Control chart based on residues: Is a good methodology to detect outliers?

Journal of Industrial Engineering International

دوره 16، شماره 3، آذر 2020، صفحه 119-130   

نویسندگان

Jean Paulo Guarnieri¹؛ Adriano Mendonça Souza¹؛ Luciane Flores Jacobi¹؛ Bianca Reichert¹؛ Claudimar Pereira da Veiga^{* 2}

¹Universidade Federal de Santa Maria, Avenida Roraima, 1000, Statistics Department Building 13, Office 1205 C - CCNE/UFSM, Santa Maria, RS, Brazil

²Department of General and Applied Administration, Federal University of Parana (UFPR), Lothário Meissner Ave, 632, Curitiba, PR, 80210-170, Brazil

چکیده

The purpose of this article is to evaluate the application of forecasting models along with the use of residual control charts to assess production processes whose samples have autocorrelation characteristics. The main objective is to determine the efficiency of control charts for individual observations (CCIO) and exponentially weighted moving average (EWMA) charts when they are applied to residuals of models of AR(1) or MA(1) to detect outlier in autocorrelated processes. Considering autocorrelation strength and sign in the data series and the outlier range, the series were simulated accomplishing 640,000 sets. The series were contaminated by anomalous observations at 100th position, an AR(1) or MA(1) model were fitted, and the residuals were evaluated by CCIO and EWMA control charts; the points correctly detected as an autocorrelation were recorded. For the parameters investigated (autocorrelation and outlier range), a detection rate was generated in each chart, and nonparametric comparison tests were applied. The result of the tests showed the superiority (p < /em> < 0.05) of the CCIO chart for both models. The study of the influence of the sign and magnitude of the autocorrelation parameter showed no significant (p < /em> > 0.05) for either AR(1) or MA(1) charts and models. In this context, control charts for individual observations (CCIO) were confirmed to effectively detect outliers through residuals in industrial autocorrelated processes originated in first-order AR and MA models.

کلیدواژه‌ها

Quality control؛ Outliers؛ Efficiency of control charts؛ Residual control charts

مراجع

Abbas N (2018) Homogeneously weighted moving average control chart with an application in substrate manufacturing process. Comput Ind Eng 120:460–470
Aparisi F, Epprecht EK, Mosquera J (2018) Statistical process control based on optimum gages. Qual. Reliab Eng Int 34:2–14
Bashiri M, Moslemi A (2013) The analysis of residuals variation and outliers to obtain robust response surface. J Ind Eng Int 9(2):1–10
Bouslah B, Gharbi A, Pellerin R (2018) Joint production, quality and maintenance control of a two-machine line subject to operation-dependent and quality-dependent failures. Int J Prod Econ 195:210–226
Box GE, Jenkins GM (1970) Time series analysis, forecasting and control. Holden Day, San Francisco, p 1970
Box G, Luceño A (1997) Statistical control by monitoring and feedback adjustment. Wiley, New York
Box GEP, Jenkins GM, Reinsel GC (1994) Time series analysis: forecasting and control. Holden-Day, San Francisco
Cancilla DA, Fang XC (1996) Evaluation and quality control of environmental analytical data from the Niagara River using multiple chemometric methods. J Great Lakes Res 22(2):241–253
Chang IH (1982) Outliers in time series. University of WisconsinMadison, Dept. of Statistics
Christino EM, Bonduelle GM, Iwakiri S (2010) Application of control charts in the production process of tauari (Couratari oblongifolia) wood fooring. Cerne 16(3):299–304
Claro FAE, Costa AFB, Machado MAG (2007) Gráfcos de controle de EWMA e de Xbar para monitoramento de processos autocorrelacionados. Produção 17(3):536–546
Costa AFB, Machado MAG (2007) Gráfcos de controle de EWMA e de X-barra para monitoramento de processos autocorrelacionados. Revista Produção 17(3):536–546
Costa AFB, Epprecht EK, Carpinetti LCR (2004) Controle estatístico da qualidade. Atlas, São Paulo Cunha JPB, de A. Machado T, Santos FL, Coelho LM (2014) Perdas na colheita de tomate industrial em função da regulagem da colhedora. Pesq Agropec Trop Goiânia 44(4):363–369
Del Castillo E (2002) Statistical control adjustment for quality control. Wiley, New York
Du S, Lv J (2013) Minimal Euclidean distance chart based on support vector regression for monitoring mean shifts of auto-correlated processes. Int J Prod Econ 141(1):377–387
Du S, Zhang R (2016) Modelling and joint monitoring of input and output of systems with arbitrary order autoregressive disturbance. Int J Prod Res 54(6):1822–1838
Duarte BPM, Saraiva PM (2008) An optimization based approach for designing attribute acceptance sampling plan. Int J Qual Reliab 25(2):824–841. https://doi.org/10.1108/02656710810898630
Dumičić K, Žmuk B (2015) Statistical control charts: performances of short term stock trading in croatia. Bus Syst Res 6(1):22–35
Enders W (2003) Applied econometric time series. Wiley series in probability and mathematical statistics. Wiley, New York
Fava VL (2000) In: Vasconcelos MAS, Alves D (eds) Manual de econometria. Editora Atlas, São Paulo
Ghomi SMTF, Sogandi F (2018) A two-sided Bernoulli-based CUSUM control chart with autocorrelated observations. J Ind
Eng Int. https://doi.org/10.1007/s40092-018-0290-6
Guo WW, Xue H (2012) An incorporative statistic and neural approach for crop yield modelling and forecasting. Neural Comput Appl 21(1):109–177
Hamilton JD (1994) Time series analysis. University Press, Princeton

