The present paper investigates the reliability analysis of industrial systems by using vague lambda-tau methodology in which information related to system components is uncertain and imprecise in nature. The uncertainties in the data are handled with the help of intuitionistic fuzzy set (IFS) theory rather than fuzzy set theory. Various reliability parameters are addressed for strengthening the analysis in terms of degree of acceptance and rejection of IFS. Performance as well as sensitivity analysis of the system parameter has been investigated for accessing the impact of taking wrong combinations on its performance. Finally results are compared with the existing traditional crisp and fuzzy methodologies results. The technique has been demonstrated through a case study of bleaching unit of a paper mill. 1. Introduction Engineering systems have become complicating day by day, and rapidly increasing the cost of the equipment challenges the plant personnel or job analyst that to maintain the system performance so that to produce the desirable profit under a predetermined time. However the failure is an inevitable phenomenon in an industrial system. Also the effects of product failures range from those that cause minor nuisances to catastrophic failures involving loss of life and property. Therefore it is difficult for the system analyst to maintain the performance of the system for a longer period of time. For this, it is common knowledge that large amount of data is required in order to estimate more accurately the failure, error or repair rates. However, it is usually impossible to obtain such a large quantity of data from any particular plant. From this point of view, fuzzy reliability is a novel concept in system engineering as fuzzy set can easily capture subjective, uncertain, and ambiguous information. Thus based on that system reliability has been evaluated by using various fuzzy arithmetic and interval of confidence operations [1–10]. After the successful applications of the fuzzy set theory since 1970, several researchers are engaged in their extensions. Out of existence of several extensions, intuitionistic fuzzy set theory (IFS) defined by Atanassov [11] is one of the most successful extensions and has been found to be well suited for dealing with problems concerning vagueness. In fuzzy set theory, it is assumed that the acceptance and rejection grades of membership are complementary in nature. But during deciding the degree of membership of an object there is always a degree of hesitation between the membership functions. This feature is
References
[1]
K.-Y. Cai, “System failure engineering and fuzzy methodology: an introductory overview,” Fuzzy Sets and Systems, vol. 83, no. 2, pp. 113–133, 1996.
[2]
H. Garg and S. P. Sharma, “Stochastic behavior analysis of industrial systems utilizing uncertain data,” ISA Transactions, vol. 51, no. 6, pp. 752–762, 2012.
[3]
J. Knezevic and E. R. Odoom, “Reliability modelling of repairable systems using Petri nets and fuzzy Lambda-Tau methodology,” Reliability Engineering and System Safety, vol. 73, no. 1, pp. 1–17, 2001.
[4]
D.-L. Mon and C.-H. Cheng, “Fuzzy system reliability analysis for components with different membership functions,” Fuzzy Sets and Systems, vol. 64, no. 2, pp. 145–157, 1994.
[5]
S. P. Sharma and H. Garg, “Behavioural analysis of urea decomposition system in a fertiliser plant,” International Journal of Industrial and Systems Engineering, vol. 8, no. 3, pp. 271–297, 2011.
[6]
L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
[7]
H. Garg, M. Rani, S. P. Sharma, et al., “Predicting uncertain behavior of press unit in a paper industry using artificial bee colony and fuzzy Lambda-Tau methodology,” Applied Soft Computing, vol. 13, no. 4, pp. 1869–1881, 2013.
[8]
R. K. Sharma, D. Kumar, and P. Kumar, “Predicting uncertain behavior of industrial system using FM-A practical case,” Applied Soft Computing Journal, vol. 8, no. 1, pp. 96–109, 2008.
[9]
R. K. Sharma and S. Kumar, “Performance modeling in critical engineering systems using RAM analysis,” Reliability Engineering and System Safety, vol. 93, no. 6, pp. 913–919, 2008.
[10]
H. Garg, “Performance analysis of reparable industrial systems using PSO and fuzzy confidence interval based methodology,” ISA Transactions, vol. 52, no. 2, pp. 171–183, 2013.
[11]
K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986.
[12]
W.-L. Gau and D. J. Buehrer, “Vague sets,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 2, pp. 610–614, 1993.
[13]
H. Bustince and P. Burillo, “Vague sets are intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 79, no. 3, pp. 403–405, 1996.
[14]
S. M. Chen, “Analyzing fuzzy system reliability using vague set theory,” International Journal of Applied Science and Engineering, vol. 1, no. 1, pp. 82–88, 2003.
[15]
J.-R. Chang, K.-H. Chang, S.-H. Liao, and C.-H. Cheng, “The reliability of general vague fault-tree analysis on weapon systems fault diagnosis,” Soft Computing, vol. 10, no. 7, pp. 531–542, 2006.
[16]
S. M. Taheri and R. Zarei, “Bayesian system reliability assessment under the vague environment,” Applied Soft Computing Journal, vol. 11, no. 2, pp. 1614–1622, 2011.
[17]
A. Kumar, S. P. Yadav, S. Kumar, et al., “Fuzzy reliability of a marine power plant using interval valued vague sets,” International Journal of Applied Science and Engineering, vol. 4, no. 1, pp. 71–82, 2006.
[18]
M. Kumar and S. P. Yadav, “A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components,” ISA Transactions, vol. 51, no. 2, pp. 288–297, 2012.
[19]
G. S. Mahapatra and T. K. Roy, “Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations,” World Academy of Science, Engineering and Technology, vol. 38, pp. 578–585, 2009.
[20]
H. Garg, “Reliability analysis of repairable systems using Petri nets and Vague Lambda-Tau methodology,” ISA Transactions, vol. 52, no. 1, pp. 6–18, 2013.
[21]
D.-F. Li, “Multiattribute decision making models and methods using intuitionistic fuzzy sets,” Journal of Computer and System Sciences, vol. 70, no. 1, pp. 73–85, 2005.
[22]
E. Szmidt and J. Kacprzyk, “Intuitionistic fuzzy sets in group decision making,” Notes on Intuitionistic Fuzzy Sets, vol. 2, no. 1, pp. 11–14, 1996.
[23]
S. K. De, R. Biswas, and A. R. Roy, “An application of intuitionistic fuzzy sets in medical diagnosis,” Fuzzy Sets and Systems, vol. 117, no. 2, pp. 209–213, 2001.
[24]
L. Dengfeng and C. Chuntian, “New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions,” Pattern Recognition Letters, vol. 23, no. 1–3, pp. 221–225, 2002.
[25]
H. Garg, M. Rani, et al., “An approach for reliability analysis of industrial systems using PSO and IFS technique,” ISA Transactions, 2013.
[26]
K. Das, “A comparative study of exponential distribution vs Weibull distribution in machine reliability analysis in a CMS design,” Computers and Industrial Engineering, vol. 54, no. 1, pp. 12–33, 2008.
[27]
T. J. Ross, Fuzzy Logic with Engineering Applications, John Wiley & Sons, New York, NY, USA, 2nd edition, 2004.
