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

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 < 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 > 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.

Control charts for health surveillance based on residuals of negative binomial regression

“…If the objective is greater sensitivity, using studentized residuals is better, but if we seek simplicity and interpretation, Pearson residuals can be used. This research showed once again the applicability of residuals of well‐adjusted models to control quality variables, as shown Guarnieri et al 33 …”

A Review of Control Charts and Exploring Their Utility for Regional Environmental Monitoring Programs

“…While programs can be designed with additional features to address high false-positive rates [54] or to prospectively plan for other foreseeable challenges [55], statistical tools are also useful for retrospectively addressing some weaknesses. Among some water quality data, using auto-regressive models for data with equal sampling intervals, e.g., [56], and applying the control chart procedure to the residuals are common approaches. Particular challenges with the water quality datasets available for the OSR, including the lower Muskeg River, include both autocorrelation and unequal intervals between the sampling events.…”

Geometric Brownian Motion-Based Time Series Modeling Methodology for Statistical Autocorrelated Process Control: Logarithmic Return Model

“…e standard practice in dealing with the autocorrelation problem is tting a time series model to the process data before applying a control chart to the residuals [10][11][12][13][14]. In general, the goal of time series modeling is to obtain accurate forecast [15].…”

“…One of the most widely used time series modeling techniques is the Box and Jenkins methodology that works to remove autocorrelation characteristics in process data and thus accepted as standard manufacturing process control practice [1,17]. Autoregressive integrated moving average model (ARIMA) which is based on the above methodology has been employed extensively across various fields, such as in production processes [18,19] and market exchange rates [12,20,21]. e ARIMA model is stable and is doubtlessly used as a benchmark for other time series methodologies.…”