He QP, Wang J (2018) Statistical process monitoring as a big data analytics tool for smart manufacturing. J Process Control 67:35–43
Kalavani F, Mohammadi-Ivatloo B, Zare K (2019) Optimal stochastic scheduling of cryogenic energy storage with wind power in the presence of a demand response program. Renew Energy 130:268–280
Lalor GC, Zhang CS (2001) Multivariate outlier detection and remediation in geochemical databases. Sci Total Environ 281:99–109
McCracken AK, Chakraborti S (2013) Control chart for joint monitoring of mean and variance: an overview. Qual Technol Quant Manage 10(1):17–36
Miranda CF (2001) Modelação linear de series temporais na presença de outliers. Dissertação, Faculdade de Ciências da Universidade do Porto, PT
Montgomery DC (2004) Introdução ao controle estatístico da qualidade. LTC, Rio de Janeiro
Montgomery DC, Runger GC (2003) Estatística aplicada e probabilidade para engenheiros. LTC, Rio de Janeiro
Morettin PA, Toloi CMC (2004) Análise de séries temporais. Edgard Blücher, São Paulo
Palma JA (1999) Estimação dos Parâmetros de Séries Temporais em Presença de Outliers. Comunicação no âmbito da conferência EST/10 anos, Escola superior de tecnologia de Setúbal
Peres FAP, Fogliatto FS (2018) Variable selection methods in multivariate statistical process control: asystematic literature review. Comput Ind Eng 115:603–619
Puchalski W, Ribeiro GT, Da Veiga CP, Freire RZ, Coelho LS (2018) Agribusiness time series forecasting using Wavelet neural networks and metaheuristic optimization: an analysis of the soybean sack price and perishable products demand. Int J Prod Econ 203:174–189
Rounaghi MM, Zadeh FN (2016) Investigation of market efciency and fnancial stability between S&P 500 and London stock exchange: monthly and yearly forecasting of time series stock returns using ARMA model. Physica A 456(15):10–21
Santos JDA, Barreto GA (2018) Novel sparse LSSVR models in primal weight space for robust system identifcation with outliers. J Process Control 67:129–140
Toledo A et al (2008) Caracterização das perdas e distribuição de cobertura vegetal em colheita mecanizada de soja. Engenharia Agrícola Jaboticabal 28(4):710–719
Trafmow D, Wang T, Wang C (2018) Means and standard deviations, or locations and scales? That is the question! New Ideas Psychol 50:34–37
Veiga CR, Veiga CP, Duclós LC (2010) The accuracy of demand forecast models as a critical factor in the fnancial performance of the food industry. Future Stud Res J 2:81–104. https://doi.org/10.24023/FutureJournal/2175-5825/2010.v2i2.58
Veiga CP, Veiga CRP, Catapan A, Silva WV, Torato U (2014) Demand forecasting in food retail: a comparison between the Holt-Winters and ARIMA models. WSEAS Trans Bus Econ 11:608–661
Veiga CP, Veiga CRP, Puchalski W, Coelho LS, Tortato U (2016) Demand forecasting based on natural computing approaches applied to the foodstuf retail segment. J Retail Consum Serv 31:174–181
Voltarelli MA, Silva RP, Zerbato C, Paixão CSS, de O. Tavares T (2015) Monitoring of mechanical sugarcane harvesting through control charts. Engenharia Agrícola 35(6):1079–1092
Werner L, Ribeiro JLD (2003) Previsão de demanda: Uma aplicação dos modelos Box-Jenkins na área de assistência técnica de computadores pessoais. Gestão & Produção 10(1):47–67
Woodall WH (2000) Controversies and contradictions in statistical process control. J Qual Technol 32(4):341–350