Reliability evaluation of weighted voting system based on D–S evidence theory

Abstract

In classic weighted voting systems (WVSs), a voting unit (VU) is subjected to a three-failure mode, and the VU's decision result is represented as a definite one-dimensional variable, which causes the loss of the decision information of the VU. The VU's decision result is not fully utilized because of the use of the majority rule. In this study, we improve the WVS model and propose two new models. We analyze the failure mode of the VU in the new model and provide a method for calculating the probability of the occurrence of a VU failure. To avoid the loss of the VUs’ decision information, we use the basic probability assignment (BPA) function to characterize the decision results in the new models and propose four rules for generating the BPA. Three theorems are proved for combining different types of decision results of the VUs. We also replace the majority rule in the WVS with the Dempster combination rule to fully utilize the decision results of the VUs. We devise two algorithms to evaluate the reliability of the two new WVS models and conduct two experiments to test the utility of the proposed algorithms and analyze the effects of system parameters on the system reliability.