PROCEDURAL FRAMEWORK FOR DOUBLE SAMPLING PLAN USING INTERVENED POISSON DISTRIBUTION
This paper aims to present the procedural framework for double sampling attribute plan using intervened Poisson characteristics and an attempt has been made to optimize the parameters using minimum angle method. Producer and consumer risks of the proposed double sampling plan procedure have been determined for the given acceptable quality level (AQL) and limiting quality level (LQL). The performance measures of the sampling plan indexed with intervened Poisson characteristics were validated by shifting the tangent angle towards ideal operating characteristic (OC) curve thus ensuring optimized producer and consumer risks. The tables of operating ratios to find the optimum sample size for a specified risk are provided using intervened Poisson distribution. The sampling strategy proposed in this study is especially beneficial for evaluating the quality of finished goods in the manufacturing field.
intervened Poisson distribution, double sampling plan, consumer risk, producer risk, acceptable quality level, limiting quality level.
Received: April 19, 2022; Accepted: June 9, 2022; Published: August 18, 2022
How to cite this article: K. Pradeepa Veerakumari and Asif T. Thottathil, Procedural framework for double sampling plan using intervened Poisson distribution, Far East Journal of Theoretical Statistics 65 (2022), 125-157. http://dx.doi.org/10.17654/0972086322010
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] Pramote Charongrattanasakul and Wimonmas Bamrungsetthapong, Designing of optimal required sample sizes for double acceptance sampling plans under the zero-inflated defective data, Current Applied Science and Technology 21(2) (2020), 227-239.[2] P. Dhanavanthan, Compound intervened Poisson distribution, Biom. J. 40 (1998), 641-646.[3] P. Dhanavanthan, Estimation of the parameters of compound intervened Poisson distribution, Biom. J. 42(3) (2000), 315-320.[4] H. F. Dodge and H. G. Romig, A method of sampling inspection, Bell System Technical Journal 8(4) (1929), 613-631.[5] H. F. Dodge and H. G. Romig, Sample Inspection Tables; Single and Double Sampling, Wiley/Chapman & Hall, 1959.[6] A. J. Duncan, Quality Control and Industrial Statistics, R. D. Irwin, 1974.[7] W. C. Guenther, Procedure for finding double sampling plans for attributes, Journal of Quality Technology 2(4) (1970), 219-225.[8] F. A. Haight, Handbook of the Poisson Distribution, Wiley, New York, 1967.[9] A. Hald, On the theory of single sampling inspection by attributes based on two quality levels, Review of the International Statistical Institute 35(1) (1967), 1-29.[10] Venugopal Haridoss and Kandasamy Subramani, Designing optimal double sampling plan using the weighted Poisson distribution, International Journal of Quality and Reliability Management 33(1) (2016), 62-77.[11] Mei-Ling Huang and Karen Yuen Fung, Intervened truncated Poisson distribution, Sankhyā Ser. B 51(3) (1989), 302-310. http://www.jstor.org/stable/25052598.[12] J. M. Cameron, Table for constructing and for computing the operating characteristics of single-sampling plans, Industrial Quality Control 9 (1952), 37-39.[13] V. Kaviyarasu and Asif T. Thottathil, Designing STDS plan for zero-inflated Poisson distribution through various quality level, International Journal of Statistics and Applied Mathematics 3(4) (2018), 44-53.[14] V. Kaviyarasu and V. Devika, Designing single sampling plan using generalized Poisson distribution, International Journal of Scientific Research in Mathematical and Statistical Sciences 5(4) (2018), 226-232.[15] C. Satheesh Kumar and D. S. Shibu, Modified intervened Poisson distribution, Statistica 71(4) (2011), 489-499.[16] A. Loganathan and K. Shalini, Determination of single sampling plans by attributes under the conditions of zero-inflated Poisson distribution, Comm. Statist. Simulation Comput. 43(3) (2014), 538-548.[17] Norman Bush, Evelyne J. Leonard and Q. M. Marvin Marchant, A method of discrimination for single and double OC curves utilizing the tangent of the point of inflection, ENSAR Report No. PR-7, Engineering Agency, 1953.[18] Paul Peach and S. B. Littauer, A note on sampling inspection, Ann. Math. Statist. 17(1) (1946), 81-84.[19] R. Radhakrishnan and S. Pratheeba, Construction of double sampling plan indexed through average quality level, International Journal of Computational Science and Mathematics 4(1) (2012), 63-68. http://www.irphouse.com.[20] Edward G. Schilling and Dean V. Neubauer, Acceptance Sampling in Quality Control, Chapman and Hall/CRC, 2009.[21] Edward G. Schilling and Lucille I. Johnson, Tables for the construction of matched single, double, and multiple sampling plans with application to MIL-STD-105D, Journal of Quality Technology 12(4) (1980), 220-229.[22] R. Shanmugam, An intervened Poisson distribution and its medical application, Biometrics 41(4) (1985), 1025-1029.[23] V. Soundararajan and A. L. Christina, Selection of single sampling variables plans based on the minimum angle, J. Appl. Stat. 24(2) (1997), 207-218.[24] V. Soundararajan and S. Devaraj Arumainayagam, A generalized procedure for selection of attribute double sampling plan, Comm. Statist. Simulation Comput. 19(3) (1990), 1015-1034.[25] K. K. Suresh and V. Sangeetha, Selection of one plan suspension system through minimum angle method, Global Journal of Mathematical Sciences: Theory and Practical 3 (2010), 121-128.[26] United States Department of Defense, Military Standard, Sampling Procedures and Tables for Inspection by Attributes, (MIL-STD -105E), U.S. Government Printing Office, Washington, DC, 1989.[27] K. Pradeepa Veerakumari and S. Azarudheen, Evaluation of single sampling plan under the conditions of intervened Poisson distribution, Comm. Statist. Simulation Comput. 46(8) (2017), 6106-6114.[28] K. Pradeepa Veerakumari and Vivian Clements, Endorsement of acceptance sampling techniques by implementing neural networks, J. Stat. Comput. Simul. 85(9) (2015), 1857-1863.