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Mathematical modeling and fuzzy availability analysis of stainless steel utensil manufacturing unit in steady state: a case study

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Abstract

In practical situation data collected or available for the complex repairable industrial systems are vague, ambiguous, qualitative and imprecise in nature due to various practical constraints. So it is not easy to calculate reliability indices of such systems up to a desired accuracy. In this paper, we calculate fuzzy availability of the stainless steel utensil manufacturing unit consisting of six sub-systems using all the available information and by introducing the membership functions which are the part of fuzzy set theory. Mathematical formulation of the problem is carried out using mnemonic rule and the governing differential equations are solved. Long run fuzzy availability of the stainless steel utensil manufacturing unit has been computed for various choices of failure and repair rates of sub-systems of this plant. The effect of variations of long run fuzzy availability for different failure, repair rates and system coverage factor is also studied.

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References

  • Cai KY (1996) Introduction to fuzzy reliability. Kluwer Academic Publishers, Norwell, MA, USA. ISBN: 0792397371

  • Cai KY, Wen CY (1990) Street-lighting lamps replacement: a fuzzy viewpoint. Fuzzy Sets Syst 37:161–172

    Article  MathSciNet  Google Scholar 

  • Cai KY, Wen CY, Zhang ML (1991a) Fuzzy reliability modeling of gracefully degradable computing systems. Reliab Eng Syst Saf 33:141–157

    Article  Google Scholar 

  • Cai KY, Wen CY, Zhang ML (1991b) Survivability index for CCNs: a measure of fuzzy reliability. Reliab Eng Syst Saf 33:71–99

    Article  Google Scholar 

  • Cai KY, Wen CY, Zhang ML (1993) Fuzzy states as a basis for a theory of fuzzy reliability. Microelectron Reliab 33:2253–2263

    Article  Google Scholar 

  • Chen SM (1996) New method for fuzzy system reliability analysis. Cybern Syst Int J 27(4):385–401

    Article  MATH  Google Scholar 

  • Chongshan G (2009) Fuzzy availability analysis of a repairable consecutive-2-out-of-3: f System. IEEE Int Conf Grey Syst Intell Serv 10–12:434–437

    Google Scholar 

  • Chowdhury SG, Misra KB (1992) Evaluation of fuzzy reliability of a non-series parallel network. Microelectron Reliab 32:1–4

    Article  Google Scholar 

  • Hafaifa A, Laaouad F, Guemana M (2009) A new engineering method for fuzzy reliability analysis of surge control in centrifugal compressor. Am J Eng Appl Sci 2(4):676–682

    Article  Google Scholar 

  • Huang HZ (1995) Reliability analysis method in the presence of fuzziness attached to operating time. Microelectron Reliab 35:1483–1487

    Article  Google Scholar 

  • Jiang MH, Zhou J, Hu M (2007) Fuzzy reliability analysis of an iSCSI-based fault tolerant storage system organization. IEEE fourth international conference on fuzzy systems and knowledge discovery (FSKD 2007)

  • Ke JC, Huang HI, Lin CH (2006) Fuzzy analysis for steady-state availability: a mathematical programming approach. Eng Optim 38(8):909–921

    Article  Google Scholar 

  • Ketata C, Rockwell MC (2006) Fuzzy evaluation of stream sample reliability. Miner Process Extr Metall Rev 27(4):281–294

    Article  Google Scholar 

  • Kumar K, Kumar P (2009) Fuzzy reliability and fuzzy availability of the serial process in butter-oil processing plant. J Math Stat (Science Publication, USA) 5(1):65–71

    MATH  Google Scholar 

  • Kumar K, Kumar P (2011) Fuzzy availability modeling and analysis of biscuit manufacturing plant: a case study. Int J Syst Assur Eng Manag (Springer) 2(3):193–204

    Article  Google Scholar 

  • Qiang X, Jing L, Chen J (2009) Fuzzy reliability analysis of deep slidin g plane in rock foundation under dam. IEEE Sixth Int Conf Fuzzy Syst Knowl Discov 6:525–529

    Google Scholar 

  • Wang T, Meng X, Guan Y, Yang J (2008) Fuzzy reliability of two units of the cold storing system. Mod Appl Sci (CCSE) 2(4):161–166

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the reviewers for providing very helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, N.C. College of Engineering, Israna, Panipat, India

    Pawan Kumar Chhoker

  2. Department of Mathematics and Computer Science, Centre for Applicable Mathematics and Systems Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, UK

    Atulya Nagar

Authors
  1. Pawan Kumar Chhoker
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  2. Atulya Nagar
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Corresponding author

Correspondence to Pawan Kumar Chhoker.

Appendix

Appendix

See Tables 1, 2, 3, 4, 5 and 6.

Table 1 Effect of failure rates and repair rates of hot rolling and annealing on long run fuzzy availability of the system
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Table 2 Effect of failure rates and repair rates of cold rolling on long run fuzzy availability of the system
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Table 3 Effect of failure rates and repair rates of circle cutting on fuzzy availability of the system
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Table 4 Effect of failure rates and repair rates of pressing machine on long run fuzzy availability of the system
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Table 5 Effect of failure rates and repair rates of machining & annealing on long run fuzzy availability of the system
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Table 6 Effect of failure rates and repair rates of polishing and packing on long run fuzzy availability of the system
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Chhoker, P.K., Nagar, A. Mathematical modeling and fuzzy availability analysis of stainless steel utensil manufacturing unit in steady state: a case study. Int J Syst Assur Eng Manag 6, 304–318 (2015). https://doi.org/10.1007/s13198-014-0269-7

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  • DOI: https://doi.org/10.1007/s13198-014-0269-7

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