Performance of a structure consisting a \(2\)-out-of-\(3:F\) substructure under human failure. (English) Zbl 1327.90060
Arab. J. Sci. Eng. 39, No. 11, 8383-8394 (2014); erratum ibid. 40, No. 3, 993 (2015).
Summary: In recent years, the studies of reliability properties of consecutive \(k\)-out-of-\(n\) structures have attracted a great impact of attention from both theoretical and practical approaches. In this paper, we have studied the reliability measures of a complex structure, which consists of two substructures namely, \(A\) and \(B\) handling by human operators. The substructure \(A\) is of the type \(2\)-out-of-\(3:F\) (with unequal components), which is connected with the substructure \(B\) in series configuration. The complete structure can be failed due to the failure of any two components of substructure \(A\), any component of \(A\) with failure of substructure \(B\) and due to human error. All failure and repair rates are assumed to be constant. The structure is analyzed by the usage of supplementary variable technique and Laplace transformation. Generalized expressions of state probabilities, availability and reliability of the structure, mean time to failure, cost analysis and sensitivity analysis are developed.
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
Keywords:
reliability measures; 2-out-of-3:F structure; system safety; cost-effectiveness; human failureReferences:
| [1] | Lakhoua M.N.: Systemic analysis of an industrial system: case study of a grain silo. Arabian J. Sci. Eng. 38(5), 1243-1254 (2013) · doi:10.1007/s13369-012-0357-4 |
| [2] | Ram M.: On system reliability approaches: a brief survey. Int. J. Syst. Assur. Eng. Manag. 4(2), 101-117 (2013) · doi:10.1007/s13198-013-0165-6 |
| [3] | Bai D.S., Yun W.Y., Chung S.W.: Redundancy optimization of k-out-of-n systems with common cause failures. IEEE Trans. Reliab. 40(1), 56-59 (1991) · Zbl 0729.90938 · doi:10.1109/24.75334 |
| [4] | Cai J.: Reliability of a large consecutive k-out-of-r-from-n:F system with unequal component-reliability. IEEE Trans. Reliab. 43(1), 107-111 (1994) · doi:10.1109/24.285122 |
| [5] | Eryilmaz S.: Mixture representations for the reliability of consecutive-k systems. Math. Comput. Model. 51(5), 405-412 (2010) · Zbl 1190.90058 · doi:10.1016/j.mcm.2009.12.007 |
| [6] | Huang J., Zuo M.J., Wu Y.: Generalized multi-state k-out-of-n:G systems. IEEE Trans. Reliab. 49(1), 105-111 (2000) · doi:10.1109/24.855543 |
| [7] | Myers A.F.: k-out-of-r-from-n:G system reliability with imperfect fault coverage. IEEE Trans. Reliab. 56(3), 464-473 (2007) · doi:10.1109/TR.2007.903229 |
| [8] | Zuo M.: Reliability and component importance of a consecutive k-out-of-n system. Microelectron. Reliab. 33(2), 243-258 (1993) · doi:10.1016/0026-2714(93)90485-H |
| [9] | Zuo M.J., Lin D., Wu Y.: 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(1), 99-104 (2000) · doi:10.1109/24.855542 |
| [10] | Boland P.J., Samaniego F.J.: Stochastic ordering results for consecutive k-out-of-n:F systems. IEEE Trans. Reliab. 53(1), 7-10 (2004) · doi:10.1109/TR.2004.824830 |
| [11] | Habib A., Al-Seedy R.O., Radwan T.: Reliability evaluation of multi-state consecutive k-out-of-r-from-n:G systems. Appl. Math. Model. 31(11), 2412-2423 (2007) · Zbl 1149.90048 · doi:10.1016/j.apm.2006.09.006 |
| [12] | Salehi E.T., Asadi M., Eryilmaz S.: Reliability analysis of consecutive k-out-of-n systems with non-identical components lifetimes. J. Stat. Plan. Inference 141(8), 2920-2932 (2011) · Zbl 1213.62163 · doi:10.1016/j.jspi.2011.03.014 |
