Control chart based on residues: Is a good methodology to detect outliers?
Subject Areas : Mathematical OptimizationJean Paulo Guarnieri 1 , Adriano Mendonça Souza 2 , Luciane Flores Jacobi 3 , Bianca Reichert 4 , Claudimar Pereira da Veiga 5
1 - Universidade Federal de Santa Maria, Avenida Roraima, 1000, Statistics Department Building 13, Office 1205 C - CCNE/UFSM, Santa Maria, RS, Brazil
2 - Universidade Federal de Santa Maria, Avenida Roraima, 1000, Statistics Department Building 13, Office 1205 C - CCNE/UFSM, Santa Maria, RS, Brazil
3 - Universidade Federal de Santa Maria, Avenida Roraima, 1000, Statistics Department Building 13, Office 1205 C - CCNE/UFSM, Santa Maria, RS, Brazil
4 - Universidade Federal de Santa Maria, Avenida Roraima, 1000, Statistics Department Building 13, Office 1205 C - CCNE/UFSM, Santa Maria, RS, Brazil
5 - Department of General and Applied Administration, Federal University of Parana (UFPR), Lothário Meissner Ave, 632, Curitiba, PR, 80210-170, Brazil
Keywords: Quality Control, Outliers, Residual control charts, Efficiency of control charts,
Abstract :
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.
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