Séminaire Majid Asadi

Jeudi 14 Avril 2011 (14h00)

Majid Asadi, Department of Statistics, University of Isfahan, IRAN.

Titre : On the reliability properties of coherent systems.

 

Résumé : The concept of ‘signature’ is a useful tool to study the stochastic and aging properties of coherent systems. Let X1:n;X2:n;...;Xn:n denote the ordered lifetimes of the components of a coherent system. Assuming that T denotes the lifetime the system, the signature of the system is defined to be a vector s = (s1; s2;...; sn) in which si = P(T = Xi:n), i = 1; 2;...; n. In this talk, we consider a coherent system and assume that there is some partial information about the failure status of the system e.g. the lifetime of the system is in a set A, where A is in [0;1).

We study various properties of the conditional signature with elements P(T = Xi:njT 2 A), i = 1; 2;...; n, where A is either of the form A = ftg, or A = (t;1) or A = (0; t), t > 0: Some coherent systems have the property that in the time of failure of the system, some of components remain unfailed in the system. We address the stochastic and aging properties of the residual lifelengths of the remaining components of the system under different conditions. There are also coherent systems with the property that, when some components of the system fail, the system remains alive. For such systems, the stochastic properties of inactivity time of the failed components in the system, under various scenarios, are investigated.