Abstract
K-out-of-n redundant systems are used to increase reliability in various industries. The failure of a component in such systems is dependent upon the failure of other components. Therefore, if an appropriate model is not developed to take dependent failures into consideration, reliability and MTTF of redundant systems are evaluated wrongly. One of the most crucial varieties of dependent failures is common cause failure. Common cause failure refers to the failure of two or more components of a k-out-of-n system which occurs simultaneously or within a short time interval and thus components are direct failures resulting from a shared cause. Another type of dependent failure in k-out-of-n redundant systems is load share, where the failure of one component leads to increased load in surviving components, hence changing their failure rate. In this paper, using Markov chain, three models are used to evaluate the MTTF of a 2-out-of-3 redundant system by taking dependent failures into account. Model I addresses the MTTF of a 2-out-of-3 redundant system by considering common cause failure based on alpha factor model. In Model II, both dependent failures (common cause failure and load share) are examined based on capacity flow and alpha factor model. In Model III, in addition to common cause failure and load share, component repair is studied, too. In order to examine the validity of the models introduced and conduct sensitivity analysis, some diagrams are drawn for each model. Considering the dependent failures in the 2-out-of-3 redundant systems, all the three proposed models can be practical and be used to evaluate MTTF.
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References
Alavi SR, Rahmati M (2016) Experimental investigation on thermal performance of natural draft wet cooling towers employing an innovative wind-creator setup. Energy Convers Manag 122:504–514
Amari SV, Bergman R (2008) Reliability analysis of k-out-of-n load-sharing systems. In: Reliability and maintainability symposium RAMS. Annual IEEE, pp 440–445
Asjad M, Kulkarni MS, Gandhi O (2013a) A life cycle cost based approach of O&M support for mechanical systems. Int J Syst Assur Eng Manag 4:159–172
Asjad M, Mohite S, Kulkarni MS, Gandhi O (2013b) Opportunistic actions for subassemblies of a reciprocating compressor: an LCC based approach. Int J Perform Eng 9:273–285
Asjad M, Kulkarni MS, Gandhi O (2015) An insight to availability for O&M support of mechanical systems. Int J Product Qual Manag 16:462–472
Asjad M, Kulkarni MS, Gandhi O (2016) Supportability issues of mechanical systems for their useful life. J Eng Des Technol 14:33–53
Byeon Y-T, Kwon K, Kim J-O (2009) Reliability analysis of power substation with common cause failure. In: International conference on power engineering, energy and electrical drives IEEE, pp 467–472
Dhillon B, Anude O (1994) Common-cause failure analysis of a redundant system with repairable units. Int J Syst Sci 25:527–540
Fleming K (1975) Reliability model for common mode failures in redundant safety systems. In: Vogt WG, Mickle MH (eds) Annual conference on modeling and simulation (IAEA), vol 6, Part 1. Pittsburgh, Pennsylvania, USA. https://inis.iaea.org/search/search.aspx?orig_q=RN:7275774
Fleming K, Kalinowski A (1983) An extension of the beta factor method to systems with high levels of redundancy. PLG-0289. Pickard, Lowe and Garrick, Inc, Newport Beach
Freund JE (1961) A bivariate extension of the exponential distribution. J Am Stat Assoc 56:971–977
Gurov SV, Utkin LV (2015) Reliability analysis of load-sharing m-out-of-n systems with arbitrary load and different probability distributions of time to failure. Int J Reliab Saf 9:21–35
Hajeeh MA (2011) Reliability and availability of a standby system with common cause failure. Int J Oper Res 11:343–363
Hassija V, Kumar CS, Velusamy K (2014) A pragmatic approach to estimate alpha factors for common cause failure analysis. Ann Nucl Energy 63:317–325
Hwang M, Kang DI (2011) Estimation of the common cause failure probabilities on the component group with mixed testing scheme. Nucl Eng Des 241:5275–5280
Jain M (2013) Availability prediction of imperfect fault coverage system with reboot and common cause failure. Int J Oper Res 17:374–397
Jain M, Gupta R (2012) Load sharing M-out of-N: G system with non-identical components subject to common cause failure. Int J Math Oper Res 4:586–605
