New Acceptance Sampling Plans Based on Percentiles for Type-II Generalized Log Logistic Distribution

G. Srinivasa Rao^1, , K. Rosaiah² and S. V. S. V. S. V. Prasad³

¹Department of Statistics, The University of Dodoma, P.O.Box: 259, Tanzania

²Department of Statistics, Acharya Nagarjuna University, Guntur - 522 510, India

³Reserve Bank of India, Nagpur-440001, India

Cite this paper:
G. Srinivasa Rao, K. Rosaiah and S. V. S. V. S. V. Prasad. New Acceptance Sampling Plans Based on Percentiles for Type-II Generalized Log Logistic Distribution. American Journal of Applied Mathematics and Statistics. 2019; 7(4):131-137. doi: 10.12691/ajams-7-4-2

Abstract

This article describes the development of an acceptance sampling plan based on percentiles for Type-II generalized log-logistic distribution (TGLLD) introduced by Rosaiah et. al. [1]. The plan is developed by considering the lifetime percentiles as a variable and the life test will be terminated at a pre-specified time. The objective of the test is to determine the minimum sample size required to achieve a specific lifetime percentile at an acceptable level of consumer and producer risks. Determined the OC values and are presented along with producer risks. The sustainability of the plan is illustrated with real data set.

Keywords:
Type-II generalized log-logistic distribution acceptance sampling truncated life test

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Rosaiah, K., Kantam, R.R.L., Prasad, S.V.S.V.S.V., and Pratapa Reddy, J., “Reliability estimation in Type-II generalized log-logistic distribution,” International Journal of Agricultural and Statistical Science, 4(2), 283-292, 2008.
[2]	Epstein, B., “Truncated life tests in the exponential case,” Annals of Mathematical Statistics, 25, 555-564, 1954.
[3]	Sobel, M. and Tischendrof, J.A., “Acceptance Sampling with new life test objectives,” Proceedings of fifth National Symposium on Reliability and Quality Control, Philadelphia Pennsylvania. 108-118, 1959.
[4]	Goode, H.P. and Kao, J.H.K., “Sampling plans based on the Weibull distribution, Proceeding of Seventh National Symposium on Reliability and Quality Control,” Philadelphia, Pennsylvania, 24-40, 1961.
[5]	Gupta, S.S. and Groll, P.A., “Gamma distribution in acceptance sampling based on life tests,” J. Amer. Statist. Assoc., 56, 942-970, 1961.
[6]	Gupta, S.S., “Life test sampling plans for normal and lognormal distribution,” Technometrics, 4, 151-175, 1962.
[7]	Fertig, F.W. and Mann, N.R., “Life-test sampling plans for two-parameter Weibull populations,” Technometrics, 22, 165-177, 1980.
[8]	Kantam, R.R.L. and Rosaiah, K., “Half logistic distribution in acceptance sampling based on life tests,” IAPQR Transactions, 23 (2), 117-125, 1998.
[9]	Kantam, R. R. L., Rosaiah, K., and Rao, G. S. “Acceptance sampling based on life tests: log-logistic models,” J. Appl. Statist., 28, 121-128, 2001.
[10]	Baklizi, A and EI Masri, A.E.K., “Acceptance sampling based on truncated life tests in the Birnbaum-Saunders model,” Risk Anal., 24, 1453-1457, 2004.
[11]	Rosaiah, K and Kantam, R.R.L., “Acceptance sampling based on the inverse Rayleigh distribution,” Economic Quality Control, 20, 277-286, 2005.
[12]	Tsai, T.-R. and Wu, S.-J. “Acceptance sampling based on truncated life tests for generalized Rayleigh distribution,” Journal of Applied Statistics, 33, 595-600, 2006.
[13]	Balakrishnan, N. Leiva, V. and Lope, J., “Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution,” Comm. Statist. Simulation Comput., 36, 643-656, 2007.
[14]	Rao, G.S., Ghitany, M.E. and Kantam, R.R.L., “Acceptance Sampling plans for Marshall-Olkin extented Lomax distribution,” Int. J. Appl. Math., 21, 315-325, 2008.
[15]	Lio, Y. L., Tsai, T.-R. and Wu, S.-J., “Acceptance sampling plans from truncated life tests based on the Burr type XII percentiles,” J. Chinese Inst. Indust. Eng., 27, 270-280, 2010.
[16]	Marshall, A.W and Olkin, I., Life Distributions –Structure of Nonparametric, Semiparametri and Parametric Families, Springer, New York, 2007.
[17]	Lio, Y. L., Tsai, T.-R. and Wu, S.-J., “Acceptance sampling plan based on the truncated life test in the Birnbaum Saunders distribution for percentiles,” Comm. Statist. Simulation Comput., 39, 119-136, 2009.
[18]	Rao, G.S. and Kantam. R.R.L., “Acceptance Sampling Plans from Truncated Life Tests based on the Log-Logistic Distributions for Percentiles,” Economic Quality Control, 25, 153-167, 2010.
[19]	Rao, G. S., “Acceptance sampling plans for percentiles based on the Marshall–Olkin extended Lomax distribution,” Int. J. Stat. Econ., 11, 83-96, 2013.
[20]	Rao, G.S., Rosaiah. K., Sridharbabu, M. and Sivakumar, D.C.U., “New Acceptance Sampling Plans Based on Percentiles for Exponentiated Frechet Distribution,” Economic Quality Control, 31(1), 37-44, 2016.
[21]	Rao, G.S., Rosaiah. K., Kalyani K. and Sivakumar, D.C.U., “New Acceptance Sampling Plans Based on Percentiles for Odds Exponential Log Logistic Distribution,” The Open Statistics & Probability Journal, 7, 45-52, 2016.
[22]	Rosaiah, K., Kantam, R.R.L., & Santosh Kumar, Ch., “Reliability of test plans for exponentiated log-logistic distribution,” Economic Quality Control, 21(2), 165-175, 2006.
[23]	Rao, G. S., Kantam, R.R.L., Rosaiah, K. and Prasad, S.V.S.V.S.V., “Reliability test plans for type-II generalized log-logistic distribution,” JRSS,, 5, 55-64, 2012.
[24]	Rao, G. S., Kantam, R.R.L. Rosaiah. K. and Prasad, S.V.S.V.S.V., “An economic reliability test plan for generalized log-logistic distribution,” International Journal of Engineering and Applied Sciences, 3, 61-68, 2012.
[25]	Balamurali, S., Aslam, M. and Fallah, Nezhad, M.S., “An acceptance sampling plan under Fréchet distribution assuring median life,” Research Journal of Applied Sciences, Engineering and Technology, 6(24), 4519-4523, 2013.
[26]	Lee, E.T. and Wang, J.W., Statistical Methods for Survival Data Analysis, 3. Wiley-Interscience, Oklahoma, 2003.
[27]	Lemonte, A.L. and Cordeiro, G. M., “An extended Lomax distribution, Statistics,” A Journal of Theoretical and Applied Statistics, 1-17, 2011.
[28]	Zea, L.M., Silva, R.B, Bourguignon, M., Santos, A.M. and Cordeiro, G.M., “The Beta Exponentiated Pareto Distribution with Application to Bladder Cancer Susceptibility,” International Journal of Statistics and Probability, 2, 1927-7032, 2012.