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The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.
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Kontoleon J M. Reliability determination of r-successive m-out-of-n: F system. IEEE Trans. Reliab. 1980; (41): 451–457.
Nashwan I I H. New Algorithms to find reliability and unreliability functions of the consecutive k-out-of-n: F linear and circular system. The International Arab Conference on Information Technology. Jordan: Isra University; 2015. 1-9.
Gökdere G, Gürcan M, Kılıç M B. A new method for computing the reliability of consecutive k-out-of-n: F Systems. Open Phys. 2016; (14): 166–170.
Shingyochi K, Yamamoto H. An Efficient Algorithm for Solving Optimal Component Arrangement Problem in Circular Consecutive-k-out-of-n: F System (< Special English Issue> Optimization and Its Applications). J. Japan Ind. Manag. Assoc. 2008 Feb 15;58(6):423-9.
Cai Z, Si Sh, Sun Sh, Li C. Optimization of linear consecutive-k-out-of-n system with a Birnbaum Importance based genetic algorithm. Reliab. Eng. Sys. Saf. 2016; (152): 248-258.
Endharta A J, Yun W Y, Yamamoto H. Preventive maintenance policy for linear consecutive-k-out-of-n: F system. J. Oper. Res. Soc. Japan. 2016; (59): 334-346.
Cai Z, Ma Ch, Wang W, Zhang P. Maintenance optimization of consecutive-k-out-of-n system with multi objective Birnbaum Importance-based particle swarm optimization. International Conference on Industrial Engineering and Engineering Management. IEEE. 2019; 1216-1220.
Mohammadia F, Cabezonb E S, Wynnc H P. Efficient multicut enumeration of k-out-of-n: F and consecutive k-out-of-n: F systems. Pattern Recognit. Lett. 2018; (102): 82–88.
Dui H, Chen L, Li J. Importance analysis in two kinds of redundant systems: k-out-of-n and consecutive k-out-of-n: F systems. Adv. Mech. Eng. 2019; (11): 1–13.
Lin C, Cui L, Coit D W, Lv M. Reliability modeling on consecutive-kr-outof-nr: F linear zigzag structure and circular polygon structure. IEEE Trans. Reliab. 2016; (65): 1509–1521.
Mo Y, Xing L, Cui L, Si Sh. MDD-Based performability analysis of multi-state linear consecutive-k-out-of-n: F systems. Reliab. Eng. Sys. Saf. 2017; (166): 24-131.
Kamalja K K, Amrutkar K P. Reliability and reliability importance of weighted-r-within-consecutive-k-outof-n: F system. IEEE Trans. Reliab. 2018; (67): 951 – 969.
Nashwan I I H. Reliability and failure functions of the consecutive k-out-of-m-from-n: F linear and circular system. Int. J. Commun. Netw. Inf. Secur. 2018; (10): 432-436.
Nashwan I I H. Reliability and failure probability functions of the consecutive-k-out-of-m-from-n: F system with multiple failure criteria. PJTAS. 2020; (3): 47-56.
Zhang Sh, Zhao J B, Zhu W J, Du L. Reliability optimization of linear consecutive k-out-of-n: F systems with Birnbaum Importance–based quantum genetic algorithm. Adv. Mech. Eng. 2019; (11): 1-16.
Amirian Y, Khodadadi A, Chatrabgoun O. Exact reliability for a consecutive circular k-out-of-r-from-n: F system with equal and unequal component probabilities. Int. J. Reliab. Qual. Saf. Eng. 2020; (27): 20500031-26.
Griffith W. On consecutive k-out-of-n failure systems and their generalizations. Amsterdam. Reliability and quality control, A P Basu. Elsevier. 1986.
Papastavridis S. m-consecutive k-out-of-n: F systems. IEEE Trans. Reliab. 1990; (39): 386-388.
Gharof N. On reliability of circular (r-consecutive-k-out-of-n: F system). Int. J. Reliab. Qual. Saf. Eng. 2013; (20): 1350014-1-11.
Makri F S, Philippou A N. Exact reliability formula for linear and circular m-consecutive k-out-of-n: F systems. Microelectron. Reliab. 1996; (36): 657-66.
Godbole A P. Approximate reliability of m-consecutive k-out-of-n: failure systems. Stat. Sin.1993; (3): 321-32.
Eryilmaz S, Koutras M V, Triantafyllou I S. Signature based analysis of m-consecutive-k-out-of-n: F systems with exchangeable components. Nav. Res. Logist. 2011; (58): 344-35.
Eryilmaz S. m-consecutive-k-out-of-n: F system with overlapping runs: Signature-Based Reliability Analysis. IJOR. 2012; (15): 64-73.
Namir G. Reliability formula and limit law of the failure time of (m-consecutive-k-out-of-n: F system). TOP. 2008; (16): 62-72.
Tang S D. A repairable linear m-consecutive-k-out-of-n: F system. Chin. Phys. Lett. 2012; (29): 098401 (1-5).
Dao T Sh, Gen H W. A repairable linear m-consecutive-k-out-of-n: F system. Chin. Phys. Lett. 2012; (29): 098401-09840.
Agarwal M, Mohan P. GERT analysis of m-consecutive-k-out-of-n: F system with overlapping runs and (k–1)-step Markov dependence. IJOR. 2008; (3): 36-51.
Gharof N. r-consecutive-k-out-of-n: F system with dependent components. Int. J. Reliab. Qual. Saf. Eng. 2007; (14): 399–410.
Mohan P, Agarwal M. Combined m-consecutive-k-out-of-n: F and consecutive kc-out-of- n Systems. IEEE Trans. Reliab. 2009; (58): 328-337.
Eryilmaz S. Reliability of combined m-consecutive-k-out-of-n: F and consecutive kc-out-of-n: F systems. IEEE Trans. Reliab. 2012; (61): 215–219.
Boushaba M, Benyahia A. Reliability and importance measures for combined m-consecutive-k-out-of-n: F and consecutive-kb-out-of-n: F systems with non-homogeneous Markov-dependent components. Int. J. Reliab. Qual. Saf. Eng. 2018; (25): 1850022.
Gera A E. Combined m1-consecutive-kc1-out-of-n and m2-consecutive-kc2 -out-of-n systems. IEEE Trans. Reliab. 2011; (60): 493–497.
Kan C. A note on circular m-consecutive-k-out-of-n: F systems. Proceeding of Trends and Perspectives in Linear Statistical Inference Conference. Springer. 2018; 132-142.
Zhua X, Boushabab M, Boulahia A, Zhao X. A linear m-consecutive-k-out-of-n system with sparse d of nonhomogeneous Markov-dependent components. J. Risk reliab. 2019; (233): 328-337.
Zhua X, Boushabab M, Coitc D W, Benyahia A. Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components. Reliab. Eng. Sys. Saf. 2017; (167): 1-9.
Makri F S. On circular m-consecutive-k, l-out-of-n: F systems. 2nd International Conference on Reliability Engineering, Materials Science and Engineering. Italy. IOP. 2017.