Reliability of 2-within Consecutive (2,2)-out-of-(m,n) : F Systems Using Markov Chain

Abstract

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.