Algorithm for new lower bounds for reliability : F systems and numerical examples
Keywords:
Consecutive-k-out of-n systems hk-within-connected-out-of-(m, n) : F systems Lower Bound of Reliability Algorithm.Abstract
This paper deals around the hk-within-connected-out-of-( , ) mn : F systems consist in rectangular sheets of components, of size m n , such that the system fails if all components in a submatrix of size h k are failing.In [5]has been given the computation of a lower bound for the reliability for such systems, in case of square matrix. We use a method presented in [11]and based on the technic of replication of components to propose new lower bounds, which, in case of square sheets, are better than these in [5]. For this purpose, we rely on an algorithm, called “consecutive columns algorithm” under the additive condition 2 n k . Finally, numerical examples are provided to evaluate the new technique.
References
Yi H, Balakrishnan N, Li X. (2024). Reliability analyses of linear two-dimensional consecutive k-type systems. Journal of Applied Probability; 61(2):439-464. doi:10.1017/jpr.2023.51.
CHANG, G. J., CUI, L. R. AND HWANG, F. K. (2000). Reliabilities of Consecutive-k Systems. Kluwer Academic Publishers, Dordrecht.
