Optimal testing and repairing a failed series system

Mikhail Y. Kovalyov (), Marie-Claude Portmann () and Ammar Oulamara ()
Additional contact information
Mikhail Y. Kovalyov: Belarusian State University
Marie-Claude Portmann: Ecole des Mines de Nancy, Parc de Saurupt
Ammar Oulamara: Ecole des Mines de Nancy, Parc de Saurupt

Journal of Combinatorial Optimization, 2006, vol. 12, issue 3, No 6, 279-295

Abstract: Abstract We consider a series repairable system that includes n components and assume that it has just failed because exactly one of its components has failed. The failed component is unknown. Probability of each component to be responsible for the failure is given. Each component can be tested and repaired at given costs. Both testing and repairing operations are assumed to be perfect, that is, the result of testing a component is a true information that this component is failed or active (not failed), and the result of repairing is that the component becomes active. The problem is to find a sequence of testing and repairing operations over the components such that the system is always repaired and the total expected cost of testing and repairing the components is minimized. We show that this problem is equivalent to minimizing a quadratic pseudo-boolean function. Polynomially solvable special cases of the latter problem are identified and a fully polynomial time approximation scheme (FPTAS) is derived for the general case. Computer experiments are provided to demonstrate high efficiency of the proposed FPTAS. In particular, it is able to find a solution with relative error ɛ = 0.1 for problems with more than 4000 components within 5 minutes on a standard PC with 1.2 Mhz processor.

Keywords: Test and repair policies; Failure diagnosis; Optimization; Pseudo-boolean functions; Fully polynomial time approximation scheme (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-006-9633-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:12:y:2006:i:3:d:10.1007_s10878-006-9633-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-006-9633-0

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().