Phase I Analysis of Nonlinear Profiles Using Anomaly Detection Techniques

Abstract

In various industries, the process or product quality is evaluated by a functional relationship between a dependent variable y and one or a few input variables x, expressed as y=fx. This relationship is called a profile in the literature. Recently, profile monitoring has received a lot of research attention. In this study, we formulated profile monitoring as an anomaly-detection problem and proposed an outlier-detection procedure for phase I nonlinear profile analysis. The developed procedure consists of three key processes. First, we obtained smoothed nonlinear profiles using the spline smoothing method. Second, we proposed a method for estimating the proportion of outliers in the dataset. A distance-based decision function was developed to identify potential outliers and provide a rough estimate of the contamination rate. Finally, PCA was used as a dimensionality reduction method. An outlier-detection algorithm was then employed to identify outlying profiles based on the estimated contamination rate. The algorithms considered in this study included Local Outlier Factor (LOF), Elliptic Envelope (EE), and Isolation Forest (IF). The proposed procedure was evaluated using a nonlinear profile that has been studied by various researchers. We compared various competing methods based on commonly used metrics such as type I error, type II error, and F2 score. Based on the evaluation metrics, our experimental results indicate that the performance of the proposed method is better than other existing methods. When considering the smallest and hardest-to-detect variation, the LOF algorithm, with the contamination rate determined by the method proposed in this study, achieved type I errors, type II errors, and F2 scores of 0.049, 0.001, and 0.951, respectively, while the performance metrics of the current best method were 0.081, 0.015, and 0.899, respectively.

Special Issue on Unsupervised Anomaly Detection

“…Cheng et al [6] compared different unsupervised point anomaly detection algorithms for detecting outliers among process or product quality profiles. In this context, a profile is a nonlinear relationship between input variables and an output variable, mapping a collective or contextual anomaly detection task to a point anomaly detection problem.…”

“…Among others, intrusion detection [2][3][4][5], payment fraud detection, public safety, complex system monitoring [6][7][8][9][10], and medical data analytics are possible application domains.…”

“…Further details about this taxonomy can also be found in Al-amri et al [5]. To solve a contextual anomaly detection task, the data can be transformed into a point anomaly detection problem [6,9] or a (multivariate) time series anomaly detection algorithm can be applied [3,4,7,[10][11][12].…”