Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
권호 표지
DOI QR코드

DOI QR Code

Sampling Plans Based on Truncated Life Test for a Generalized Inverted Exponential Distribution

  • Singh, Sukhdev (Department of Mathematics, Indian Institute of Technology) ;
  • Tripathi, Yogesh Mani (Department of Mathematics, Indian Institute of Technology) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, Pohang University of Science and Technology)
  • Received : 2015.04.24
  • Accepted : 2015.06.04
  • Published : 2015.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose a two-stage group acceptance sampling plan for generalized inverted exponential distribution under truncated life test. Median life is considered as a quality parameter. Design parameters are obtained to ensure that true median life is longer than a given specified life at certain level of consumer's risk and producer's risk. We also explore situations under which design parameters based on median lifetime can be used for other percentile points. Tables and specific examples are reported to explain the proposed plans. Finally a real data set is analyzed to implement the plans in practical situations and some suggestions are given.

Keywords

References

  1. Abouammoh, A. M. and Alshingiti, A. M. (2009), Reliability estimation of generalized inverted exponential distribution, Journal of Statistical Computation and Simulation, 79, 1301-1315. https://doi.org/10.1080/00949650802261095
  2. Aslam, M., Azam, M., Lio, Y. L., and Jun, C. H. (2013), Two-stage group acceptance sampling plan for Burr type X percentiles, Journal of Testing and Evaluation, 41, 525-533.
  3. Aslam, M. and Jun, C. H. (2009a), A group acceptance sampling plans for truncated life test having Weibull distribution, Journal of Applied Statistics, 36, 1021-1027. https://doi.org/10.1080/02664760802566788
  4. Aslam, M. and Jun, C. H. (2009b), A group acceptance sampling plans for truncated life tests based on the inverse Rayleigh and log-logistic distributions, Pakistan Journal of Statistics, 25, 107-119.
  5. Aslam, M. and Jun, C. H. (2010), A double acceptance sampling plans for generalized log-logistic distribution with known shape parameter, Journal of Applied Statistics, 37, 405-414. https://doi.org/10.1080/02664760802698979
  6. Aslam, M., Jun, C. H., and Ahmad, M. (2009), A group sampling plan based on truncated life test for Gamma distributed items, Pakistan Journal of Statistics, 25, 333-340.
  7. Aslam, M., Jun, C. H., and Ahmed, M. (2011a), New acceptance sampling plans based on life tests for Birnbaum-Saunders distributions, Journal of Statistical Computation and Simulation, 81, 461-470. https://doi.org/10.1080/00949650903418883
  8. Aslam, M., Jun, C. H. and Ahmed, M. (2011b), Twostage group sampling plan based on truncated life tests for a general distribution, Journal of Statistical Computation and Simulation, 81, 1927-1938. https://doi.org/10.1080/00949655.2010.508745
  9. Aslam, M., Jun, C. H., Lee, H., Ahmad, M., and Rasool, M. (2011), Improved group sampling plans based on time-truncated life tests, Chilean Journal of Statistics, 2, 85-97.
  10. Aslam, M., Kundu, D., and Ahmad, M. (2010), Time truncated acceptance sampling plans for generalized exponential distribution, Journal of Applied Statistics, 37, 555-566. https://doi.org/10.1080/02664760902769787
  11. Balakrishnan, N., Leiva, L., and Lopez, J. (2007), Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution, Communications in Statistics-Simulation and Computation, 36, 643-656. https://doi.org/10.1080/03610910701207819
  12. Balasooriya, U. (1995), Failure-censored reliability sampling plans for the exponential distribution, Journal of Statistical and Computation Simulation, 52, 337-349. https://doi.org/10.1080/00949659508811684
  13. Dey, A. K. and Kundu, D. (2009), Discriminating among the log-normal, Weibull, and generalized exponential distributions, IEEE Transactions on Reliability, 58, 416-424. https://doi.org/10.1109/TR.2009.2019494
  14. Dey, S. (2007), Inverted exponential distribution as a life distribution model from a Bayesian viewpoint, Data Science Journal, 6, 107-113. https://doi.org/10.2481/dsj.6.107
  15. Dey, S. and Pradhan, B. (2013), Generalized inverted exponential distribution under hybrid censoring, Statistical Methodology, http://dx.doi.org/10.1016/j.stamet.2013.07.007.
  16. Epstein, B. (1954), Truncated life tests in the exponential case, Annals of Mathematical Statistics, 25, 55-564.
  17. Goode, H. P. and Kao, J. H. K. (1961), Sampling plans based on the Weibull distribution, Proceeding of the Seventh National Symposium on Reliability and Quality Control, Philadelphia, 24-40.
  18. Gupta, S. S. (1962), Life test sampling plans for normal and lognormal distributions, Technometrics, 4, 151-175. https://doi.org/10.1080/00401706.1962.10490002
  19. Killer, A. Z. and Kamath, A. R. (1982), Reliability analysis of CNC Machine Tools, Reliability Engineering, 3, 449-473. https://doi.org/10.1016/0143-8174(82)90036-1
  20. Krishna, H. and Kumar, K. (2013), Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample, Journal of Statistical Computation and Simulation, 83, 1007-1019. https://doi.org/10.1080/00949655.2011.647027
  21. Lawless, J. (2003), Statistical Models and Methods for Lifetime Data, New York, Wiley.
  22. Lin, C. T., Duran, B. S., and Lewis, T. O. (1989), Inverted gamma as life distribution, Microelectron Reliability, 29, 619-626. https://doi.org/10.1016/0026-2714(89)90352-1
  23. Lio, Y. L., Tsai, T. R., and Wu, S. J. (2010), Acceptance sampling plans from truncated life tests based on the Birnbaum-Saunders distribution for percentiles, Communications in Statistics-Simulation and Computation, 39, 119-136.
  24. Nadarajah, S. and Kotz, S. (2003), The exponentiated Frechet distribution, available at: Interstat, Statjournals, Net, 0312001. 2003.
  25. Rao, G. S. (2010), A group acceptance sampling plans for lifetimes following a generalized exponential distribution, Economic Quality Control, 24, 75-85.
  26. Rosaiah, K. and Kantam, R. R. L. (2005), Acceptance sampling based on the inverse Rayleigh distribution, Economic Quality Control, 20, 277-286.
  27. Rosaiah, K., Kantam, R. R. L., and Kumar, C. S. (2006), Reliability of test plans for exponentiated log-logistic distribution, Economic Quality Control, 21, 165-175.
  28. Tsai, T. R. and Wu, S. J. (2006), Acceptance sampling based on truncated life tests for generalized Rayleigh distribution, Journal of Applied Statistics, 33, 595-600. https://doi.org/10.1080/02664760600679700

Cited by

  1. Designing of multiple deferred state sampling plan for generalized inverted exponential distribution vol.36, pp.1, 2017, https://doi.org/10.1080/07474946.2016.1275459
  2. Determination of optimal quick switching system with varying sample size for assuring mean life under Weibull distribution vol.37, pp.2, 2018, https://doi.org/10.1080/07474946.2018.1466536
  3. Designing of repetitive group sampling plan under truncated life test based on generalized inverted exponential distribution vol.21, pp.6, 2018, https://doi.org/10.1080/09720510.2018.1461785
  4. Multiple dependent state repetitive group sampling plan for Burr XII distribution vol.28, pp.2, 2015, https://doi.org/10.1080/08982112.2015.1068331