American Journal of Theoretical and Applied Statistics

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Generalized Regression Control Chart for Monitoring Crop Production

Received: 31 January 2020    Accepted: 07 April 2020    Published: 28 May 2020
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Abstract

Recently, Nigeria focused on Agriculture as a way to diversify her economy. Crop production, which is a proxy to measure agricultural output is considered very important. So, controlling crop production (output) among states in Nigeria is very key. In this study, the generalized regression control chart was used rather than the conventional control chart. The conventional control chart does not put into consideration factor(s) that affect crop production. The generalized regression control chart considers the factor (independent variable) that affect crop production (dependent variable). The normal distribution is a special case of the generalized regression control chart. The possibility of using Weibull regression and other non-normal models were considered. In this research, Gaussian distribution was used as the underlying distribution because it fitted the crop production data. The cost of seed/seedling was selected from a set of independent variables, because it is most significant among other independent variables. The data were collected from secondary sources, precisely National Bureau of Statistics (NBS). All the 36 states in Nigeria, including the Federal Capital Territory (FCT) were involved in the study. The result of the generalized regression control chart showed that crop production is not in control in Nigeria, which was traced to assignable cause of variation in FCT, Abuja. This implied that FCT, Abuja produced below the lower control limit of crop production, despite the relative cost of seed/seedlings.

DOI 10.11648/j.ajtas.20200904.12
Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 4, July 2020)
Page(s) 90-100
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

Conventional Control Chart, Crop Production, Exponential Family, Gaussian Regression Model, Generalized Regression Control Chart

References
[1] Shewhart, W. A. (1931). Statistical Method from an Engineering Viewpoint. Journal of the American Statistical Association, 26, 262-269.
[2] Montgomery, D. C., and Woodall, W. H. (1997). A Discussion of Statistically-Based Process Monitoring and Control.
[3] Alwan, L. C. and Roberts, H. V. (1988). Time Series Modeling for Statistical Process Control. Journal of Business and Economic Statistics, 6(1), 87–95.
[4] Karaoglan, A. D. and Bayhan, G. M. (2014). A regression control chart for autocorrelated processes. Int. J. Industrial and Systems Engineering, 16(2), 238-256.
[5] Wallis, W. A. and Roberts, H. V. (1956). Statistics: A New Approach. The Free Press, Chicago, III, 549-553.
[6] Mendel, B. J. (1967). The Regression Control Chart – A Multipurpose Tool of Management, Universal Postal Union, International Bureau, Bern, Switzerland, September, 1967.
[7] Mendel, B. J. (1967). Statistical Programs of the United States Post Office Department. Industrial Quality Control, 23(11), 535-538.
[8] Karvanen, J. (2009). Generalized linear models. Available online at www.wiki.helsinki.fi. University of Helsinki, spring.
[9] Mendel, B. J. (1969). The Regression Control Chart. Journal of Quality Technology, 1(1), 1-9.
[10] Grant, E. L., and Leavenworth, R. S. (1980). Statistical Quality Control, 5th ed., McGraw-Hill, New York.
[11] Juran, J. M. and Gryna, F. M. (1988). Quality control handbook, (4th. ed.), McGraw-Hill, New York.
[12] Woodall, W. H., Spitzner, D. J., Montgomery, D. C. and Gupta, S. (2004). Using Control Charts to Monitor Process and Product Quality Profiles. Journal of Quality Technology, 36, 309–320.
[13] NBS (2017). National Bureau of Statistics Agricultural Data. Retrieved 22 June 2017.
[14] Arowolo, O. T., Aribike, E. and Ekum, M. I. (2017). Panel Predictive Modeling of Agricultural Production Among States in Nigeria. IOSR Journal of Mathematics (IOSR-JM), 13(5), 76-89.
[15] Bayer, F. M., Tondolo, C. M. and Muller, F. M. (2018). Beta regression control chart for monitoring fractions and proportions. Preprint submitted to Computers & Industrial Engineering.
[16] Canterle, D. R. and Bayer, F. M. (2017). Variable dispersion beta regressions with parametric link functions. Statistical Papers (Forthcoming), DOI: 10.1007/s00362-017-0885-9.
Author Information
  • Department of Mathematics & Statistics, Lagos State Polytechnic Ikorodu, Lagos, Nigeria

