Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process

Ronald W. Wanyonyi; Kennedy L. Nyongesa; Adu Wasike

doi:doi:10.11648/j.ajtas.20150406.34

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Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process

Ronald W. Wanyonyi, Kennedy L. Nyongesa, Adu Wasike

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)

Received: 7 November 2015 Accepted: 27 November 2015 Published: 22 December 2015

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Abstract

Batch testing involves testing items in a group rather than testing the items individually for resource saving purposes. Estimation of proportion of a trait of interest using batch testing model insulates individuals of a population against stigma. In this paper, an estimator of the unknown proportion of a trait in batch testing model based on a quality control process is constructed and its properties discussed. In quality control, a batch is rejected if constituent defective members are greater than l, the cut off value. It is observed that if l = 0, then the obvious batch testing strategy is obtained. Hence when l > 0, the batch testing strategy is generalized. The proposed model is superior to the existing models when the proportion of a trait is relatively high. The application of the model on Genetically Modified Organisms contamination is carried out.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.34
Page(s)	619-629
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Quality Control, Batching Testing, Cut off Value, Proportion, Genetically Modified Organisms

References

[1]	Dorfman, R. (1943). The detection of defective members of large population. Annals of Matematical Statistics, 14, 436-440.
[2]	Johnson, N. I., Kotz, S. and Wu, X. (1991). Inspection errors for Attributes in Quality Control. London; Chapman and Hall.
[3]	Nyongesa, L. K. (2004). Testing For the Presence of Disease by Pooling Samples. Aust. N. Z. J. Stat., 46, 901 -909.
[4]	Thomson, K. H. (1962). Estimation of the Proportion of Vectors in a Natural Population of Insects, Biometrics, 18, 568-578.
[5]	Sobel, M., and Elashoff, R.M., (1975). Group -testing with a new goal, Estimation. Biometrika, 62, 181-193.
[6]	Gastwirth, L. J. 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.
[7]	Brookmeyer, R. (1999). Analysis of Multistage Pooling Studies of Biological Specimens for Estimating Disease Incidence and Prevalence. Biometrics, 55, 608-612.
[8]	Hughes-Oliver, M. J. and Swallow, H. W. (1994). A Two-Stage Adaptive Procedure for Estimating Small Proportions. Journal of the American Statistical Association, 89, 982-993.
[9]	Tu, M. X., Litvak, E. and Pagano, M. (1995). On the Informative and Accuracy of Pooled Testing in Estimating Prevalence of a Rare Disease: Application to HIV Screening. Biometrika, 82, 287-297.
[10]	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.
[11]	Hepworth, G. (1999). Estimation of Proportions by Group Testing. PhD thesis, University of Melbourne.
[12]	Biggerstaff, B. (2008). Confidence Intervals for the Difference of two proportions Estimated from Pooled samples. Journal of Agricultural, Biological and Environmental Statistics, 13, 478-496.
[13]	Nyongesa, L. K., (2011). Dual Estimation of Prevalence and Disease Incidence in Pool-Testing Strategy. Communication in Statistics Theory and Method. 40, 1-12.
[14]	Tebbs, J. M., McMaham, C. S. and Bilder, C. R. (20130. Two-stage Hierarchical Group Testing for Multiple Infections with Application to the Infertility Prevention Project, Biometrics, 69, 1064-1073.
[15]	Hepworth, G. and Watson, R. (2015). Revisiting Retesting in the Estimation of Proportions by Group- Testing, Communications in Statistics-simulation and Computation, DOI:10.1080/03610918.2014.960725.
[16]	McMaham, C. S., Tebbs, J. M. and Bilder, C. R. (2013). Regression Models for Group Testing Data with Pool Dilution Effects, Biostatistics, 14, 284-298.
[17]	Montegmery, D. C. (2009). Introduction to Statistical Quality Control (6^th edition). New York, John Wiley and Sons.
[18]	Hepworth, G. and Watson, R. (2009). Debiased Estimation of Proportions in Group Testing. Applied Statistics, 58, 105-121.
[19]	Schaarschmidt, F. (2007). Experimental Design for One-sided Confidence Intervals or Hypothesis tests in Binomial Group Testing. Communications in Biometry and Crop Science, 2, 32-40.
[20]	Bhattacharyya, G. K., Karandinos, M. G., and DeFoliart, G. R. (1979). Point Estimates and Confidence Intervals for Infection Rates Using Pooled Organisms in Epidemiologic Studies. American Journal of Epidemiology, 109, 124-131.
[21]	Swallow, W. H. (1985). Group Testing for Estimating Infection Rates and Probability of Disease Transmission. Phytopathology, 75, 882-889.
[22]	Lovison, G., Gore, S. D. and Patil, G. P. (1994). Design and Analysis of Composite Sampling Procedures: a review. In Handbook of Statistics, 12, 103-166. Amsterdam: Elsevier.
[23]	Hung, M. and Swallow, H. W. (2000). Use of Binomial Group Testing In Tests of Hypotheses for Classification or Quantitative Covariates. Biometrics, 56, 204-212.
[24]	Remund, K. M., Wright, D. L. and Holden, L. R. (2001). Statistical Considerations in Seed purity testing for transgenic traits. Seed Science Research, 11, 101-120.
[25]	Kobilinsky, A. and Bertheau, Y. (2005). Minimum Cost Acceptance sampling plans for Grain Control with application to GMO detection. Chemometrics and Intelligent Laboratory Systems, 75, 189-200.
[26]	Montesinos-Lopes, O. A., Montesinos, A., Eskridge, K. and Crossa, J. (2014). Estimating a Proportion based on Group Testing for Correlated Binary Response. J Biomet biostat, 5, 185-196.
[27]	Liu, C., Liu, A., Zhang, B. and Zhang, Z. (2013). Improved Confidence Intervals of a small Probability from Pooled Testing with Misclassification. Frontiers in Public Health, DOI: 10.3389/fpubh.2013.00039.

