pages)

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and an efficient linear programming based bounding methodology, which takes advantage of the advanced optimization techniques, probability theory, and the state-of-the-art tools, to obtain robust and efficiently computable bounds for the probabilities that at least k and exactly k-out-of- n events occur is developed. The k-out-of- n type probability bounding problem is formulated as linear programs under the assumption that the probability distribution is unimodal. The dual feasible bases structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability that at least k and exactly k-out-of-n events occur are obtained in the form of formulas. A dual based linear programming algorithm is proposed to obtain bounds as the customized algorithmic solutions of the LP's formulated. Numerical examples are presented to show that the use of shape constraint significantly improves on the bounds for the probabilities that at least k and exactly k-out-of- n events occur when only first a few binomial moments are known. An application in PERT, where the shape of the underlying probability distribution can be used to obtain bounds for the distribution of the critical path length, is presented.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355200522Subjects--Topical Terms:

573517
Operations research.
Index Terms--Genre/Form:

554714
Electronic books.

New Bounds for the k-out-of-n Type Probabilities and Their Applications.
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245 1 0 $a New Bounds for the k-out-of-n Type Probabilities and Their Applications.
264 0 $c 2017
300 $a 1 online resource (128 pages)
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337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
500 $a Adviser: Munevver Mine Subasi.
502 $a Thesis (Ph.D.) $c Florida Institute of Technology $d 2017.
504 $a Includes bibliographical references
520 $a The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and an efficient linear programming based bounding methodology, which takes advantage of the advanced optimization techniques, probability theory, and the state-of-the-art tools, to obtain robust and efficiently computable bounds for the probabilities that at least k and exactly k-out-of- n events occur is developed. The k-out-of- n type probability bounding problem is formulated as linear programs under the assumption that the probability distribution is unimodal. The dual feasible bases structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability that at least k and exactly k-out-of-n events occur are obtained in the form of formulas. A dual based linear programming algorithm is proposed to obtain bounds as the customized algorithmic solutions of the LP's formulated. Numerical examples are presented to show that the use of shape constraint significantly improves on the bounds for the probabilities that at least k and exactly k-out-of- n events occur when only first a few binomial moments are known. An application in PERT, where the shape of the underlying probability distribution can be used to obtain bounds for the distribution of the critical path length, is presented.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Operations research. $3 573517
655 7 $a Electronic books. $2 local $3 554714
690 $a 0796
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Florida Institute of Technology. $b Mathematical Sciences. $3 1182333
773 0 $t Dissertation Abstracts International $g 79-01B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10646751 $z click for full text (PQDT)

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