  • Department of Mathematics & Statistics, Lagos State Polytechnic Ikorodu, Lagos, Nigeria

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    Olatunji Taofik Arowolo, Matthew Iwada Ekum. (2020). Generalized Regression Control Chart for Monitoring Crop Production. American Journal of Theoretical and Applied Statistics, 9(4), 90-100. https://doi.org/10.11648/j.ajtas.20200904.12

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    Olatunji Taofik Arowolo; Matthew Iwada Ekum. Generalized Regression Control Chart for Monitoring Crop Production. Am. J. Theor. Appl. Stat. 2020, 9(4), 90-100. doi: 10.11648/j.ajtas.20200904.12

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    AMA Style

    Olatunji Taofik Arowolo, Matthew Iwada Ekum. Generalized Regression Control Chart for Monitoring Crop Production. Am J Theor Appl Stat. 2020;9(4):90-100. doi: 10.11648/j.ajtas.20200904.12

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  • @article{10.11648/j.ajtas.20200904.12,
      author = {Olatunji Taofik Arowolo and Matthew Iwada Ekum},
      title = {Generalized Regression Control Chart for Monitoring Crop Production},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {9},
      number = {4},
      pages = {90-100},
      doi = {10.11648/j.ajtas.20200904.12},
      url = {https://doi.org/10.11648/j.ajtas.20200904.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20200904.12},
      abstract = {Recently, Nigeria focused on Agriculture as a way to diversify her economy. Crop production, which is a proxy to measure agricultural output is considered very important. So, controlling crop production (output) among states in Nigeria is very key. In this study, the generalized regression control chart was used rather than the conventional control chart. The conventional control chart does not put into consideration factor(s) that affect crop production. The generalized regression control chart considers the factor (independent variable) that affect crop production (dependent variable). The normal distribution is a special case of the generalized regression control chart. The possibility of using Weibull regression and other non-normal models were considered. In this research, Gaussian distribution was used as the underlying distribution because it fitted the crop production data. The cost of seed/seedling was selected from a set of independent variables, because it is most significant among other independent variables. The data were collected from secondary sources, precisely National Bureau of Statistics (NBS). All the 36 states in Nigeria, including the Federal Capital Territory (FCT) were involved in the study. The result of the generalized regression control chart showed that crop production is not in control in Nigeria, which was traced to assignable cause of variation in FCT, Abuja. This implied that FCT, Abuja produced below the lower control limit of crop production, despite the relative cost of seed/seedlings.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Generalized Regression Control Chart for Monitoring Crop Production
    AU  - Olatunji Taofik Arowolo
    AU  - Matthew Iwada Ekum
    Y1  - 2020/05/28
    PY  - 2020
    N1  - https://doi.org/10.11648/j.ajtas.20200904.12
    DO  - 10.11648/j.ajtas.20200904.12
    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  - 90
    EP  - 100
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20200904.12
    AB  - Recently, Nigeria focused on Agriculture as a way to diversify her economy. Crop production, which is a proxy to measure agricultural output is considered very important. So, controlling crop production (output) among states in Nigeria is very key. In this study, the generalized regression control chart was used rather than the conventional control chart. The conventional control chart does not put into consideration factor(s) that affect crop production. The generalized regression control chart considers the factor (independent variable) that affect crop production (dependent variable). The normal distribution is a special case of the generalized regression control chart. The possibility of using Weibull regression and other non-normal models were considered. In this research, Gaussian distribution was used as the underlying distribution because it fitted the crop production data. The cost of seed/seedling was selected from a set of independent variables, because it is most significant among other independent variables. The data were collected from secondary sources, precisely National Bureau of Statistics (NBS). All the 36 states in Nigeria, including the Federal Capital Territory (FCT) were involved in the study. The result of the generalized regression control chart showed that crop production is not in control in Nigeria, which was traced to assignable cause of variation in FCT, Abuja. This implied that FCT, Abuja produced below the lower control limit of crop production, despite the relative cost of seed/seedlings.
    VL  - 9
    IS  - 4
    ER  - 

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