Reliability of Simple 3-Dimnesional Consecutive k-Out-of-n: F Systems | Science Publications

Journal of Mathematics and Statistics

E. M. El-Sayed¹  M. Gharib¹  I. I. Nashwan¹ 

关键词: (1;    2 and 3) D-consecutive k-out-of-n: F system;    k-within (k1;    k2;    k3) -out-of- (m;    n;    l): F system;    Markov chains;   

DOI  :  10.3844/jmssp.2010.261.264

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: In this study, the reliability of some special cases of a 3-dimnesional consecutive k-out-of-n: F system and k-within consecutive (2,2,2) -out-of- (m,2,2): F system were discussed. Approach: The 3 dimensional systems is a generalization of 1 and 2 dimensional, systems. Projections from 3 dimensional systems to 2 or 1 dimension as special cases is very helpful to find the reliability of these 3 dimensional systems. Results: Many reliability expressions for the 3-dimensional consecutive (k₁,k₂,k₃) -out-of- (m,n,l): F system for some special values of k₁, k₂, k₃, m, n,l are presented. Further, the reliability of k-within (2, 2, 2)-out-of-(m,2,2): F system using Markov chains is considered. Conclusion/Recommendations: In general, it is difficult to find the reliability of (k₁,k₂,k₃) -out-of- (m,n,l): F system, we studied special cases of this system and recommend generalizing the result for any value of k₁, k₂, k₃, m, n,l. This study presented the reliability formulas of simple 3D systems using results of consecutive k-out-of-n: F systems and 2D consecutive k-out-of-n: F systems and Markov chains.

【 授权许可】

Unknown