A Two-Stage Group Sampling Plan Based on Truncated Life Tests for Exponentiated Half Logistic Distribution
Rao Gadde S. 1*, Rosaiah Kanaparthi 2, Naidu Chukka R. 3
1 Department of Mathematics and Statistics, The University of Dodoma
Dodoma, PO. Box: 259, Tanzania
2 Department of Statistics, Acharya Nagarjuna University
Guntur – 522 007, India
3 Department of Statistics, Dilla University
Dilla, PO. Box: 419, Ethiopia
*E-mail: gaddesrao@gmail.com
Received:
Received: 9 June 2020; revised: 26 June 2020; accepted: 27 June 2020; published online: 29 June 2020
DOI: 10.12921/cmst.2020.0000017
Abstract:
When the life time of a product follows exponentiated half logistic distribution we can recommend a two-stage group acceptance sampling plan for truncated life tests. The acceptance of the lot can be done at the first or second stage based on the number of failures in each group. In this paper, we obtained the number of groups essential for each of two stages for the underlying lifetime distribution so as to minimize the average sample number under the constraints of satisfying the producer’s and consumer’s risks simultaneously. Single-stage group sampling plans are also considered as special cases of the stated plan and compared with the proposed plan in terms of the average sample number and the operating characteristics.
Key words:
average sample number, consumer’s risk, exponentiated half logistic distribution, operating characteristics, producer’s risk
References:
[1] B. Epstein, Truncated life tests in the exponential case, The Annals of Mathematical Statistics 25(3), 555–564 (1954).
[2] M. Sobel, J.A. Tischendrof, Acceptance sampling with sew life test objective, Proceedings of Fifth National Symposium on Reliability and Quality Control, 108–118, Philadelphia (1959).
[3] S.S. Gupta, P.A. Groll, Gamma distribution in acceptance sampling based on life tests, Journal of the American Statis- tical Association 56, 942–970 (1961).
[4] H. Goode, J. Kao, Sampling plans based on the Weibull dis- tribution, Proceeding of the Seventh National Symposium on Reliability and Quality Control, 24–40 (1961).
[5] S. Gupta, Life test sampling plans for normal and lognormal distributions, Technometrics 4(2), 151–175 (1962).
[6] F. Fertig, N. Mann, Life-test sampling plans for two-para- meter Weibull populations, Technometrics 22(2), 165–177 (1980).
[7] R.R.L. Kantam, K. Rosaiah, Half logistic distribution in ac- ceptance sampling based on life tests, IAPQR Transactions 23(2), 117–125 (1998).
[8] R.R.L. Kantam, K. Rosaiah, G.S. Rao, Acceptance sampling based on life tests: Log- logistic models, Journal of Applied Statistics 28(1), 121–128 (2001).
[9] A. Baklizi, Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind, Advances and Applications in Statistics 3(1), 33–48 (2003).
[10] A. Baklizi, A. EI Masri, Acceptance sampling based on trun- cated life tests in the Birnbaum-Saunders model, Risk Anal- ysis 24(6), 1453–1457 (2004).
[11] T.-R. Tsai, S.-J. Wu, Acceptance sampling based on trun- cated life tests for generalized Rayleigh distribution, Journal of Applied Statistics 33(6), 595–600 (2006).
[12] N. Balakrishnan, V. Leiva, J. Lopez, Acceptance sam- pling plans from truncated life tests based on the gener- alized Birnbaum-Saunders distribution, Communication in Statistics-Simulation and Computation 36, 643–656 (2007).
[13] M. Aslam, Double acceptance sampling based on truncated life tests in Rayleigh distribution, European Journal of Scien- tific Research 7(4), 605–610 (2007).
[14] G.S. Rao, M.E. Ghitany, R.R.L. Kantam, Acceptance sam- pling plans for Marshall-Olkin extended Lomax distribution, International Journal of Applied Mathematics 21(2), 315– 325 (2008).
[15] A.I. Al-Omari, Acceptance sampling plans based on trun- cated life tests for sushila distribution, Journal of mathemat- ical and fundamental sciences 50(1), 72–83 (2018).
[16] G.S. Rao, A group acceptance sampling plans based on trun- cated life tests for generalized exponential distribution, Eco- nomic Quality Control 24(1), 75–85 (2009).