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APA Style

Ronald W. Wanyonyi, Kennedy L. Nyongesa, Adu Wasike. (2015). Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. American Journal of Theoretical and Applied Statistics, 4(6), 619-629. https://doi.org/10.11648/j.ajtas.20150406.34

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ACS Style

Ronald W. Wanyonyi; Kennedy L. Nyongesa; Adu Wasike. Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. Am. J. Theor. Appl. Stat. 2015, 4(6), 619-629. doi: 10.11648/j.ajtas.20150406.34

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AMA Style

Ronald W. Wanyonyi, Kennedy L. Nyongesa, Adu Wasike. Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. Am J Theor Appl Stat. 2015;4(6):619-629. doi: 10.11648/j.ajtas.20150406.34

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@article{10.11648/j.ajtas.20150406.34,
  author = {Ronald W. Wanyonyi and Kennedy L. Nyongesa and Adu Wasike},
  title = {Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {619-629},
  doi = {10.11648/j.ajtas.20150406.34},
  url = {https://doi.org/10.11648/j.ajtas.20150406.34},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.34},
  abstract = {Batch testing involves testing items in a group rather than testing the items individually for resource saving purposes. Estimation of proportion of a trait of interest using batch testing model insulates individuals of a population against stigma. In this paper, an estimator of the unknown proportion of a trait in batch testing model based on a quality control process is constructed and its properties discussed. In quality control, a batch is rejected if constituent defective members are greater than l, the cut off value. It is observed that if l = 0, then the obvious batch testing strategy is obtained. Hence when l > 0, the batch testing strategy is generalized. The proposed model is superior to the existing models when the proportion of a trait is relatively high. The application of the model on Genetically Modified Organisms contamination is carried out.},
 year = {2015}
}

