Reliability of three-dimensional consecutive k-type systems

Three-dimensional consecutive k-type systems are widely found in reliability practice such as in sensing systems, but it is not an easy task to evaluate reliability of these systems. In this paper, several three-dimensional consecutive k-type systems, namely, linear connected -(k1, k2, k3)-out-of -(n1, n2, n3) : F system, linear con-nected -(k1, k2, k3)!-out-of -(n1, n2,n3) : F system, and linear l-connected -(k1, k2, k3)-out-of -(n1, n2, n3) : F system, without/with overlapping, are studied. Reliability of these systems is determined by using finite Markov chain imbedding approach (FMCIA), and some specific techniques are employed to reduce the state space of the involved Markov chain. Some numerical illustrative examples are then provided to demonstrate the accuracy and efficiency of the proposed method, and finally some possible applications and generalizations are pointed out.