Skip to main content
Log in

Median ranked acceptance sampling plans for exponential distribution

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

We develop a ranked acceptance sampling plan by attribute for exponential distribution assuming that the life test is truncated at a pre-assigned time. Two main requirements are essential for the proposed ranked sampling plans; namely; the life times of the test units are assumed to follow the exponential distribution; and the data are selected by using a free cost sampling method, the median ranked set sampling scheme from a large lot. The main advantage of using the median rank set sampling is to reduce producer’s risk, and it is one of the ranked scheme that produces a judgment order statistics that are mutually independent and identically distributed random variables to meet the binomial theory assumptions. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; then the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the sampling plans based on the ranked samples and producer’s risk are presented. A comparisons with sampling plan based on simple random sampling and an illustrative example are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Al-Nasser, A.D., Gogah, F.S.: On using the median ranked set sampling for developing reliability test plans under generalized exponential distribution. Pak. J. Stat. Oper. Res. 13(4), 757–774 (2017)

    Article  MathSciNet  Google Scholar 

  2. Al-Nasser, A.D., Al-Omari, A.I.: Acceptance sampling plan based on truncated life tests for exponentiated Frechet distribution. J. Stat Manag. Syst. 16(1), 13–24 (2013)

    Article  Google Scholar 

  3. Al-Nasser, A.D.: L ranked set sampling: a generalization procedure for robust visual sampling. Commun. Stat. Simul. Comput. 36, 33–44 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Al-Nasser, A.D., Bani-Mustafa, A.: ARobust extreme ranked set sampling. J. Stat. Comput. Simul. 79, 859–867 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Al-Nasser, A.D., Al-Omari, A.I.: Information theoretic weighted mean based on truncated ranked set sampling. J. Stat. Theory Pract. 9(2), 313–329 (2015)

    Article  MathSciNet  Google Scholar 

  6. Al-Omari, A.I.: Acceptance sampling plan based on truncated life tests for three parameter kappa distribution. Stoch. Qual. Control 29(1), 53–62 (2014)

    Google Scholar 

  7. Al-Omari, A.I.: Time truncated acceptance sampling plans for generalized inverted exponential distribution. Electron. J. Appl. Stat. Anal. 8(1), 1–12 (2015)

    MathSciNet  Google Scholar 

  8. Al-Talib, M., Al-Nasser, A.D.: Estimation of Gini-Index from continuous distribution based on ranked set sampling. Electron. J. Appl. Stat. Anal. 1, 37–48 (2008)

    MATH  Google Scholar 

  9. Aslam, M., Kundu, D., Ahmad, M.: Time truncated acceptance sampling plans for generalized exponential distribution. J. Appl. Stat. 37(4), 555–566 (2010)

    Article  MathSciNet  Google Scholar 

  10. Aslam, M., Azam, M., Lio, Y.L., Jun, C.-H.: Two-stage group acceptance sampling plan for Burr Type X percentiles. J. Test. Eval. 41(4), 525–533 (2013)

    Article  Google Scholar 

  11. Baklizi, A., El-Masri, A., Al-Nasser, A.D.: Acceptance sampling plans in the Raleigh Model. Korean Commun. Stat. 12(1), 11–18 (2005)

    Google Scholar 

  12. Balakrishnan, N., Leiva, V., López, J.: Acceptance sampling plans from truncated life tests based on the generalized Birnbaum–Saunders distribution. Commun. Stat. Simul. Comput. 36, 643–656 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Balakrishnan, N., Basu, A.P.: Exponential Distribution: Theory, Methods and Applications. Wiley, New York (1995)

    MATH  Google Scholar 

  14. Ciavolino, E., Al-Nasser, A.D.: Information theoretic estimation improvement to the nonlinear Gompertz’s Model based on ranked set sampling. J. Appl. Quant. Methods 5(2), 317–330 (2010)

    Google Scholar 

  15. Epstein, B.: Truncated life tests in the exponential case. Ann. Math. Stat. 25, 555–564 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  16. David, H., Nagaraja, H.: Order Statistics, 3rd edn. Wiley, New Jersey (2003)

    Book  MATH  Google Scholar 

  17. Jemain, A., Al-Omari, A.I.: Double quartile ranked set samples. Pak. J. Stat. 22, 217–228 (2006)

    MathSciNet  MATH  Google Scholar 

  18. Jemain, A., Al-Omari, A., Ibrahim, K.: Some variations of ranked set sampling. Electron. J. Appl. Stat. Anal. 1(1), 1–15 (2008)

    MATH  Google Scholar 

  19. Johnson, N., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions: vol. 1. Wiley, New York (1994)

    MATH  Google Scholar 

  20. Habib, E.: Linear moments study under ranked set sampling. Electron. J. Appl. Stat. Anal. 3(2), 134–149 (2010)

    Google Scholar 

  21. Hussain, J., Razzaque Mughal, A., Pervaiz, M.K., Aslam, M., Rehman, A.: Economic reliability group acceptance sampling plans for lifetimes following a generalized exponential distribution. Electron. J. Appl. Stat. Anal. 4(2), 124–130 (2011)

    MathSciNet  Google Scholar 

  22. Kantam, R.R.L., Rosaiah, K., Rao, G.S.: Acceptance sampling based on life tests: log-logistic models. J. Appl. Stat. 28(1), 121–128 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Klufa, J.: Exact calculation of the Dodge-Romig LTPD single sampling plans for inspection by variables. Stat. Pap. 51(2), 297–305 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  24. McIntyre, G.A.: A method of unbiased selective sampling using ranked sets. Aust. J. Agric. Res. 3, 385–390 (1952)

    Article  Google Scholar 

  25. Muttlak, H.: Median ranked set sampling. J. Appl. Stat. Sci. 6, 245–255 (1997)

    MATH  Google Scholar 

  26. Pagano, M., Valadez, J.J.: Commentary: understanding practical lot quality assurance sampling. Int. J. Epidemiol. 39(1), 69–71 (2010)

    Article  Google Scholar 

  27. Raqab, M., Ahsanullah, M.: Estimation of the location and scale parameters of generalized exponential distribution based on order statistics. J. Stat. Comput. Simul. 69, 109–12 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Schilling, E.G., Neubauer, D.V.: Acceptance Sampling in Quality Control, 2nd edn. CRC Press, Boca Raton (2009)

    MATH  Google Scholar 

  29. Sobel, M., Tischendrof, J.A.: Acceptance sampling with new life test objectives. In: Proceedings of the fifth national symposium on reliability and quality control, pp. 108–118. Philadelphia, Pennsylvania (1959)

Download references

Acknowledgements

The authors would like to thank the chief editor and all referees for their helpful comments and valuable suggestions which improved the presentation of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amjad D. Al-Nasser.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gogah, F., Al-Nasser, A.D. Median ranked acceptance sampling plans for exponential distribution. Afr. Mat. 29, 477–497 (2018). https://doi.org/10.1007/s13370-018-0555-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-018-0555-7

Keywords

Mathematics Subject Classification

Navigation