An Extension of the Target Theory in Biology Applied to System Reliability

Thierry Bastogne () and Pierre Vallois
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Thierry Bastogne: INRIA-BIGS, CNRS UMR 7039, BP 239
Pierre Vallois: INRIA-BIGS, CNRS UMR 7502, BP 239

A chapter in Models and Methods in Economics and Management Science, 2014, pp 155-181 from Springer

Abstract: Abstract We consider rough products produced by a factory. Each product coming from the plant has $$m$$ m vital elements and some elements can be damaged. To obtain a perfect product (i.e. all the constitutive $$m$$ m elements are safe) all the damaged elements are repaired and a test phase follows. The result of this two-steps procedure is random. We suppose that the number $$Z_k$$ Z k of non-damaged elements is a Markov chain valued in the set $$\{0,1,\ldots ,m\}$$ { 0 , 1 , … , m } , where $$k$$ k is the number of applied repairing-test phases. We have a qualitative result which says that if the repair phase is efficient then $$P(Z_k=m)$$ P ( Z k = m ) is close to $$1$$ 1 . As for production of a large number $$n$$ n of products, the former result allows us to give conditions under which either the $$n$$ n elements or a fraction of these $$n$$ n elements are (is) safe after the application of $$k$$ k previous maintenance phases.

Keywords: Reliability; Repairing procedure; Target theory; Treatment of cancer by radiotherapy; Damaged cell; Markov chain; Large deviations (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-00669-7_9

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