Two-sided sampling plan for exponential distribution under type II censored samples

Year 2022, Volume: 51 Issue: 1, 327 - 337, 14.02.2022

Hacene Belbachir , Mohamed Benahmed

https://doi.org/10.15672/hujms.812606

Cited By: 2

Abstract

Acceptance sampling plan paid the attention of many researchers in the last few years, their works focused basically on Bayesian sampling plans under one-sided decision function and different forms of censoring. In the present paper, a single variable sampling plan for exponential distribution based on type II censored samples under random decision function is developed. For a polynomial loss function, an explicit expression for the Bayes risk is determined. To obtain an approximation for the optimal sampling plan, a simple algorithm based on a discretization method is presented. Finally, an illustrative example and a simulation study followed by extensive tables for the proposed sampling plan are provided.

Keywords

Bayesian sampling, type II censored samples, random decision function

References

• [1] M. Aslam, A variable acceptance sampling plan under neutrosophic statistical interval method, Symmetry 11 (1), 114, 2019.
• [2] M. Aslam, A new attribute sampling plan using neutrosophic statistical interval method, Complex Intell. Systems 5 (4), 365370, 2019.
• [3] M. Aslam, Product acceptance determinations using new nonparametric sign sampling plan, Int. J. Stat. Manag. Syst. 23 (8), 1561-1570, 2020.
• [4] M. Aslam, P. Jeyadurga, S. Balamurali, M. Azam and A. AL-Marshadi, Economic determination of modified multiple dependent state sampling plan under some lifetime distributions, J. Math., Doi:10.1155/2021/7470196, 2021.
• [5] M. Aslam, M.A. Raza and L. Ahmad, Acceptance sampling plans for two-stage process for multiple manufacturing lines under neutrosophic statistics, J. Intell. Fuzzy Syst. 37 (6), 7839-7850, 2019.
• [6] S. Balamurali, M. Aslam, L. Ahmad and C.H. Jun, A mixed double sampling plan based on $C_{pk}$, Comm. Statist. Theory Methods Communications 49 (8), 1840-1857, 2019.
• [7] R. Bhattacharya and M. Aslam, Generalized multiple dependent state sampling plans in presence of measurement data, IEEE Access 8, 162775-162784, 2020.
• [8] L.S. Chen, M.C. Yang and T. Liang, Curtailed Bayesian sampling plans for exponential distributions based on Type-II censored samples, J. Stat. Comput. Simul. 87 (6), 1160-1178, 2017.
• [9] A. Childs, B. Chandrasekar, N. Balakrishnan and D. Kundu, Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution, Ann. Inst. Statist. Math. 55 (2), 319-330, 2003.
• [10] W.C. Guenther, On the determination of single sampling attribute plans based upon a linear cost model and a prior distribution, Technometrics 13 (3), 483-498, 1971.
• [11] A. Hald, Asymptotic properties of Bayesian single sampling plans, J. R. Stat. Soc. Ser. B. Stat. Methodol. 29 (1), 162-173, 1968.
• [12] G. Işık and İ. Kaya, Effects of neutrosophic binomial distribution on double acceptance sampling plan, Conference Proceeding Science and Technology 3 (1), 68-76, 2020.
• [13] Y. Lam, An optimal single variable sampling plan with censoring, The Statistician 39 (1), 53-67, 1990.
• [14] Y. Lam, Bayesian variable sampling plans for the exponential distribution with type I censoring, Ann. Statist. 22 (2), 696-711, 1994.
• [15] C.T. Lin, Y.L. Huang and N. Balakrishnan, Exact Bayesian variable sampling plans for the exponential distribution based on type-I and type-II hybrid censored samples, Comm. Statist. Simulation Comput. 37 (6), 1101-1116, 2008.
• [16] Y.P Lin, L. Tachen and W.T. Huang, Bayesian sampling plans for exponential distribution based on the type I censoring data, Ann. Inst. Statist. Math. 54 (1), 100-113, 2002.
• [17] D. Prajapati, S. Mitra and D. Kundu, A new decision theoretic sampling plan for exponential distribution under type-I censoring, Comm. Statist. Simulation Comput. 49 (2), 453-471, 2020.
• [18] G.B. Wetherill, Sampling Inspection and Quality Control, 2nd ed., Chapman and Hall, London, 1977.
• [19] G.B. Wetherill and G.E.G. Campling, The decision theory approach to sampling inspection, J. R. Stat. Soc. Ser. B. Stat. Methodol. 28 (3), 381-416, 1966.
• [20] M.C. Yang, L.S. Chen and T. Liang, Optimal Bayesian variable sampling plans for exponential distributions based on modified type-II hybrid censored samples, Comm. Statist. Simulation Comput. 46 (6), 4722-4744, 2017.