Advertisement

Estimation of stress–strength reliability for Maxwell distribution under progressive type-II censoring scheme

  • Sachin Chaudhary
  • Sanjeev K. TomerEmail author
Original Article
  • 187 Downloads

Abstract

This paper deals with the estimation of stress–strength reliability \(P=P[Y<X]\), when the strength X and stress Y both follow Maxwell distribution with different parameters. We obtain maximum likelihood and Bayes estimates of P using progressive type-II censored samples. We also provide procedures to evaluate asymptotic and bootstrap confidential intervals, as well as, Bayesian credible and highest posterior density intervals for P. We present simulation study and analyze a real data set for numerical illustrations.

Keywords

Asymptotic confidence intervals Bayes estimator Bootstrap Credible intervals Highest posterior density Maximum likelihood estimator Stress–strength model 

Notes

Acknowledgements

We are thankful to the editor and reviewers for their helpful suggestions that greatly improved the original manuscript. The first author’s research work is supported by University Grant Commission in the form of Basic Scientific Research fellowship.

References

  1. Babayi S, Khorram E (2017) Inference of stress–strength for the Type-II generalized logistic distribution under progressively Type-II censored samples. Commun Stat Simul Comput (just-accepted).  https://doi.org/10.1080/03610918.2017.1332214
  2. Bader M, Priest A (1982) Statistical aspects of fibre and bundle strength in hybrid composites. In: Progress in science and engineering of composites, Proceedings of the Fourth International Conference on Composite Materials, ICCM-IV, Tokyo, Japan, pp 1129–1136Google Scholar
  3. Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Springer, BerlinCrossRefGoogle Scholar
  4. Balakrishnan N, Cramer E (2014) The art of progressive censoring. Springer, BerlinCrossRefzbMATHGoogle Scholar
  5. Bekker A, Roux J (2005) Reliability characteristics of the Maxwell distribution: a Bayes estimation study. Commun Stat Theory Methods 34(11):2169–2178MathSciNetCrossRefzbMATHGoogle Scholar
  6. Chaturvedi A, Tomer SK (2002) Classical and Bayesian reliability estimation of the negative binomial distribution. J Appl Stat Sci 11(1):27–32MathSciNetzbMATHGoogle Scholar
  7. Chaturvedi A, Tomer SK (2003) UMVU estimation of the reliability function of the generalized life distributions. Stat Pap 44(3):301–313MathSciNetCrossRefzbMATHGoogle Scholar
  8. Chen M-H, Shao Q-M (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92MathSciNetGoogle Scholar
  9. Efron BT (1993) An introduction to the bootstrap. Chapman & Hall, New YorkCrossRefzbMATHGoogle Scholar
  10. Genc AI (2013) Estimation of \(\text{{P}}(\text{{X}}>\text{{Y}}\)) with Topp–Leone distribution. J Stat Comput Simul 83(2):326–339MathSciNetCrossRefzbMATHGoogle Scholar
  11. Gradshteyn I, Ryzhik IM (1965) Tables of integrals, series and products. Academic Press, New YorkGoogle Scholar
  12. Herd GR (1956) Estimation of the parameters of a population from a multi-censored sample. Ph.D thesis, Iowa State College, Ames, IowaGoogle Scholar
  13. Johnson RA (1988) Stress–strength models for reliability. Handb Stat 7:27–54CrossRefGoogle Scholar
  14. Johnstone MA (1983) Bayesian estimation of reliability in the stress–strength context. J Wash Acad Sci 73:140–150Google Scholar
  15. Kotz S, Lumelskii Y, Pensky M (2003) The stress–strength model and its generalizations. Theory and applications, vol 43. World Scientific, Singapore, p 44CrossRefzbMATHGoogle Scholar
  16. Krishna H, Malik M (2009) Reliability estimation in Maxwell distribution with type-II censored data. Int J Qual Reliab Manag 26(2):184–195CrossRefGoogle Scholar
  17. Krishna H, Malik M (2012) Reliability estimation in Maxwell distribution with progressively type-II censored data. J Stat Comput Simul 82(4):623–641MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kumar K, Krishna H, Garg R (2015) Estimation of \(\text{{P}}(\text{{Y}} < \text{{X}})\) in Lindley distribution using progressively first failure censoring. Int J Syst Assur Eng Manag 6(3):330–341CrossRefGoogle Scholar
  19. Kundu D, Gupta R (2006) Estimation of \(\text{{P}}(Y< X)\) for Weibull distribution. IEEE Trans Reliab 55(2):270–280CrossRefGoogle Scholar
  20. Lawless JF (2003) Statistical models and methods for lifetime data. Wiley, New YorkzbMATHGoogle Scholar
  21. Metropolis N, Ulam S (1949) The monte carlo method. J Am Stat Assoc 44(247):335–341CrossRefzbMATHGoogle Scholar
  22. Panwar M, Kumar J, Tomer SK (2015) Competing risk analysis of failure censored data from Maxwell distribution. Int J Agric Stat Sci 11(1):29–34Google Scholar
  23. Rao C (1973) Linear statistical inference and its applications. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  24. Raqab MZ, Madi MT, Kundu D (2008) Estimation of P \((\text{{Y}}<\text{{X}})\) for the three-parameter generalized exponential distribution. Commun Stat Theory Methods 37(18):2854–2864MathSciNetCrossRefzbMATHGoogle Scholar
  25. Saraçoğlu B, Kinaci I, Kundu D (2012) On estimation of \(R= P (Y< X)\) for exponential distribution under progressive type-II censoring. J Stat Comput Simul 82(5):729–744MathSciNetCrossRefzbMATHGoogle Scholar
  26. Tomer SK, Panwar M (2015) Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. J Stat Comput Simul 85(2):339–356MathSciNetCrossRefGoogle Scholar
  27. Tyagi R, Bhattacharya S (1989) A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica 41(137):73–79MathSciNetGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2018

Authors and Affiliations

  1. 1.Department of StatisticsBanaras Hindu UniversityVaranasiIndia

Personalised recommendations