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TY  - JOUR
T1  - Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process
AU  - Ronald W. Wanyonyi
AU  - Kennedy L. Nyongesa
AU  - Adu Wasike
Y1  - 2015/12/22
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.34
DO  - 10.11648/j.ajtas.20150406.34
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 619
EP  - 629
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.34
AB  - Batch testing involves testing items in a group rather than testing the items individually for resource saving purposes. Estimation of proportion of a trait of interest using batch testing model insulates individuals of a population against stigma. In this paper, an estimator of the unknown proportion of a trait in batch testing model based on a quality control process is constructed and its properties discussed. In quality control, a batch is rejected if constituent defective members are greater than l, the cut off value. It is observed that if l = 0, then the obvious batch testing strategy is obtained. Hence when l > 0, the batch testing strategy is generalized. The proposed model is superior to the existing models when the proportion of a trait is relatively high. The application of the model on Genetically Modified Organisms contamination is carried out.
VL  - 4
IS  - 6
ER  -

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Author Information

Ronald W. Wanyonyi

Department of Mathematics, Egerton University, Nakuru, Kenya
Kennedy L. Nyongesa

Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya
Adu Wasike

Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya

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APA Style

Ronald W. Wanyonyi, Kennedy L. Nyongesa, Adu Wasike. (2015). Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. American Journal of Theoretical and Applied Statistics, 4(6), 619-629. https://doi.org/10.11648/j.ajtas.20150406.34

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ACS Style

Ronald W. Wanyonyi; Kennedy L. Nyongesa; Adu Wasike. Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. Am. J. Theor. Appl. Stat. 2015, 4(6), 619-629. doi: 10.11648/j.ajtas.20150406.34

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AMA Style

Ronald W. Wanyonyi, Kennedy L. Nyongesa, Adu Wasike. Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process. Am J Theor Appl Stat. 2015;4(6):619-629. doi: 10.11648/j.ajtas.20150406.34

Copy | Download

@article{10.11648/j.ajtas.20150406.34,
  author = {Ronald W. Wanyonyi and Kennedy L. Nyongesa and Adu Wasike},
  title = {Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {619-629},
  doi = {10.11648/j.ajtas.20150406.34},
  url = {https://doi.org/10.11648/j.ajtas.20150406.34},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.34},
  abstract = {Batch testing involves testing items in a group rather than testing the items individually for resource saving purposes. Estimation of proportion of a trait of interest using batch testing model insulates individuals of a population against stigma. In this paper, an estimator of the unknown proportion of a trait in batch testing model based on a quality control process is constructed and its properties discussed. In quality control, a batch is rejected if constituent defective members are greater than l, the cut off value. It is observed that if l = 0, then the obvious batch testing strategy is obtained. Hence when l > 0, the batch testing strategy is generalized. The proposed model is superior to the existing models when the proportion of a trait is relatively high. The application of the model on Genetically Modified Organisms contamination is carried out.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Estimation of Proportion of a Trait by Batch Testing Model in a Quality Control Process
AU  - Ronald W. Wanyonyi
AU  - Kennedy L. Nyongesa
AU  - Adu Wasike
Y1  - 2015/12/22
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.34
DO  - 10.11648/j.ajtas.20150406.34
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 619
EP  - 629
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.34
AB  - Batch testing involves testing items in a group rather than testing the items individually for resource saving purposes. Estimation of proportion of a trait of interest using batch testing model insulates individuals of a population against stigma. In this paper, an estimator of the unknown proportion of a trait in batch testing model based on a quality control process is constructed and its properties discussed. In quality control, a batch is rejected if constituent defective members are greater than l, the cut off value. It is observed that if l = 0, then the obvious batch testing strategy is obtained. Hence when l > 0, the batch testing strategy is generalized. The proposed model is superior to the existing models when the proportion of a trait is relatively high. The application of the model on Genetically Modified Organisms contamination is carried out.
VL  - 4
IS  - 6
ER  -

Copy | Download