Reliability Modeling and Analysis of Generalized Majority Systems by Stochastic Computation

The
$k$
-out-of-
$n$
: G(F) majority voter consists of n components (or modules) and a number of the components are required to be operating correctly for the overall system to be correct. As per the state discretization of the components, such a system is usually classified as either a binary system or a multi-state system. In practice, the operating conditions of different components may contribute differently to the operation of the entire system. In this manuscript, the
$k$
-out-of-
$n$
: G(F) majority voter is generalized as a consecutive-weighted-
$k$
-out-of-
$n$
: G(F) voter with either binary states or multiple states. To overcome the drawbacks of existing approaches, a stochastic analysis is proposed for assessing the system reliability. In the stochastic analysis, the input signal probabilities are encoded into non-Bernoulli sequences with fixed numbers of 0s and 1s for the Boolean case, or randomly permuted sequences for the multi-state scenario. By using stochastic logic, the reliability of a general system consisting of consecutive-weighted-
$k$
-out-of-
$n$
majority voters is efficiently and accurately predicted. The results are validated by an analysis of several case studies. Although the accuracy of the stochastic analysis is closely related with the employed sequence length, it is shown that a stochastic approach is more efficient than a universal generating function (UGF) method, while still retaining an acceptable accuracy.