Robust Process Monitoring in Phase I via Local Outlier Factor and Principal Component Analysis for High-dimensional Data

Abstract

Today's consumer markets experience an ever-increasing demand for better products and services. Customers expect continuously improved quality products and/or services even when they pay less for them than the previous purchase prices. It is therefore logical that if a company wishes to be competitive, one of its main aims should be to focus upon producing products of a consistently high quality. Statistical process control(SPC) is a statistical technique used to control processes and to reduce variation. Variation reduction is a key aspect to improve quality. The most popular technique in SPC is a control chart that can be used to monitor process and detect any operational deviations. However, when the data set in Phase I may contain outliers with abnormal values irregularly larger or smaller than the normal observations, those outlying observations cause problems in Phase II because they may strongly influence the result of discriminating power. For the reason, outlier detection is an important task in Phase I prior to estimating the in-control process parameters. In this paper, we propose a methodology integrating PCA and LOF to establish much robust monitoring scheme with faster updating a set of estimated parameters by reducing the computation time required to detect outliers in Phase I. Firstly we apply PCA to high dimensional data in Phase I to obtain lower dimensional data. Secondly, we calculate each observation's LOF score to evaluate the degree of isolation so that we are able to identify outliers. Thirdly, using the cleaned data after removing outliers, we can estimate robust parameters for Hotelling's T2 procedure. To examine the effectiveness of the proposed method, several experiments incorporating different hyper-parameters such as contamination rates and portion of outlier removal were conducted. In addition to the simulated data sets, a real-life data set was used in the experiments. The proposed method demonstrated a significantly faster computation for estimating robust control chart parameters with predictable and acceptable trade-off in terms of actual type I & II error rates.