Evaluating MTTF of 2-out-of-3 redundant systems with common cause failure and load share based on alpha factor and capacity flow models

K-out-of-n redundant systems are used to increase reliability in various industries. The failure of a component in such systems is dependent upon the failure of other components. Therefore, if an appropriate model is not developed to take dependent failures into consideration, reliability and MTTF of redundant systems are evaluated wrongly. One of the most crucial varieties of dependent failures is common cause failure. Common cause failure refers to the failure of two or more components of a k-out-of-n system which occurs simultaneously or within a short time interval and thus components are direct failures resulting from a shared cause. Another type of dependent failure in k-out-of-n redundant systems is load share, where the failure of one component leads to increased load in surviving components, hence changing their failure rate. In this paper, using Markov chain, three models are used to evaluate the MTTF of a 2-out-of-3 redundant system by taking dependent failures into account. Model I addresses the MTTF of a 2-out-of-3 redundant system by considering common cause failure based on alpha factor model. In Model II, both dependent failures (common cause failure and load share) are examined based on capacity flow and alpha factor model. In Model III, in addition to common cause failure and load share, component repair is studied, too. In order to examine the validity of the models introduced and conduct sensitivity analysis, some diagrams are drawn for each model. Considering the dependent failures in the 2-out-of-3 redundant systems, all the three proposed models can be practical and be used to evaluate MTTF.