Reliability of 2-within consecutive (2, 2)‎-out-of-(m, n)‎ : F systems using Markov chain

Abstract EN

The 2-dimensional k-within-consecutive (r,s)-out-of-(m,n): F linear (rectangle) and circular (cylindrical) system fails if there is at least k failed components through the sub matrix r ×s components.

For example, the 2-within-consecutive (2,2)-out-of-(m,n): F linear (rectangle) and circular (cylindrical) system fails if there is at least 2 failed components through any sub matrix 2× 2 components.

In this paper, a new algorithm is obtained to imbed the 2-withinconsecutive (2,2)-out-of-(m,n): F rectangle (cylindrical) system in a Markov chain; this gives the possibility for computing the reliability in terms of the transition probabilities matrix of the considered Markov chain.

Furthermore, the computational process of the reliability of the cylindrical system is simpler than the rectangle system since the number of states of the Markov chain in the cylindrical case is less than that in the rectangle case.