Adaptive optimal designs for dose-finding studies and an adaptive multivariate CUSUM control chart

This paper is a study on the multivariate CUSUM control charts using three di er-ent control statistics for monitoring covariance matrix. We get control limits and ARLsof the proposed multivariate CUSUM control charts using three di erent control statis-tics by using computer simulations. The performances of these proposed multivariateCUSUM control charts have been investigated by comparing ARLs. The purpose ofcontrol charts is to detect assignable causes of variation so that these causes can befound and eliminated from process, variability will be reduced and the process willbe improved. We show that the charts based on three di erent control statistics arevery e ective in detecting shifts, especially shifts in covariances when the variables arehighly correlated. When variables are highly correlated, our overall recommendationis to use the multivariate CUSUM control charts using trace for detecting changes incovariance matrix.Keywords: Average run length, covariance matrix, multivariate CUSUM control chart.

Similar to the univariate CUSUM chart, a multivariate CUSUM (MCUSUM) chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for the noncentrality parameter. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate statistical process control chart based on a sequential χ2 test to detect a change in the noncentrality parameter. The statistical properties of the proposed test statistic are explored. The average runs length (ARL) performance of the proposed charts is compared with other MCUSUM charts for process mean monitoring. The experimental results reveal that the proposed charts achieve superior, both zero-state and steady-state, ARL performance over a wide range of mean shifts, especially when the dimension of measurements is large.

A multivariate T 2 chart is developed based on the Generalized Likelihood Ratio Test (GLRT) without a priori information about potential mean deviations. Identification of response variables from a T 2 chart is challenging and has received considerable attention recently. By highlighting the intrinsic relationship between various multivariate control charts and statistical hypothesis testing, this paper presents a theoretical framework for various individual multivariate control charts including the T 2 chart, regression-adjusted chart and M chart. The performance of these control charts is compared under different correlation structures among variables and different mean deviations. A hybrid control chart is also proposed based on the GLRT and union-intersection test, which can serve as a complementary diagnosis tool for the T 2 chart.

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.

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.

Application of in-line near infrared spectroscopy and multivariate batch modeling for process monitoring in fluid bed granulation

DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS

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.

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.

Traditional multivariate control charts such as Hotelling’s χ2 and T2 control charts are designed to monitor vectors of variable quality characteristics. However, in certain situations, data are expressed in linguistic terms and, under these circumstances, variable or attribute multivariate control charts are not suitable choices for monitoring purposes. Fuzzy multivariate control charts such as fuzzy Hotelling’s T2 could be considered as efficient tools to overcome the problems of linguistic observations. The purpose of this paper is to develop a fuzzy multivariate exponentially weighted moving average (F-MEWMA) control chart. In this paper, multivariate statistical quality control and fuzzy set theory are combined to develop the proposed method. Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature, and humanity. Through a numerical example, the performance of the proposed control chart was compared to the fuzzy Hotelling’s T2 control chart. Results indicate uniformly superior performance of the F-MEWMA control chart over Hotelling’s T2 control chart.

Multivariate statistical process control deserves particular attention in the recent scenario. Though, Hotelling T2 control chart is quite popular and widely used technique in this field but its performance is deteriorated when the underlying distribution of the quality characteristics is not following multivariate normal distribution. Hence the need of developing a non-parametric multivariate control chart arises which does not require any underlying distribution. In this work a multivariate non-parametric control chart based on bivariate sign test is proposed. Its performance in both in control and out of control state was evaluated by simulating data from multivariate normal and multivariate t distribution and compared with those of existing multivariate parametric control chart.

Multivariate modelling of fish freshness index based on ion mobility spectrometry measurements

In recent decades, multivariate statistical methods for monitoring and controlling of industrial processes have received increasing attention. Multivariate process control charts such as Hotelling's T2 and multivariate exponentially weighted moving average have gained acceptance as manufacturing process control tools especially for the semiconductor industry. We propose in this paper a novel multivariate nonparametric control chart based on the permutation and nonparametric combination (NPC) methodology. The proposed NPC chart is always an exact inferential procedure for every finite sample size and overcomes some limitations of traditional approaches such as the ability to include a large number of variables. Moreover, NPC chart offers several advantages because it is a robust solution with respect to the true underlying random error distribution, and it is not affected by the problem of the loss of degrees of freedom when keeping fixed the number of observations. Unlike traditional methods, when the number of informative variables increases its power monotonically increases as well (finite sample consistency property of NPC test). As confirmed by an extensive simulation study and by an application to some real case studies in the field of microelectronics, the NPC charts are certainly good alternatives with respect to the traditional multivariate control charts such as Hotelling's T2 especially in cases of asymmetric or heavy‐tailed error distributions. Finally, NPC chart represents a suitable solution for monitoring a multivariate process when the number of observed process variables may be larger than the number of observations. Copyright © 2013 John Wiley & Sons, Ltd.

Multivariate control charts based on net analyte signal (NAS) for characterization of the polymorphic composition of Piroxicam using near infrared spectroscopy

Robust adaptive multivariate Hotelling's T2 control chart based on kernel density estimation for intrusion detection system