LASSO-based multivariate linear profile monitoring

Abstract: Multivariate control charts are essential tools in multivariate statistical process control (MSPC). “Shewhart-type” charts are control charts using rational subgroupings which are effective in the detection of large shifts. Recently, the one-class classification problem has attracted a lot of interest. Three methods are typically used to solve this type of classification problem. These methods include the k−center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. In this paper, we reformulate the standard support vector data description and derive a least squares version of the method. This least-squares support vector data description (LS-SVDD) is used to design a control chart for monitoring the mean vector of processes. We compare the performance of the LS-SVDD chart with the SVDD and T2 chart using out-of-control Average Run Length (ARL) as the performance metric. The experimental results indicate that the proposed control chart has very good performance.

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

The T 2 control chart is widely adopted in multivariate statistical process control. However, when dealing with asymmetrical or multimodal distributions using the traditional T 2 control chart, some points with relatively high occurrence possibility might be excluded, while some points with relatively low occurrence possibility might be accepted. Motived by the thought of the highest posterior density credible region, we develop a control chart based on the highest possibility region to solve this problem. It is shown that the proposed multivariate control chart will not only meet the false alarm requirement, but also ensure that all the in-control points are with relatively high occurrence possibility. The advantages and effectiveness of the proposed control chart are demonstrated by some numerical examples in the end.

In multivariate statistical process control (MSPC) applications, process mean shifts sometimes occur in only a few components. To solve this MSPC problem, many control charts were proposed in the literature. Most of these charts assumed that the multivariate quality characteristics are normally distributed. Among them, the control chart proposed by Zou and Qiu (2009), incorporating the least absolute shrinkage and selection operator (LASSO) method into the EWMA scheme, has the best overall performance. In this paper, we extend the classical multivariate LASSO control chart to a robust version that has an affine-invariance property and is distribution free under the family of elliptical direction distributions, indicating that the in-control run-length distribution is the same for any continuous distribution in this family and the control limit can be acquired from the multivariate standard normal distribution. Our simulation results show that the proposed method is very efficient in detecting various sparse shifts under heavy-tailed and skewed multivariate distributions. In addition, it is easy to implement with an iterative algorithm and the least angle regression (LARS) algorithm. White-wine data illustrates that the proposed control chart performs quite well in applications.

Statistical process control charts are important tools for monitoring process stability in manufacturing and service industries. Using multivariate control charts to monitor two or more related quality characteristic has become increasingly popular in today’s environment. Out-of-control signals in multivariate control charts may be caused by one or more variables or a set of variables. In the practice of quality control, in addition to the quick detection of process change, it is also critical to diagnose the change and identify which variable(s) has changed after an out-of-control signal occurred. In this paper, we propose a decision tree (DT)-based ensemble classifier to approach the problem of diagnosing out-of-control signal. The focus of this paper is on the variance shifts of a multivariate process. Simulation studies indicate that the proposed ensemble classification model is a successful method in identifying the source of variance change. A comparative study also reveals that DT using extracted features as input vector has slightly better classification performance than using raw data as input. The proposed method could be a useful diagnostic aid in monitoring shifts in process dispersion.

Multivariate statistical process control (MSPC) charts are particularly useful when there is a need to simultaneously monitor several quality characteristics of a process. Most of the control charts in MSPC assume that the quality characteristics follow some parametric multivariate distribution, such as the normal. This assumption is almost impossible to be justified in practice. Distribution-free MSPC charts are attractive, as they can overcome this hurdle by guaranteeing a stable (or in-control (IC)) performance of the control chart without the assumption of a parametric multivariate process distribution. Utilizing an existing distribution-free multivariate tolerance interval, we propose a Phase II Shewhart-type distribution-free MSPC chart for individual observations, with control limits based on Phase I order statistics. In addition to being easy to interpret, the proposed chart preserves the original scale of measurements and can easily identify out-of-control variables after a signal. The exact in-control performance based on the conditional and unconditional perspectives is presented and examined along with the control limits determination. The out-of-control performance of the chart is studied by simulation for data from a number of multivariate distributions. Illustrative examples are provided for chart implementation, using both real and simulated data, along with a summary and conclusions.

