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

In: Models and Methods in Economics and Management Science

Author

Listed:
  • Thierry Bastogne

    (INRIA-BIGS, CNRS UMR 7039, BP 239)

  • Pierre Vallois

    (INRIA-BIGS, CNRS UMR 7502, BP 239)

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.

Suggested Citation

  • Thierry Bastogne & Pierre Vallois, 2014. "An Extension of the Target Theory in Biology Applied to System Reliability," International Series in Operations Research & Management Science, in: Fouad El Ouardighi & Konstantin Kogan (ed.), Models and Methods in Economics and Management Science, edition 127, pages 155-181, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-00669-7_9
    DOI: 10.1007/978-3-319-00669-7_9
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