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A solution to determining the reliability of products "Using Generalized Lambda Distribution"

Author Affiliations

  • 1Management Department, Firoozkooh Branch, Islamic Azad University, Firoozkooh, IRAN
  • 2 Industrial Engineering Dep., Firoozkooh Branch, Islamic Azad University, Firoozkooh, IRAN

Res. J. Recent Sci., Volume 2, Issue (10), Pages 41-47, October,2 (2013)


At the end of the manufacturing cycle, performance tests are often carried out to ensure that the product meets or exceeds all specified performance parameters. In addition to initial performance, customers are interested in knowing how long the product will last, how many products will fail per year, and how many will last more than some number of years. One method for determining the reliability is the application of statistical distributions. Of the most significant and common distributions currently utilized are normal, weibull, exponential, and lognormal distributions, which are used to study most of the products’ and systems’ reliability. However, there are products that do not follow a specified lifetime distribution and cannot be investigated by these distributions. Instead, Generalized Lambda Distribution (GLD) can be deployed to investigate the identified and unidentified distributions, so it can resolve the problem. In this research, we introduce a method for determining the reliability, using GLD in a practical and operational way.


  1. Besterfield and Dale H., Quality Control fifth edition, Prentice Hall, Upper Saddle River, New Jersey, Columbus, Ohio, (1979)
  2. Barlow R.E. and Proschen J.A., Statistical theory of reliability and life testing, Holt, Rinehart, and Winson, New York, (1975)
  3. Johnson N.L. and Kots S., Continuous univariate distributions, Vol. 1 and 2, Houghton Miffin, Boston, 1970)
  4. Harrison M., Wadsworth, Kenneth, S. Stephens, A. Blanton Godfrey, Modern Methods for quality control and improvement, John Wiley & sons, Inc, (2002)
  5. Fournier B., Rupin N., Bigerelle M., Najjar D., Iost A. Wilcox R., Estimating the parameters of a generalized lambda distribution, Computational Statistics & Data Analysis (51), 2813 – 2835 (2007)
  6. Nili Ahmadabadi M., Farjami Y. and Bamenimoghadam M., Preparation of control chart based on the generalized lambda distribution, Pajouheshgar, Quarterly scientific journal of management, ), 61-74, In Persian, (2009)
  7. Tukey J.W., The future of data analysis, annals of mathematical statistics, 33), 1-67 (1962)
  8. Joiner B.L. and Rsenblatt J.R., Some properties of the range in samples from Tukey’s symmetric lambda distribution, Journal of the American statistical association (66), 394 (1971)
  9. Ganeshan R., Are more supplier better? Generating the Gau and Ganeshan procedure, J., Oper. Res. Soc., (52), 122-123 (2001)
  10. Delaney H. D. and Vargha A., The effect on non-normality on student’s two-sample t-test the annual meeting of the American educational research association, New Orlean, 2000)
  11. Ozturk A. and Dale R.F., A study of fitting the generalized lambda distribution to solar radiation data, J. Appl. Meteorol. (21), 995-1004 (1982)
  12. Fournier B., Rupin N., Bigerelle M., Najjar D. and Iost A., Application of the generalized lambda distribution in a statistical process control methodology, J. Process control, 16), 1087-1098 (2006)
  13. Gawand H., Mundada R.S. and Swaminathan P., Design Patterns to Implement Safety and Fault Tolerance, International Journal of Computer Applications, 18), 2011)
  14. Dengiz B., The generalized lambda distribution in simulation of m/m/1 queue systems, J. Fac. Engng. Arch., Gazi univ. (), 161-171 (1988)
  15. Zaven A., Karian and Edvard, J., Dudewiz, Fitting statistical distributions The generalized lambda distribution and generalized bootstrap methods, CRC press, (2000)
  16. Thakur N.S., Yadav K. and Pathak S., On Mean Estimation with Imputation in Two- Phase Sampling Design, Re. J. of Mathematical and Statistical Sci., ), 1-9 (2013)
  17. Rekha R.C. and Vikas S., Retailer’s profit maximization Model for Weibull deteriorating items with Permissible Delay on Payments and Shortages, Re. J. of Mathematical and Statistical Sci., ), 16-20 (2013)
  18. Roman U.C., Porey P.D., Patel P.L. and Vivekanandan N., Assessing Adequacy of Probability Distributional Model for Estimation of Design Storm, ISCA J. of Engineering Sci., ), 19-25 (2012)
  19. Bigerelle M., Najjar D., Fournier B., Rupin N. and Iost A., Application of lambda distribution and bootstrap analysis to the prediction of fatigue lifetime and confidence intervals, Internet. J. Fatigue (28), 223-236 (2006)
  20. Karvanen J. and Nuutinen A., Characterizing the generalized lambda distribution by L-moments, Math. ST, (2008)
  21. Karian Z.A. and Dudewicz E.J., Fitting statistical distributions: the generalized lambda distribution and generalized bootstrap method, CRC press, (2000)
  22. Tarsitano A., Estimation of the generalized lambda distribution parameters for grouped data, J. ofCommunication in statistics theory and methods, (34), 1689-1709 (2005)
  23. Lakhany A. and Mausser H., Estimating the Parameters of the Generalized Lambda Distribution, J. of Algo Research Quarterly, ), 47-58 (2000)
  24. Ramberg J. and Schmeiser B., an approximate method for generating asymmetric random variables, Communications J. of the ACM, ), 78-82 (1974)