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This paper examines the chaotic properties of the elementary cellular automaton rule 40. Rule 40 has been classified into Wolfram's class I and also into class 1 by G. Braga et al. These classifications mean that the time-space patterns generated by this cellular automaton die out in a finite time and so are not interesting. As such, we may hardly realize(More)
The present paper considers multi-state systems which are regarded as a generalization of binary systems, and generalizes the concepts of BW systems proposed by R. E. Barlow and Alexander S. Wu. Since the structure function of a BW system is defmed by using tht: minimal path sets of a binary coherent system, the BW system has a strict restriction that the(More)
In this paper we exactly calculate the Lyapunov exponents and two kinds of spreading rates for elementary cellular automaton (ECA) rule 40. One spreading rate, simply called the spreading rate, is defined by following A. Ilachinski [1], and the other one originally defined in this paper is called the strict spreading rate. For the Lyapunov exponents, we use(More)
This paper deals with the M + 1-out-of-N:G system with correlated failure and single repair facility, where correlated failure means that i (1 ~ i ~ N) operating units in the system are possible to fail at the same time. We consider two repair policies, and under each repair policy Laplace transform of point-wise availability and reliability, meantime to(More)
In the reliability theory th,e joint life distribution of units is usually derived under the assumption of stochastic independence for the behavior of units. But it is seen in the practical situation that the stochastic dependence arises by the cause of putting the units in a same environment and so on. A shock model is used to formulate the joint life(More)
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