Application of robust multivariate control chart with Winsorized Mean: a case study

Subject Areas : Mathematical Optimization

Angellys P.  Ariza Guerrero ¹ (Universidad del Atlántico, Km 7, Puerto, Colombia)
Rister  Barreto Pombo ² (Universidad del Atlántico, Km 7, Puerto, Colombia)
Roberto J.  Herrera Acosta ³ (Universidad del Atlántico, Km 7, Puerto, Colombia)

Received: 2020-10-09 Accepted : 2020-10-09 Published : 2020-06-01

Keywords: fungicide, variability, Outliers, Determinant,

Abstract :

Water pH and active ingredient concentration are two of the most important variables to consider in the manufacturingprocess of fungicides. If these variables do not meet the required standards, the quality of the product may be compromisedand lead to poor fungicide performance when water is used as the application carrier, which is in most cases. Given thecorrelation between the variables, these kinds of manufacturing processes must be analyzed in multivariate settings. Thus,this paper analyzes the variables involved in the process using the multivariate control chart S introduced by J. A. Vargas.In the original chart, the arithmetic mean is used as the mean vector estimator. However, in this investigation the arithmeticmean was replaced by the Winsorized Mean for the purpose of evaluating the chart performance with a robust estimator.The results show that using the new estimator, the control chart is able to detect shifts in the variation of the mean vectorthat the traditional estimator did not. Furthermore, different subgroup sizes for the data were studied in order to examinethe performance of the chart in each case. It was found that the proposed control chart is more sensible to changes when thesubgroups consist of less observations, since it is able to better identify the outliers in the sample.

References:

Al-Khazaleh AMH, Al Wadi S, Ababneh F (2015) Wavelet transform asymmetric Winsorized Mean in detecting outlier values. Far East J Math Sci (FJMS) 96:339–351
Costa FSL, Pedroza RHP, Porto DL, Amorim MVP, Lima KMG (2015) Multivariate control charts for simultaneous quality monitoring of isoniazid and rifampicin in a pharmaceutical formulation using a portable near infrared spectrometer. J Braz Chem Soc 26:64–73. https://doi.org/10.5935/0103-5053.20140214
Deer HM, Beard R (2001) Efect of water pH on the chemical stability of pesticides. Utah State University Extension vol 14, pp 1–3. https://extension.usu.edu/. Accessed 31 Jan 2019
Dixon WJ (1960) Simplifed estimation from censored normal samples. Ann Math Stat 2:385–391
Du S, Lv J, Xi L (2012) On-line classifying process mean shifts in multivariate control charts based on multiclass support
vector machines. Int J Prod Res 50:6288–6310. https://doi.org/10.1080/00207543.2011.631596
Du S, Huang D, Lv J (2013) Recognition of concurrent control chart patterns using wavelet transform decomposition and multiclass support vector machines. Comput Ind Eng 66:683–695. https://doi.org/10.1016/j.cie.2013.09.012
Goodwyn F (2012) The utility of robust means in statistics. Paper presented at the annual meeting of the Southwest Educational Research Association, Texas A&M University, pp 1–13
Haridy S, Wu Z (2009) Univariate and multivariate control charts for monitoring dynamic-behavior processes: a case study. J Ind Eng Manag 3:464–498. https://doi.org/10.3926/jiem.v2n3.p464-498
Huber PJ (1981) Robust statistics. Wiley, Hoboken
Lee MH, Khoo MBC (2016) Optimal designs of multivariate synthetic |S| control chart based on median run length. Commun Stat Theor Methods 4:3034–3053. https://doi.org/10.1080/03610926.2015.1048884
Levinson WA (2011) Statistical process control for real-world applications. Taylor & Francis Group, LLC, New York
McGrath MT (2009) What are fungicides? Plant Health Instr. https://doi.org/10.1094/phi-i-2004-0825-01
McKie P, Johnson W (2002) Water pH and its efect on pesticide stability. University of Nevada, Reno. https://www.unce.unr.edu/. Accessed 01 Feb 2019
Montgomery DC (2009) Introduction to statistical quality control, 6th edn. Wiley, Hoboken
Morales V, Vargas JA (2008) EWMA chart based on the efective variance for monitoring the variability of multivariate quality control process. Rev Colomb Estad 31:131–143
Rivest LP (1994) Statistical properties of Winsorized Means for skewed distributions. Biometrika 81:373–383
Rogalewicz M (2012) Some notes on multivariate statistical process control. Manag Prod Eng Rev 4:80–86. https://doi.org/10.2478/v10270-012-0036-7
Schilder A (2008) Efect of water pH on the stability of pesticides. Michigan State University Extension. http://msue.anr.msu.edu. Accessed 30 Aug 2018
Secrest R (n.d.) How products are made: pesticide. http://www.madehow.com/Volume-1/Pesticide.html. Accessed 02 Feb 2019
Smart NA (2003) Encyclopedia of food sciences and nutrition. Elsevier, Maryland Stefatos G, Hamza AB (2009) Fault detection using robust multivariate control chart. Expert Syst Appl 3:5888–5894. https://doi.org/10.1016/j.eswa.2008.07.028
Thompson B (2006) Foundations of behavioral statistics: An insightbased approach. The Guilford Press, New York
Vargas JA (2003) Robust estimation in multivariate control charts for individual observations. J Qual Technol 4:367–376. https://doi.org/10.1080/00224065.2003.11980234
Vargas JA (2006) Control Estadístico de Calidad. Universidad Nacional de Colombia, Bogotá
Wilcox RR (2001) Fundamentals of modern statistical methods. Springer, New York