Minorants de la fiabilité pour des systèmes à recouvrements.

Zineb Azouz (1)

1 Université de Constantine

In [14], Yi-Chih Hsieh and Ta-Cheng Chen provided a lower bound for the reliability of systems which are generalizations of the well-known linear k-consecutive-out-of-n systems. The combinatorial difficulty in computing the reliability of these systems has led to look for lower bounds. We justify the method for computing such a lower bound, easy to build, proposed in [14] and we generalize it for systems which we call ''with recovering". We also compute for these systems lower bounds which are better than those which would be obtained by following the ideas of [14]and for which the combinatorial difficulty lies between the one due to explicit computation and the one deduced from the method in [14]. Proofs and complements on compilations for linear (dimension 1) k-consecutive-out-of-n systems are provided here; the case of dimension 2 systems will be studied in an incoming paper. Computational methods for such lower bounds are presented for linear (dimension 1) k-consecutive-out-of-n systems and their generalization, of any dimension. in the "Annexe". Their adequacy is studied through numerical studies for such systems in dimension 1. In another paper, we shall extend these computations of lower-bounds to the case of dimension 2.

Mots clés: Relaibility; Lower bounds; Coherent system; k-consecutive-out-of-n; k-consecutive-out-of-n.

Domaines: Probabilités [math.PR]

Zineb Azouz. Minorants de la fiabilité pour des systèmes à recouvrements.. 2012. ⟨hal-00701690⟩