200
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A Monte Carlo simulation study of two-sided tolerance intervals in balanced one-way random effects model for non-normal errors

&
Pages 2329-2344 | Received 11 Nov 2012, Accepted 02 Apr 2013, Published online: 27 Apr 2013

References

  • Wilks S S. Determination of sample sizes for setting tolerance limits. Ann Math Stat. 1941; 12:91–96 doi: 10.1214/aoms/1177731788
  • Wilks S S. Statistical prediction with special reference to the problem of tolerance limits. Ann Math Stat. 1942; 13:400–409 doi: 10.1214/aoms/1177731537
  • Guttman IStatistical tolerance regions: classical and Bayesian. London: Charles Griffin and Company; 1970
  • Hahn G J, Meeker W Q. Statistical intervals: a guide for practitioners. New York: Wiley; 1991
  • Krishnamoorthy K, Mathew TStatistical tolerance regions: theory, applications and computation. Hoboken, NJ: Wiley; 2009
  • Mee R W, Owen D B. Improved factors for one-sided tolerance limits for balanced one-way ANOVA random model. J Am Stat Assoc. 1983; 78:901–905 doi: 10.1080/01621459.1983.10477038
  • Mee R W. β-Expectation and β-content tolerance limits for balanced one-way ANOVA random model.. Technometrics 1984; 26:251–254 doi: 10.1080/00401706.1984.10487962
  • Vangel M G. New methods for one-sided tolerance limits for a one-way balanced random-effects ANOVA model. Technometrics. 1992; 34:176–185 doi: 10.1080/00401706.1992.10484906
  • Bhaumik D K, Kulkarni P M. A simple and exact method of constructing tolerance intervals for the one-way ANOVA with random effects. Am Stat. 1996; 50:319–323
  • Krishnamoorthy K, Mathew T. One-sided tolerance limits in balanced and unbalanced one-way random models based on generalized confidence intervals. Technometrics. 2004; 46:44–52 doi: 10.1198/004017004000000103
  • Liao C T, Lin T Y, Iyer H K. One- and two-sided tolerance intervals for general balanced mixed models and unbalanced one-way random models. Technometrics. 2005; 47:323–335 doi: 10.1198/004017005000000102
  • Beckman R J, Tietjen G L. Two-sided tolerance limits for balanced random-effects ANOVA models. Technometrics. 1989; 31:185–197 [Correction: 1998;40:269]. doi: 10.1080/00401706.1989.10488512
  • Sharma G, Mathew T. One-sided and two-sided tolerance intervals in general mixed and random effects models using small-sample asymptotics. J Am Stat Assoc. 2012; 107:258–267 doi: 10.1080/01621459.2011.640592
  • Wolfinger R D. Tolerance intervals for variance component models using Bayesian simulation. J Qual Technol. 1998; 30:18–32
  • Ong S H, Mukerjee R. Probability matching priors for two-sided tolerance intervals in balanced one-way and two-way nested random effects models. Statistics. 2011; 45:403–411 doi: 10.1080/02331881003797585
  • Graybill F A, Wang C M. Confidence intervals on non-negative linear combinations of variances. J Am Stat Assoc. 1980; 75:869–873 doi: 10.1080/01621459.1980.10477565
  • Krishnamoorthy K, Lian X. Closed-form approximate tolerance intervals for some general linear models and comparison studies. J Stat Comput Simul. 2012; 82:547–563 doi: 10.1080/00949655.2010.545061
  • Azzalini A. A class of distributions which includes the normal ones. Scand J Stat. 1985; 12:171–178
  • Karian Z A, Dudewicz E J. Fitting statistical distributions: the generalized lambda distribution and generalized bootstrap methods. Boca Raton, FL: CRC Press; 2000
  • Nason G P. On the sum of t and Gaussian random variables. Stat Probab Lett. 2006; 76:1280–1286 doi: 10.1016/j.spl.2006.01.006

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.