| [13] | Arulmozhi G.: Direct method for reliability computation of k-out-of-n systems. Appl. Math. Comput. 143(2-3), 421-429 (2003) · Zbl 1082.90020 · doi:10.1016/S0096-3003(02)00373-9 |
| [14] | Asadi M., Bayramoglu I.: The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans. Reliab. 55(2), 314-318 (2006) · doi:10.1109/TR.2006.874934 |
| [15] | Triantafyllou I.S., Koutras M.V.: On the signature of coherent systems and applications. Probab. Eng. Inf. Sci. 22, 19-35 (2008) · Zbl 1137.90460 · doi:10.1017/S0269964808000028 |
| [16] | Pham H.: On the estimation of reliability of k-out-of-n systems. Int. J. Syst. Assur. Eng. Manag. 1(1), 32-35 (2010) · doi:10.1007/s13198-010-0010-0 |
| [17] | 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. 58(4), 344-354 (2011) · Zbl 1214.90038 · doi:10.1002/nav.20449 |
| [18] | Van Gemund A.J.C., Reijns G.L.: Reliability analysis of k-out-of-n system with single cold standby using Pearson’s distribution. IEEE Trans. Reliab. 61(2), 526-532 (2012) · doi:10.1109/TR.2012.2192587 |
| [19] | Xing L., Amari S.V., Wang C.: Reliability of a k-out-of-n systems with phased mission requirements and imperfect fault coverage. Reliab. Eng. Syst. Saf. 103, 45-50 (2012) · doi:10.1016/j.ress.2012.03.018 |
| [20] | Li W., Zuo M.J.: Reliability evaluation of multi state weighted of a k-out-of-n systems. Reliab. Eng. Syst. Saf. 93(1), 160-167 (2008) · doi:10.1016/j.ress.2006.11.009 |
| [21] | Ebrahimipur V., Qurayshi S.F., Shabni A., Maleki-Shoja B.: Reliability optimization of multi-state weighted k-out-of-n systems by fuzzy mathematical programming and genetic algorithm. Int. J. Syst. Assur. Eng. Manag. 2(4), 312-318 (2011) · doi:10.1007/s13198-012-0084-y |
| [22] | Dhillon B.S.: Human errors: a review. Microelectron. Reliab. 29(3), 299-304 (1989) · doi:10.1016/0026-2714(89)90612-4 |
| [23] | Dhillon B.S., Liu Y.: Human errors in maintenance: a review. J. Qual. Maint. Eng. 12(1), 21-36 (2006) · doi:10.1108/13552510610654510 |
| [24] | Dhillon B.S., Rayapati S.N.: Reliability analysis of non-maintained parallel systems subject to hardware failure and human error. Microelectron. Reliab. 25(1), 111-122 (1985) · doi:10.1016/0026-2714(85)90452-4 |
| [25] | Dhillon B.S., Rayapati S.N.: Human performance reliability modelling. Microelectron. Reliab. 28(1), 573-580 (1988) · doi:10.1016/0026-2714(88)90143-6 |
| [26] | Dhillon B.S., Yang N.: Stochastic analysis of standby systems with common cause failures and human errors. Microelectron. Reliab. 32(12), 1699-1712 (1992) · doi:10.1016/0026-2714(92)90268-P |
| [27] | Dhillon B.S., Yang N.: Availability of a man-machine system with critical and non-critical human error. Microelectron. Reliab. 33(10), 1511-1521 (1993) · doi:10.1016/0026-2714(93)90105-8 |
| [28] | Dhillon B.S., Yang N.: Probabilistic analysis of a maintainable system with human error. J. Qual. Maint. Eng. 1(2), 50-59 (1995) · doi:10.1108/13552519510089592 |
| [29] | Giuntini, R.E.: Mathematical characterization of human reliability for multi-task system operations. IEEE International Conference on Systems, Man, and Cybernetics, vol. 2, pp. 1325-1329 (2000) |
| [30] | Sawaragi, T.: Modeling and analysis of human interactions with and within complex systems. IEEE International Conference on Systems, Man, and Cybernetics, vol. 1, pp. 701-707 (1999) |
| [31] | Sutcliffe A.G., Gregoriades A.: Automating scenario analysis of human and system reliability. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 37(2), 249-261 (2007) · doi:10.1109/TSMCA.2006.886375 |
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