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 engineer- ing 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.
