Two-stage weighted intervened decision systems

This paper deals with the reliability and cost evaluation of a type of weighted voting systems under supervision. Both the input and output for each voting unit are binary, 0 or 1. In particular, the decision behavior of each unit is considered to be influenced and intervened by some control mechanism. In addition, the time for each unit to provide the result is a random variable and the probability that each unit will provide a correct result is a function of time. This system is called intervened decision system with weighted voting mechanism. This type of system can be encountered in many areas such as human decision systems, security systems and software development. The formulation and derivation of this paper is based on a human organization system and can be extended to other applications with some modification.