Stochastic behaviour of a complex system with bulk failure and priority repairs

— Behaviour of a complex System consisting of two classes of components L\ and La is considérée, where failure in class L\ results in complete breakdown of the system and that in class L& brings the system to a reduced efficiency state. In class Li failure follows exponential distribution but unlike the earlier studies [1, 2, 4], in class L& bulk failure is assumed. In both the classes, repair follows gênerai distribution. Use of Laplace Transforms and Supplementary variable technique have been made to obtain the solution. Asymptotic behaviour of the system has also been examined. INTRODUCTION In many operating Systems, it is observed that there are components or parts which when fail, bring the system to a reduced efficiency state. Quite a good number of studies evaluating the behaviour of such Systems have been carried out [1, 2, 3, 4], In all such studies, it has been assumed that in a small interval of time, only one component fails. But in many reaîistic situations like Téléphone exchanges and electronic computers, it is observed that components do fail in bulk. Keeping this in view, a complex system comprising of two classes of components (denoted hereafter as class L1 and L2) has been considered. Class Lt consists of N components Connecting in series where failure of a component brings about the complete breakdown of the system wherein failure and repair of components of this class follow exponential and gênerai distributions, respectively. Class L2 consists of several components which fail in bulk and the failure form a Poisson process with an average failure rate X'. The failure of components in class L2 causes the system to work in reduced efficiency state. For repair purposes, it has been furthur assumed that the failed components of class Lx join priority class and those of class L2 join the non-priority class. Behaviour of such a system has been evaluated under I Head of Line | (1) Directorate of Scientific Evaluation, Ministry of Defence, New Delhi (India). Revue Française d'Informatique et de Recherche opérationnelle n° V-l, 1971.