[17] G.S. Rao, A group acceptance sampling plans based on trun- cated life tests for Marshall-Olkin extended Lomax distribu- tion, Electronic Journal of Applied Statistical Analysis 3(1), 18–27 (2010).
[18] M. Aslam, C.-H. Jun, A group acceptance sampling plan for truncated life test having Weibull distribution, Journal of Ap- plied Statistics 39, 1021–1027 (2009).
[19] M. Aslam, C.-H. Jun, 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 (2009).
[20] C.-H. Jun, S. Balamurali, S.-H. Lee, Variables sampling plans for Weibull distributed lifetimes under sudden death testing, IEEE Transactions on Reliability 55(1), 53–58 (2006).
[21] J.-W. Wu, T.-R. Tsai, L.-Y. Ouyang, Limited failure-censored life test for the Weibull distribution, IEEE Transactions on Reliability 50(1), 107–111 (2001).
[22] F. Pascual, W. Meeker, The modified sudden death test: plan- ning life tests with a limited number of test positions, Journal of Testing and Evaluation 26(5), 434–443 (1998).
[23] G.S. Rao, Acceptance sampling plans from truncated life tests based on the Marshall-Olkin extended exponential dis- tribution for percentiles, Brazilian Journal of Probability and Statistics 27(2), 117–132 (2013).
[24] G.S. Rao, R.R.L. Kantam, Acceptance sampling plans from truncated life tests based on the log-logistic distribution for percentiles, Economic Quality Control 25(2), 153–167 (2010).
[25] Y. Lio, T.-R. Tsai, S.-J. Wu, Acceptance sampling plan based on the truncated life test in the Birnbaum Saunders distribu- tion for percentiles, Communications in Statistics-Simulation and Computation 39, 119–136 (2009).
[26] Y.L. Lio, T.-R. Tsai, S.-J. Wu, Acceptance sampling plans from truncated life tests based on the Burr type XII per- centiles, Journal of the Chinese Institute of Industrial Engi- neers 27(4), 270–280 (2010).
[27] A.W. Marshall, I. Olkin, Life Distributions-Structure of Nonparametric, Semiparametric, and Parametric Families, Springer Series in Statistics (2007).
[28] M. Aslam, C.-H. Jun, M. Rasool, M. Ahmad, A time trun- cated two-stage group sampling plan for Weibull distribution, Communications of the Korean Statistical Society 17, 89–98 (2010).
[29] M. Aslam, C.-H. Jun, M. Ahmad, A two-stage group sam- pling plan based on truncated life tests for a general dis- tribution, Journal of Statistical Computation and Simulation 81(12), 1927–1938 (2011).
[30] G.S. Rao, A Two-stage group sampling plan based on trun- cated life tests for a M-O extended exponential distribution, International Journal of Quality Engineering & Technology 3(4), 319–331 (2013).
[31] G.S. Rao, K. Rosaiah, M. Sridhar babu, D.C.U. Sivakumar, A two-stage group acceptance sampling plans based on truncated life tests for exponentiated frechet distribution, Euro- pean Scientific Journal 10(33), 145–160 (2014).
[32] G.S. Rao, C.N. Ramesh, Acceptance sampling plans for percentiles based on the exponentiated half logistic distri- bution, Applications and Applied Mathematics: An Interna- tional Journal 9(1), 39–53 (2014).
[33] S.V. Prasad, K. Rosaiah, G.S. Rao, A two stage group sam- pling plans based on truncated life tests for Type II general- ized log-logistic distribution, International Journal of Scien- tific Research in Mathematical and Statistical Sciences 5(6), 228–243 (2018).
[34] G.S. Rao, K. Kalyani, K. Rosaiah, D.C.U. Sivakumar, A time- truncated two-stage group acceptance sampling plan for odds exponential log-logistic distribution, Life Cycle Reli- ability and Safety Engineering 8(4), 337–345 (2019).
[35] D.C.U. Sivakumar, G.S. Rao, K. Rosaiah, K. Kalyani, A two- stage group acceptance sampling plans based on truncated life tests for an odd generalized exponential log-logistic dis- tribution, Current journal of applied science and technology 35(4), 1–14 (2019).
[36] G. Cordeiro, M. Alizadeh, E. Ortega, The exponentiated half logistic family of distributions: properties and applications, Journal of Probability and Statistics 2014, 1–21 (2014).
