In this paper, a method to determine the reliability index of distributed parameter systems by using a method of approximation the multi-condition dependent probability by a one-condition dependent probability is proposed. Therefore, the problem of the reliability index of distributed parameter system is transformed into the defined case. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 22, 2000, No 4 (248 - 256) RELIABILITY INDEX OF DISTRIBUTED PARAMETER SYSTEM NGUYEN VAN PHO Hanoi University of Civil Engineering ABSTRACT. In this paper, a method to determine the reliability index of distributed parameter systems by using a method of approximation the multi-condition dependent probability by a one-condition dependent probability is proposed. Therefore, the problem of the reliability index of distributed parameter system is transformed into the defined case. To illustrate for the method, the reliability index of air tube is considered. 1. Introduction The reliability of a system in general, and that of structures in particular, have been studied for many years. Some works have either directly or indirectly referred to the reliability of distributed parameter system (DPS) [1-9]. DPS herein means a system of which parameters depend on space and time variables. Until now, studies on DPS have limited themselves to the level of formulation of problem or consideration of simple cases. In general, mechanical systems are systems with distributed parameters, whose solutions have to satisfy a system of differential equations. It is not easy however, to modelize DPS by electrical networks, in order to facilitate the reliability computation. On the other hand, DPS is composed of elements linked together by relations of equational and inequational forms . Consequently, to compute the reliability of DPS, we have to consider the problem of the cross, a level in multidimensional space of a stochastic process [9]. Many difficulties are therefore faced. The many problems of mechanics, such as; optimal design problem; limit analysis problem; shakdown problem; etc., the number of conditions expressed by equation forms is less than that of the unknowns; therefore, the schema for computation of reliability given in [2, 5] is not available. 248 As we know [1], in case the probability is dependent upon one .
