A New Group Acceptance Sampling Plans based on Percentiles for the Weibull Fréchet Model

  • Basma Ahmed Department of Information System, Higher Institute for Specific Studies
  • Haitham Yousof Department of Statistics, Mathematics and Insurance, Benha University
Keywords: Life test, Weibull Fréchet distribution, Minimum number of group sampling strategy, Consumer’s risk, Operating characteristic function.


When the life test is truncated at a pre-determined duration, group acceptance sampling plans for the WeibullFrchet distribution percentiles are introduced in this article. Under a given group size, acceptance limit, and customer risk, the minimum number of groups needed to guarantee the specified life percentile is calculated. The operating characteristic values are discovered, additionally the producer’s risk. To illustrate the process mentioned here, two experimental are given. Also, real data set is used to demonstrate the flexibility of the Weibull Frchet model.


Afify, A. Z., Yousof, H. M., Cordeiro, G. M., Ortega, E. M., and Nofal, Z. M. , The Weibull Frchet distribution and its applications, Journal of Applied Statistics, 43(14), 2608-2626, 2016.

Aslam, M. and Jun, C.H. , A group acceptance sampling plans for truncated life tests based on the inverse Rayleigh and log-logistic distribution, Pakistan Journal of Statistics, 25 (2), 107-119, 2009a.

Aslam, M. and Jun, C.H. , A group acceptance sampling plan for truncated life test having Weibull distribution, Journal of applied statistic, 36(9), 1021-1027, 2009b.

Aslam, M., Kundu, D., Jun, C.H. and Ahmed M. , Time truncated group acceptance sampling plans for generalized exponential distribution, Journal of testing and evaluation, 39(4), 1 C 7, 2011.

Aslam, M., Jun, C.H. and Ahmed, M. , A group acceptance sampling plan based on truncated life test for gamma distributed items, Pakistan Journal of Statistics, 25(3), 333-340, 2009.

Aslam, M., Ahmed, M. and Mughal, A. , Group acceptance sampling plan for lifetime data using generalized Pareto distribution,

Pakistan Journal of Commerce and Social Sciences, 4(2), 185-193, 2010.

Balakrishnan, N., Lieiva, V. and Lpez, J. , Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution, Communications in Statistics-Simulation and Computation, 36(3), 643-656, 2007.

Balamurali, S. Park, H., Jun, C.H., Kim, K. and Lee, J. , Designing of variables repetitive group sampling plan involving minimum average sample number, Communication in Statistics-Simulation and Computation, 34(3), 799-809, 2005.

Duncan, A. J. , Quality Control and Industrial Statistics, Homewood, III, Richard D. Irwin. , 1974.

Epstein, B. , Truncated life tests in the exponential case, Annals of Mathematical Statistics, 25, 555-564, 1954.

Goode, H.P. and Kao, J.H.K. , Sampling plans based on the Weibull distribution, Proceedings of Seventh National Symposium on Reliability and Quality Control, Philadelphia, Pennsylvania, 24-40, 1961.

Gupta, S.S. , Life test sampling plans for normal and log-normal distributions, Technometrics, 4(2), 151-175, 1962.

Gupta, S.S. and Groll, P.A. , Gamma distribution in acceptance sampling based on life test, Journal of the American Statistical Association, 56(296), 942-970, 1961.

Jun, C.H., Balamurali, S. and Lee, S.H. , Variable sampling plans for Weibull distributed lifetimes under sudden death testing, IEEE Transactions on Reliability, 55(1), 53-58, 2006.

Kantam, R.R.L. and Rosaiah, K. , Half logistic distribution in acceptance sampling based on life tests, IAPQR Transactions, 23(2), 117-125, 1998.

Kantam, R.R.L., Rosaiah, K. and Srinivasarao, G , Acceptance sampling based on life tests: Log-logistic model, Journal of Applied Statistics (UK), 28(1), 121-128, 2001.

Mahdy, M., Aslam, M., Ahmed, B.,and Aldosari, M. S. , Some distributions in single acceptance sampling plan with application, Calitatea, 19(162), 46-50, 2018.

Nichols, M. D., and Padgett, W. J. , A bootstrap control chart for Weibull percentiles, Quality and reliability engineering international, 22(2), 141-151, 2006.

Pascual, F.G., and Meeker, W.Q. , The modified sudden death test: planning life tests with a limited number of test positions, Journal of Testing and Evaluation, 26(5), 434-443, 1998.

Rao, G.S. , A group acceptance sampling plans for lifetimes following a generalized exponential distribution, Economic Quality Control, 24(1), 75-85, 2009.

Rao, G.S. , A group acceptance sampling plans based on truncated life tests for Marshall-Olkin extended Lomax distribution, Electronic Journal of Applied Statistical Analysis, 3(1), 18-27, 2010.

Rao, G.S. , A group acceptance sampling plans for lifetimes following a Marshall-Olkin extended exponential distribution, Applications and Applied Mathematics, An international Journal, 6(2), 592-601, 2011.

Rosaiah, K. and Kantam, R.R.L. , Acceptance sampling based on the inverse Rayleigh distribution, Economic Quality Control, 20 (2), 277-286, 2005.

Stephens, K.S. , The Handbook of Applied Acceptance Sampling Plans, Procedures and Principles, ASQ Quality Press, Milwaukee, 2001.

Vlcek, B. L., Hendricks, R. C., and Zaretsky, E. V. , Monte Carlo simulation of sudden death bearing testing, Tribology Transactions, 47(2), 188-199, 2004.

How to Cite
Ahmed, B., & Yousof, H. (2022). A New Group Acceptance Sampling Plans based on Percentiles for the Weibull Fréchet Model. Statistics, Optimization & Information Computing, 11(2), 409-421. https://doi.org/10.19139/soic-2310-5070-1320
Research Articles