[37] I. Abdul-Moniem, M. Seham, Transmuted Gompertz distri- bution, Computational and Applied Mathematics 1(3), 88–96 (2015).
[38] D.F. Andrews, A.M. Herzberg, Data: A Collection of Prob- lems from Many Fields for the Student and Research Worker, Springer Series in Statistics (2012).
When the life time of a product follows exponentiated half logistic distribution we can recommend a two-stage group acceptance sampling plan for truncated life tests. The acceptance of the lot can be done at the first or second stage based on the number of failures in each group. In this paper, we obtained the number of groups essential for each of two stages for the underlying lifetime distribution so as to minimize the average sample number under the constraints of satisfying the producer’s and consumer’s risks simultaneously. Single-stage group sampling plans are also considered as special cases of the stated plan and compared with the proposed plan in terms of the average sample number and the operating characteristics.
Key words:
average sample number, consumer’s risk, exponentiated half logistic distribution, operating characteristics, producer’s risk
References:
[1] B. Epstein, Truncated life tests in the exponential case, The Annals of Mathematical Statistics 25(3), 555–564 (1954).
[2] M. Sobel, J.A. Tischendrof, Acceptance sampling with sew life test objective, Proceedings of Fifth National Symposium on Reliability and Quality Control, 108–118, Philadelphia (1959).
[3] S.S. Gupta, P.A. Groll, Gamma distribution in acceptance sampling based on life tests, Journal of the American Statis- tical Association 56, 942–970 (1961).
[4] H. Goode, J. Kao, Sampling plans based on the Weibull dis- tribution, Proceeding of the Seventh National Symposium on Reliability and Quality Control, 24–40 (1961).
[5] S. Gupta, Life test sampling plans for normal and lognormal distributions, Technometrics 4(2), 151–175 (1962).
[6] F. Fertig, N. Mann, Life-test sampling plans for two-para- meter Weibull populations, Technometrics 22(2), 165–177 (1980).
[7] R.R.L. Kantam, K. Rosaiah, Half logistic distribution in ac- ceptance sampling based on life tests, IAPQR Transactions 23(2), 117–125 (1998).
[8] R.R.L. Kantam, K. Rosaiah, G.S. Rao, Acceptance sampling based on life tests: Log- logistic models, Journal of Applied Statistics 28(1), 121–128 (2001).
[9] A. Baklizi, Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind, Advances and Applications in Statistics 3(1), 33–48 (2003).
[10] A. Baklizi, A. EI Masri, Acceptance sampling based on trun- cated life tests in the Birnbaum-Saunders model, Risk Anal- ysis 24(6), 1453–1457 (2004).
[11] T.-R. Tsai, S.-J. Wu, Acceptance sampling based on trun- cated life tests for generalized Rayleigh distribution, Journal of Applied Statistics 33(6), 595–600 (2006).
[12] N. Balakrishnan, V. Leiva, J. Lopez, Acceptance sam- pling plans from truncated life tests based on the gener- alized Birnbaum-Saunders distribution, Communication in Statistics-Simulation and Computation 36, 643–656 (2007).
[13] M. Aslam, Double acceptance sampling based on truncated life tests in Rayleigh distribution, European Journal of Scien- tific Research 7(4), 605–610 (2007).
[14] G.S. Rao, M.E. Ghitany, R.R.L. Kantam, Acceptance sam- pling plans for Marshall-Olkin extended Lomax distribution, International Journal of Applied Mathematics 21(2), 315– 325 (2008).
[15] A.I. Al-Omari, Acceptance sampling plans based on trun- cated life tests for sushila distribution, Journal of mathemat- ical and fundamental sciences 50(1), 72–83 (2018).
[16] G.S. Rao, A group acceptance sampling plans based on trun- cated life tests for generalized exponential distribution, Eco- nomic Quality Control 24(1), 75–85 (2009).
[17] G.S. Rao, A group acceptance sampling plans based on trun- cated life tests for Marshall-Olkin extended Lomax distribu- tion, Electronic Journal of Applied Statistical Analysis 3(1), 18–27 (2010).
[18] M. Aslam, C.-H. Jun, A group acceptance sampling plan for truncated life test having Weibull distribution, Journal of Ap- plied Statistics 39, 1021–1027 (2009).
