This paper presents an overview of the research performed on reliability studies of consecutive k-out-of-n and related systems during the last decade. In particular, methods for reliability evaluation, importance and optimal arrangements of components, lifetime distribution, and stochastic orderings of such systems are presented, also research results on related systems are summarized.
YamR. C. M.ZuoM. JZhangY. L‘A method for evaluation of reliability indices for repairable circular consecutive k-out-of-n:F systems’Reliab. Engng Syst. Saf.79 (2003): 1–9
2.
KuoW.ZuoM. JOptimal reliability modeling, principles and applications (New York: John Wiley & Sons2003)
3.
ChangG. JCuLHwangF. KReliabilities of consecutive-k systems (Dordrecht, The Netherlands: Kluwer Academic Publishers2000)
4.
KontoleonJ. M‘Reliability determination of a r-successive-out-of-n:F system’IEEE Trans. Reliab.29 (1980): 437–437
HwangF. KWrightP. E‘An O(k3log(n/k)) algorithm for the consecutive k-out-of-n:F system’IEEE Trans. Reliab.44 (1995): 128–131
7.
LinM.-S.‘An O(k2log(n)) algorithm for computing the reliability of consecutive k-out-of-n:F systems’IEEE Trans. Reliab.53 (2004): 3–6
8.
CluzeauT.KellerJSchneeweissW‘An efficient algorithm for computing the reliability of consecutive k-out-of-n:F systems’IEEE Trans. Reliab.57 (2008): 84–87
9.
FuJ. C‘Reliability of consecutive k-out-of-n:F systems with (k − 1) step Markov dependence’IEEE Trans. Reliab.35 (1986): 602–606
10.
FuJ. CHuB‘On reliability of large consecutive k-out-of-n:F system with (k − 1) step Markov dependence’IEEE Trans. Reliab.36 (1987): 75–77
11.
GeraA. E‘A consecutive k-out-of-n:G system with dependent elements–a matrix formulation and solution’Reliab. Engng Syst. Saf.68 (2000): 61–67
12.
FuJ. CWangLLouW. Y. W.‘On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials’J. Appl. Prob.40 (2003): 346–360
DuD.-Z.HwangF. KJiaXNgoH. Q‘Optimal consecutive k-out-of-n:G cycle for n ≤ 2k + 1’SIAM J. Discrete Math.15 (2002): 305–316
24.
JalaliA.HawkesA. GCuiLHwangF. K‘The optimal consecutive k-out-of-n:G line for n ≤ 2k.J. Stat. Plan. Inference128 (2005): 281–287
25.
CuiL.HawkesA. G‘A note on the proof for the optimal consecutive k-out-of-n:G line for n ≤ 2k.J. Stat. Plan. Inference138 (2008): 1516–1520
26.
SamaniegoF.‘On closure of the IFR class under formation of coherent systems’IEEE Trans. Reliab.34 (1985): 69–72
27.
KocharS.MukerjeeHSamaniegoF‘The “signature” of a coherent system and its application to comparison among systems’Nav. Res. Logist.46 (1999): 507–523
28.
NavarroJ.RychlikT‘Reliability and expectation bounds for coherent systems with exchangeable components’J. Multivariate Anal.98 (2007): 102–113
29.
NavarroJ.SamaniegoF. JBalakrishnanNBhattacharyaD‘On the application and extension of system signatures in engineering reliability’Nav. Res. Logist.55 (2008): 313–327
30.
SamaniegoF. JSystem signatures and their applications in engineering reliability (New York: Springer2007)
31.
DavidH. ANagarajaH. NOrder statistics (New Jersey: John Wiley and Sons2003)
32.
BolandP. J‘Signatures of indirect majority systems’J. Appl. Prob.38 (2001): 597–603
33.
TriantafyllouI. SKoutrasM. V‘On the signature of coherent systems and applications’Prob. Engng Inf. Sci.22 (2008): 19–35
34.
EryilmazS.‘Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components’Reliab. Engng Syst. Saf.94 (2009): 350–356
35.
EryilmazS.‘Mixture representations for the reliability of consecutive-k systems’Math. Comput. Model.51 (2010): 405–412
36.
ShakedM.ShanthikumarJ. GStochastic orders (New York: Springer2007)
NavarroJ.GuillamonARuizM‘Generalized mixtures in reliability modelling: applications to the construction of bathtub shaped hazard models and the study of systems’Appl. Stoch. Models Bus. Ind.25 (2009): 323–337
43.
ZhangY. LZuoM. J.YamR. C. M.‘Reliability analysis for a circular consecutive 2-out-of-n:F repairable system with priority in repair’Reliab. Engng Syst. Saf.68 (2000): 113–120
44.
ChengK.ZhangY. L‘Analysis for a consecutive k-out-of-n:F repairable system with priority in repair’Int. J. Syst. Sci.32 (2001): 591–598
45.
LamH. K. Y.NgT‘A general model for consecutive k-out-of-n:F repairable system with exponential distribution and (k − 1)-step Markov dependence,’Eur. J. Oper. Res.129 (2001): 663–682
46.
XiaoG.LiZLiT‘Dependability for non-Markov consecutive k-out-of-n:F repairable systems by fast simulation’Reliab. Engng Syst. Saf.92 (2007): 293–299
47.
WuY.GuanJ‘Repairable consecutive k-out-of-n:G systems with r repairmen’IEEE Trans. Reliab.54 (2005): 328–337
48.
GuanJ.WuY‘Repairable consecutive k-out-of-n:F system with fuzzy states’Fuzzy Sets Syst.157 (2006): 121–142
EryilmazS.KanCAk/i c/iF‘Consecutive k-within-m-out-of-n:F system with exchangeable components’Nav. Res. Logist.56 (2009): 503–510
54.
GriffithW. SBasuA. P‘On consecutivek-out-of-n failure systems and their generalizations’ Reliability and quality control (Amsterdam, The Netherlands: Elsevier 1986): 157–165
55.
AgarwalM.SenKMohanP‘GERT analysis of m-consecutive-k-out-of-n:F systems’IEEE Trans. Reliab.56 (2007): 26–34
56.
GhorafN.‘Reliability formula & limit law of the failure time of “m-consecutive-k-out-of-n:F system”’Top16 (2008): 62–72
ZuoM. JLinDWuY‘Reliability evaluation of combined k-out-of-n:F, consecutive k-out-of-n: F, and linear connected (r, s)-out-of-(m,n): F system structures’IEEE Trans. Reliab.49 (2000): 99–104
61.
CuiL.KuoWLiJXieM‘On the dual reliability systems of (n, f, k) and 〈n, f, k〉’Stat. Prob. Lett.76 (2006): 1081–1088