Multivariate cumulative sum control chart and measure of process capability based on bivariate ranked set schemes

Multivariate monitoring and control schemes based on latent variable methods have been receiving increasing attention by industrial practitioners in the last 15 years. Several companies have enthusiastically adopted the methods and have reported many success stories. Applications have been reported where multivariate statistical process control, fault detection and diagnosis is achieved by utilizing the latent variable space, for continuous and batch processes, as well as, for process transitions as for example start ups and re‐starts. This paper gives an overview of the latest developments in multivariate statistical process control (MSPC) and its application for fault detection and isolation (FDI) in industrial processes. It provides a critical review of the methodology and describes how it is transferred to the industrial environment. Recent applications of latent variable methods to process control as well as to image analysis for monitoring and feedback control are discussed. Finally it is emphasized that the multivariate nature of the data should be preserved when data compression and data preprocessing is applied. It is shown that univariate data compression and reconstruction may hinder the validity of multivariate analysis by introducing spurious correlations. Copyright © 2005 John Wiley & Sons, Ltd.

Process modeling and control applied to real-time monitoring of distillation processes by near-infrared spectroscopy

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] There are many areas where optimal designs are applied to, for example, the development of a new drug, where a conventional dose- finding study involves learning about the dose-response curve in order to bring forward right doses of drug to late-stage development. The first part of this dissertation focus on three pharmacodynamics sigmoid Emax models, we derive the corresponding simple formats of the adaptive optimal designs regardless of the optimality criteria or parameters of interest. An algorithm for deriving a specific adaptive optimal design is developed. A simulation study comparing the adaptive optimal designs and the uniform designs is also performed. The second part of this dissertation focuses on the statistical process control, we proposed an adaptive approach for the multivariate CUSUM statistical process control chart for signaling a range of location shifts. This method is based on the multivariate CUSUM control chart proposed by Pignatiello and Runger in 1990. We used the exponentially moving weighted average (EMWA) statistic to estimate the current process mean shift and change the reference value adaptively in each run. By specifying the minimal magnitude of the mean shift through the non-centrality parameter, our proposed control chart can achieve an overall good performance for detecting a range of shifts rather than a single value.

A multivariate control region can be considered to be a pattern that represents the normal operating conditions of a process. Reference data can then be generated and used to learn the difference between this region and random noise. Then multivariate statistical process control can be converted to a supervised learning task. This can dramatically reshape the control region and open the control problem to a rich collection of supervised learning tools. Such tools provide generalization error estimates that can be used to specify error rates. The effectiveness of such an approach is shown here. Such a computational approach is now easily accomplished with modern computing resources. Examples use random forests and a regularized least squares classifier as the learners.

Autoregressive coefficients based Hotelling’s T2 control chart for structural health monitoring

Multivariate Statistical Process Control (MSPC) is to control several quality characteristics simultaneously during a production process. When a process is statistically under control, only common causes of variability affect the process. The MSPC techniques help to detect the special causes of variability on the process. In the last few years multivariate quality control has been thoroughly studied and there are different but those charts don't let control de multivariate dispersion on process. Recently the generalized variance control chart /S/, has been develop to control multivariate dispersion. Nevertheless, this chart is unhelpful to work with incomplete databases or with missing data, that are commonly found in a great deal of processes due to the failure of certain sensors. In this sense, Garcia‐Diaz developed the effective variance control chart, /Sp/1/p, to control multivariate dispersion with missing data. To design the economic‐statistical of the Variance Effective control chart, attempting to obtain the values of the parameters in the sampling plan that minimize the expected operation costs by time unit, according to the restrictions of a minimum ARL value under control, and a maximum ARL value when the process is out of control.

Multivariate process control has recently gained significant attention because it takes into account the correlation between process variables and offers a more comprehensive understanding of the overall process behavior. In line with this phenomenon, this paper proposes the multivariate triple sampling Hotelling’s T 2 (MTS) control chart as an efficient process monitoring method in multivariate statistical process control. The mathematical properties of the MTS chart are also derived. The performance of the MTS chart is assessed using key performance metrics, such as average run length (ARL), average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS). The performance of the MTS chart is compared with that of the existing multivariate double sampling Hotelling’s T 2 (MDS) chart. The findings indicate that the MTS chart consistently surpasses the MDS chart across all performance metrics, demonstrating its superior capability in detecting shifts for a multivariate process. Notably, the MTS chart exhibits lower ARL, ANOS and EANOS values, emphasizing its effectiveness in promptly identifying process shifts. In terms of practical application, an example is given to elucidate the execution of the MTS chart.

This article considers the economic statistical process control for two dependent processes with a failure mechanism which obeys Weibull shock model and has an increasing failure rate. We construct individual economic statistical X control chart to monitor the quality variable produced by the first process, and use the cause-selecting control chart to monitor the specific quality produced by the second process with minimal cost and required statistical properties. By using the proposed control charts, we can effectively and economically distinguish which process is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and optimization method is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Sensitivity analysis that illustrates the effects of the cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts is also presented.