An extension of the target theory in biology applied to system reliability

Thierry Bastogne (1, 2) , Pierre Vallois (1, 3)

1 BIGS - Biology, genetics and statistics
2 CRAN - Centre de Recherche en Automatique de Nancy
3 IECL - Institut Élie Cartan de Lorraine

We consider rough products produced by a factory. Each product coming from the plant has m vital elements and some elements can be damaged. To obtain a perfect product (i.e. all the constitutive 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 Zk of non-damaged elements is a Markov chain valued in the set {0,1,...,m}, where 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(Zk=m) is close to 1. As for production of a large number n of products, the former result allows us to give conditions under which either the n elements or a fraction of these n elements are (is) safe after the application of k previous maintenance phases.

Mots clés: large deviation; Markov chain; damaged cell; treatment of cancer by radiotherapy; target theory; repairing procedure; Reliability

Domaines: Probabilités [math.PR]; Applications [stat.AP]; Cancer

Thierry Bastogne, Pierre Vallois. An extension of the target theory in biology applied to system reliability. Fouad El Ouardighi and Konstantin Kogan. Models and Methods in Economics and Management Science: Essays in Honor of Charles S. Tapiero, Springer, pp.155-181, 2014, International Series in Operations Research & Management Science, 978-3-319-00668-0. ⟨hal-00911872⟩