The quality of products manufactured or procured by
organizations is an important aspect of their survival in the global market.
The quality control processes put in place by organizations can be resource-intensive
but substantial savings can be realized by using acceptance sampling in
conjunction with batch testing. This paper considers the batch testing model
based on the quality control process where batches that test positive are
re-tested. The results show that re-testing greatly improves the efficiency
over one stage batch testing based on quality control. This is observed using
Asymptotic Relative Efficiency (ARE), where for values of p computed ARE > 1 implying that our estimator has a smaller
variance than the one-stage batch testing. Also, it was found that the model is
more efficient than the classical two-stage batch testing for relatively high
values of proportion.
References
[1]
Mwangi, O.W., Islam, A. and Luke, O. (2015) Bootstrap Confidence Intervals for Proportions of Unequal Sized Groups Adjusted for Overdispersion. Open Journal of Statistics, 5, 502-510. https://doi.org/10.4236/ojs.2015.56052
[2]
Dorfman, R. (1943) The Detection of Defective Members of Large Populations. Annals of Mathematical Statistics, 14, 436-440.
https://doi.org/10.1214/aoms/1177731363
[3]
Thompson, K.H. (1962) Estimation of the Proportion of Vectors in a Natural Population of Insects. Biometrics, 18, 568-578. https://doi.org/10.2307/2527902
[4]
Gastwirth, J.L. and Johnson, W.O. (1994) Screening with Cost-Effective Quality Control: Potential Applications to HIV and Drug Testing. Journal of the American Statistical Association, 89, 972-981.
https://doi.org/10.1080/01621459.1994.10476831
[5]
Tu, X., Litvak, E. and Pagano, M. (1995) On the Informativeness and Accuracy of Pooled Testing in Estimating Prevalence of a Rare Disease: Application to HIV Screening. Biometrika, 82, 287-297. https://doi.org/10.1093/biomet/82.2.287
[6]
McV Messam, L.L., Branscum, A.J., Collins, M.T. and Gardner, I.A. (2008) Frequentist and Bayesian Approaches to Prevalence Estimation Using Examples from Johne’s Disease. Animal Health Research Reviews, 9, 1-23.
https://doi.org/10.1017/S1466252307001314
[7]
Swallow, W.H. (1985) Group Testing for Estimating Infection Rates and Probabilities of Disease Transmission. Phytopathology, 75, 882-889.
https://doi.org/10.1094/Phyto-75-882
[8]
Chick, S.E. (1996) Bayesian Models for Limiting Dilution Assay and Group Test Data. Biometrics, 52, 1055-1062. https://doi.org/10.2307/2533066
[9]
Montesinos-López, O., Montesinos-López, A., Crossa, J., Eskridge, K. and Sáenz, R.A. (2011) Erratum: Optimal Sample Size for Estimating the Proportion of Transgenic Plants Using the Dorfman Model with a Random Confidence Interval. Seed Science Research, 21, 235-245. https://doi.org/10.1017/S0960258511000055
[10]
Montgomery, D.C. (2020) Introduction to Statistical Quality Control. John Wiley & Sons, Hoboken.
[11]
Hwang, F.K. (1976) Group Testing with a Dilution Effect. Biometrika, 63, 671-680.
https://doi.org/10.1093/biomet/63.3.671
[12]
Remund, K.M., Dixon, D.A., Wright, D.L. and Holden, L.R. (2001) Statistical Considerations in Seed Purity Testing for Transgenic Traits. Seed Science Research, 11, 101-119. http://europepmc.org/abstract/AGR/IND23232809
[13]
Kennedy, N.L. (2004) Multistage Group Testing Procedure (Group Screening). Communications in Statistics—Simulation and Computation, 33, 621-637.
https://doi.org/10.1081/SAC-200033231
[14]
Brookmeyer, R. (1999) Analysis of Multistage Pooling Studies of Biological Specimens for Estimating Disease Incidence and Prevalence. Biometrics, 55, 608-612.
https://doi.org/10.1111/j.0006-341X.1999.00608.x
[15]
Wanyonyi, R.W., Nyongesa, K. and Wasike, A.A.M. (2015) Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. American Journal of Theoretical and Applied Statistics, 4, 619-629.
https://doi.org/10.11648/j.ajtas.20150406.34
[16]
Kennedy, N.L. (2011) Dual Estimation of Prevalence and Disease Incidence in Pool-Testing Strategy. Communications in Statistics—Theory and Methods, 40, 3218-3229. https://doi.org/10.1080/03610926.2010.493257
[17]
Kline, R.L., Brothers, T.A., Brookmeyer, R., Zeger, S. and Quinn, T.C. (1989) Evaluation of Human Immunodeficiency Virus Seroprevalence in Population Surveys Using Pooled Sera. Journal of Clinical Microbiology, 27, 1449-1452.
https://doi.org/10.1128/JCM.27.7.1449-1452.1989
[18]
Damaschke, P. (2006) Threshold Group Testing. In: Ahlswede, R., Baumer, L., Cai, N., Aydinian, H., Blinovsky, V. and Deppe, C., Eds., General Theory of Information Transfer and Combinatorics, Springer, Berlin, 707-718.
[19]
Chen, H.-B. and De Bonis, A. (2011) An Almost Optimal Algorithm for Generalized Threshold Group Testing with Inhibitors. Journal of Computational Biology, 18, 851-864. https://doi.org/10.1089/cmb.2010.0030
[20]
Xie, M., Tatsuoka, K., Sacks, J. and Young, S.S. (2001) Group Testing with Blockers and Synergism. Journal of the American Statistical Association, 96, 92-102.
https://doi.org/10.1198/016214501750333009
[21]
Wanyonyi, R.W., Nyongesa, K.L. and Wasike, A. (2015) Estimation of Proportion of a Trait by Batch Testing with Errors in Inspection in a Quality Control Process. International Journal of Statistics and Applications, 5, 268-278.
http://article.sapub.org/10.5923.j.statistics.20150506.02.html
https://doi.org/10.11648/j.ajtas.20150406.34
[22]
Okoth, A.W., et al. (2017) Multi-Stage Adaptive Pool Testing Model with Test Errors, Improved Efficiency. IOSR Journal of Mathematics, 13, 43-55.
https://doi.org/10.9790/5728-1301024355
[23]
Matiri, G., Nyongesa, K. and Islam, A. (2017) Sequentially Selecting Between Two Experiment for Optimal Estimation of a Trait with Misclassification. American Journal of Theoretical and Applied Statistics, 6, 79-89.
https://doi.org/10.11648/j.ajtas.20170602.12
[24]
Lk, N. (2018) Multiple-Test Pool-Testing Strategy for Estimating HIV/AIDS-Prevalence and Its Extension to Multi-Stage.
[25]
Lehmann, E.L. and Casella, G. (1998) Theory of Point Estimation (Springer Texts in Statistics). Second Edition, Springer, Berlin.
