Quantitative System Management with Hierarchized Cellular Automata (1st Report, Fundamental Theory)

If a system is composed of only one element, it is possible to evaluate the stability of the system with the Stress-Strength model. However, it is impossible to evaluate the stability of a complex system in which huge amounts of element are linked to each other. To estimate the stability of a complex system, we need to consider the whole structure of the system including interaction between the elements. In this paper, we propose a hierarchized Cellular Automata (HCA) for rational and quantitative system management. In the HCA method, the system is expressed as a lamination structure, which is composed of some hierarchies. Each hierarchy is composed of some elements; each element has a characteristic status value, inputs and outputs. With the HCA method, we can understand the stability of the whole system in terms of probability, by considering local interactions between the elements. As a numerical example, the HCA method is applied to a model of a human organization's conscious changing process. The stability of this model is calculated by numerical simulation, and a probability distribution of the stability of the system is obtained. In conclusion, it is found that the stability of the whole system can be evaluated using the probability distribution.