Priority effect on pointwise availability of the system

Abstract

Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle, tome 6, n o V1 (1972), p. 47-56. <http://www.numdam.org/item?id=RO_1972__6_1_47_0> © AFCET, 1972, tous droits réservés. L'accès aux archives de la revue « Revue française d'automatique, d'informatique et de recherche opérationnelle. Recherche opérationnelle » implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/ legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Dynamic analysis of a complex system under preemptive repeat repair discipline

“…Hence, the time-dependent reliability of the system, by a similar argument, converges to a constant number, i.e., Remark 5.1 If we add the normalizing condition P 0 (t) + 3 n=1 ∞ 0 P i (t, x) dx = 1, then in the steady-state case we obtain the results in Govil [27]. In other words, our results imply the results in Govil [27].…”

“…By the supplementary variable technique, the above system can be described by the following system of partial differential equations (see Govil [27]):…”

“…One of these methods is to assign priority according to the nature of components of the system. Govil [27] considered the system composed of two types (denoted hereafter as Type I and II) of components, in which Type I component has the priority with preemptive repeat repair disciplines. The model proposed in that paper was based on the supplementary variable technique and gave the Laplace transform of the probability generating function which was defined by the time-dependent solution.…”