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

Existing studies about two-dimensional consecutivek-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-k-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.