Multivariate Control Chart Based on Kernel PCA for Monitoring Mixed Variable and Attribute Quality Characteristics

Muhammad Ahsan,Muhammad Hisyam Lee,Wibawati Wibawati,Muhammad Mashuri,Hidayatul Khusna

doi:10.3390/sym12111838

Muhammad Ahsan, Muhammad Hisyam Lee + Show 3 more

Open Access

https://doi.org/10.3390/sym12111838

Copy DOI

Abstract

The need for a control chart that can visualize and recognize the symmetric or asymmetric pattern of the monitoring process with more than one type of quality characteristic is a necessity in the era of Industry 4.0. In the past, the control charts were only developed to monitor one kind of quality characteristic. Several control charts were created to deal with this problem. However, there are some problems and drawbacks to the conventional mixed charts. In this study, another approach is used to monitor mixed quality characteristics by applying the Kernel Principal Component Analyisis (KPCA) method. Using the Hotelling’s T2 statistic, the kernel PCA mix chart is proposed to simultaneously monitor the variable and attribute quality characteristics. Due to its ability to estimate the asymmetric pattern of the mixed process, the kernel density estimation (KDE) used in the proposed chart has successfully estimated the control limits that produce ARL0 at about 370 for α=0.00273. Through several experiments based on the proportion of the attribute characteristics and kernel functions, the proposed chart demonstrates better performance in detecting outlier and shift in the process. When it is applied to monitor the synthetic data, the proposed chart can detect the shift accurately. Additionally, the proposed chart outperforms the performance of the conventional mixed chart based on PCA mix by producing lower false alarm with more accurate detection of out of control processes.

Highlights

The control chart can visualize the quality characteristics in a graphical form and calculate its control limit based on the symmetric or asymmetric distribution of the monitored processes.In statistical process control (SPC), two types of control chart have been developed based on the monitored quality characteristics, namely the variable and attribute charts [1]
The proposed chart outperforms the performance of the conventional mixed chart based on principal component analysis (PCA) mix by producing lower false alarm with more accurate detection of out of control processes
Based on the above considerations, this paper proposes a mixed multivariate control chart based on the Kernel Principal Component Analyisis (KPCA) method that can accommodate the different types of quality characteristics, named KPCA

Summary

Introduction

The control chart can visualize the quality characteristics in a graphical form and calculate its control limit based on the symmetric or asymmetric distribution of the monitored processes. In statistical process control (SPC), two types of control chart have been developed based on the monitored quality characteristics, namely the variable and attribute charts [1]. The variable control chart is developed to monitor the metric quality characteristics (variable or ratio scale) such as length or height. To monitor the nonmetric quality characteristics (categorical scale), the attribute chart is used. Some works have developed the variable and attribute charts, especially to monitor more than one characteristic (multivariable or multiattribute characteristics). The Shewhart, multivariate exponentially weighted moving average (MEWMA), and multivariate cumulative sum (MCUSUM) type charts are developed to accommodate the multivariable characteristics [1]

Results

Discussion

Conclusion