Two-dimensional linear connected-κ system with trinary states and its reliability

Existing studies about two-dimensional consecutive-κ-out-of-n: F system is dealt with two states (either component or system): working or failure. A new model for two-dimensional linear consecutive-κ-out-of-n: F system is proposed, in which the components and systems can be at any of the three states: full working, derating working, and failure. Furthermore, two engineering concrete instances of the new system are given. By using the finite Markov chain imbedding approach, the system reliability is presented in a unified formula with the product of matrices for the case of independent and identically distributed component states which can be extended to the independent but non-identical case easily. Finally, an example is given to illustrate the effectiveness of the above approach and tractability of various problems.