[19] M. Aslam, C.-H. Jun, 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 (2009).
[20] C.-H. Jun, S. Balamurali, S.-H. Lee, Variables sampling plans for Weibull distributed lifetimes under sudden death testing, IEEE Transactions on Reliability 55(1), 53–58 (2006).
[21] J.-W. Wu, T.-R. Tsai, L.-Y. Ouyang, Limited failure-censored life test for the Weibull distribution, IEEE Transactions on Reliability 50(1), 107–111 (2001).
[22] F. Pascual, W. Meeker, The modified sudden death test: plan- ning life tests with a limited number of test positions, Journal of Testing and Evaluation 26(5), 434–443 (1998).
[23] G.S. Rao, Acceptance sampling plans from truncated life tests based on the Marshall-Olkin extended exponential dis- tribution for percentiles, Brazilian Journal of Probability and Statistics 27(2), 117–132 (2013).
[24] G.S. Rao, R.R.L. Kantam, Acceptance sampling plans from truncated life tests based on the log-logistic distribution for percentiles, Economic Quality Control 25(2), 153–167 (2010).
[25] Y. Lio, T.-R. Tsai, S.-J. Wu, Acceptance sampling plan based on the truncated life test in the Birnbaum Saunders distribu- tion for percentiles, Communications in Statistics-Simulation and Computation 39, 119–136 (2009).
[26] Y.L. Lio, T.-R. Tsai, S.-J. Wu, Acceptance sampling plans from truncated life tests based on the Burr type XII per- centiles, Journal of the Chinese Institute of Industrial Engi- neers 27(4), 270–280 (2010).
[27] A.W. Marshall, I. Olkin, Life Distributions-Structure of Nonparametric, Semiparametric, and Parametric Families, Springer Series in Statistics (2007).
[28] M. Aslam, C.-H. Jun, M. Rasool, M. Ahmad, A time trun- cated two-stage group sampling plan for Weibull distribution, Communications of the Korean Statistical Society 17, 89–98 (2010).
[29] M. Aslam, C.-H. Jun, M. Ahmad, A two-stage group sam- pling plan based on truncated life tests for a general dis- tribution, Journal of Statistical Computation and Simulation 81(12), 1927–1938 (2011).
[30] G.S. Rao, A Two-stage group sampling plan based on trun- cated life tests for a M-O extended exponential distribution, International Journal of Quality Engineering & Technology 3(4), 319–331 (2013).
[31] G.S. Rao, K. Rosaiah, M. Sridhar babu, D.C.U. Sivakumar, A two-stage group acceptance sampling plans based on truncated life tests for exponentiated frechet distribution, Euro- pean Scientific Journal 10(33), 145–160 (2014).
[32] G.S. Rao, C.N. Ramesh, Acceptance sampling plans for percentiles based on the exponentiated half logistic distri- bution, Applications and Applied Mathematics: An Interna- tional Journal 9(1), 39–53 (2014).
[33] S.V. Prasad, K. Rosaiah, G.S. Rao, A two stage group sam- pling plans based on truncated life tests for Type II general- ized log-logistic distribution, International Journal of Scien- tific Research in Mathematical and Statistical Sciences 5(6), 228–243 (2018).
[34] G.S. Rao, K. Kalyani, K. Rosaiah, D.C.U. Sivakumar, A time- truncated two-stage group acceptance sampling plan for odds exponential log-logistic distribution, Life Cycle Reli- ability and Safety Engineering 8(4), 337–345 (2019).
[35] D.C.U. Sivakumar, G.S. Rao, K. Rosaiah, K. Kalyani, A two- stage group acceptance sampling plans based on truncated life tests for an odd generalized exponential log-logistic dis- tribution, Current journal of applied science and technology 35(4), 1–14 (2019).
[36] G. Cordeiro, M. Alizadeh, E. Ortega, The exponentiated half logistic family of distributions: properties and applications, Journal of Probability and Statistics 2014, 1–21 (2014).
[37] I. Abdul-Moniem, M. Seham, Transmuted Gompertz distri- bution, Computational and Applied Mathematics 1(3), 88–96 (2015).
[38] D.F. Andrews, A.M. Herzberg, Data: A Collection of Prob- lems from Many Fields for the Student and Research Worker, Springer Series in Statistics (2012).