Jia X, Wang L, Wei C (2014) Reliability research of dependent failure systems using copula. Commun Stat Simul Comput 43:1838–1851
Kang DI, Hwang MJ, Han SH (2011) Estimation of common cause failure parameters for essential service water system pump using the CAFE-PSA. Prog Nucl Energy 53:24–31
Kumar DR, Sankar V (2016) Approximate system reliability analysis of distribution networks with repairable components and common cause failures. i-Manag J Electr Eng 9:32
Lin H-H, Chen K-H, Wang R-T (1993) A multivariant exponential shared-load model. IEEE Trans Reliab 42:165–171
Maatouk I, Chatelet E, Chebbo N (2011) Reliability of multi-states system with load sharing and propagation failure dependence. In: Quality, reliability, risk, maintenance, and safety engineering (ICQR2MSE) international conference on IEEE, pp 42–46
Mosleh A, Siu N (1987) A multi-parameter common cause failure model. In: Transactions of the 9th international conference on structural mechanics in reactor technology. Vol. M
Mosleh A, Fleming K, Parry G, Paula H, Worledge D, Rasmuson DM (1988) Procedures for treating common cause failures in safety and reliability studies: vol 1, procedural framework and examples: final report. Pickard, Lowe and Garrick, Inc. Newport Beach, CA (USA)
Mosleh A, Rasmuson DM, Marshall F (1998) Guidelines on modeling common-cause failures in probabilistic risk assessment. Safety Programs Division, Office for Analysis and Evaluation of Operational Data, US Nuclear Regulatory Commission
Platz O (1984) A Markov model for common-cause failures. Reliab Eng 9:25–31
Pozsgai P, Neher W, Bertsche B (2003) Models to consider load-sharing in reliability calculation and simulation of systems consisting of mechanical components. In: Reliability and maintainability symposium annual IEEE, pp 493–499
Rahmati M, Alavi SR, Sedaghat A (2016) Thermal performance of natural draft wet cooling towers under cross-wind conditions based on experimental data and regression analysis. In: 6th conference on thermal power plants (CTPP). IEEE, pp 1–5
Ram M, Nagiya K (2016) Performance evaluation of mobile communication system with reliability measures. Int J Qual Reliab Manag 33:430–440
Rausand M, Høyland A (2004) System reliability theory: models, statistical methods, and applications, vol 396. Wiley, New York
Shao J, Lamberson LR (1991) Modeling a shared-load k-out-of-n: G system. IEEE Trans Reliab 40:205–209
Sharifi M, Memariani A, Noorossanah R (2009) Real time study of a k-out-of-n system: n identical elements with increasing failure rates. Iran J Oper Res 1:56–67
Sridharan V (2006) Availabilty and MTTF of a system with one warm standby component. Appl Sci 8:167–171
Troffaes M, Gledhill J, Škulj D, Blake S (2015) Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair
Wang K-H, Dong W-L, Ke J-B (2006) Comparison of reliability and the availability between four systems with warm standby components and standby switching failures. Appl Math Comput 183:1310–1322
Yen T-C, Wang K-H, Chen W-L (2013) Comparative analysis of three systems with imperfect coverage and standby switching failures. In: The fifth international conference on advances in future internet, Barcelona, Spain, (AFIN 2013)
Yun WY, Cha JH (2010) A stochastic model for a general load-sharing system under overload condition. Appl Stoch Models Bus Ind 26:624–638
Yusuf I, Hussaini N (2012) Evaluation of reliability and availability characteristics of 2-out of-3 standby system under a perfect repair condition. Am J Math Stat 2:114–119
Yusuf I, Yusuf B, Bala SI (2014) Mean time to system failure analysis of a linear consecutive 3-out-of-5 warm standby system in the presence of common cause failure. J Math Comput Sci 4:58–66
Zheng X, Yamaguchi A, Takata T (2013) α-Decomposition for estimating parameters in common cause failure modeling based on causal inference. Reliab Eng Syst Saf 116:20–27
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Mortazavi, S.M., Karbasian, M. & Goli, S. Evaluating MTTF of 2-out-of-3 redundant systems with common cause failure and load share based on alpha factor and capacity flow models. Int J Syst Assur Eng Manag 8, 542–552 (2017). https://doi.org/10.1007/s13198-016-0553-9
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DOI: https://doi.org/10.1007/s13198-016-0553-9