Reliability Modeling on Consecutive- <tex-math notation="LaTeX">kᵣ</tex-math> -out-of- <tex-math notation="LaTeX">nᵣ</tex-math> :F Linear Zigzag Structure and Circular Polygon Structure

We propose the consecutive-k r -out-of-n r :F linear zigzag structure and circular polygon structure, which extend the consecutive-k-out-of-n:F system model. By employing the finite Markov chain imbedding approach, we have proven the equations for calculating the reliability of consecutive-k-out-of-n:F system with different patterns given the state of the first and(or) the last component(s). Based on those reliability equations, we provide the rules for obtaining the reliability of the linear zigzag structure and circular polygon structure. Numerical examples are presented as an illustration of our new system model and demonstrate the use of the equations and rules proposed in this paper.