English

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.

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.

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

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.

There have been some advances in multivariate control charts in recent years. This paper presents a new simultaneous scheme for monitoring both the mean and variability of a multivariate normal process in a single chart, which is developed by improving and modifying another recently proposed scheme. We not only propose a new control scheme but also make it adaptive by varying all control chart parameters. Our scheme, for the first time, considers the process variability in two forms: “covariance matrix” and “multivariate coefficient of variation (MCV)”. This scheme, again for the first time, considers simultaneous monitoring of the MCV with another process parameter (in our case, the mean vector). In addition, we develop a Markov chain model to compute the average run length and average time to signal values. We conduct extensive numerical analyses to measure the performance of the proposed scheme in two scenarios of process variability. At last, we present a numerical example by using a real dataset from a healthcare process to illustrate how the scheme can be implemented in practice.

Multivariate Control Chart is an effective tool in Statistical Process Control to identify either an out-of-control process or in-control process. Hotelling T2 control chart is a quite popular and widely used technique in this field. However, its performance is deteriorated when the underlying distribution of the quality characteristics is not following the multivariate normal distribution. Multivariate control chart usually recommends a procedure in the phase-in Hotelling T2 control chart although there is difficulty in interpreting the signals from multivariate control charts more work is needed on data reduction methods and graphics techniques. Basically, the multivariate control chart refers to the theory of prediction interval. Therefore, it’s called predictive multivariate control charts. The purpose of this research is to construct what so-called predictive multivariate control chart both classical in this part in the phase-in Hotelling T2 and Copula-based ones. We argue that appropriate joint distribution function may be well estimated by employing Copula. A numerical analysis is carried out to illustrate that an Application Copula-based Multivariate control chart outperforms than bivariate control chart and others.

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

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.

In the present study, dietary fibre incorporated functional sausage was prepared by optimising the ingredients viz. tuna mince, wheat and oats dietary fibre using response surface methodology. D-optimal mixture response surface experimental design with 13 runs was formulated for the development of dietary fibre incorporated tuna sausage. The optimum combinations of sausage were found to be 62.5% fish mince, 2.5% wheat and 5% oats fibre and 66.8% fish mince and 1.6% of oats and wheat fibre each. The quality evaluation of combination sausage prepared at optimum conditions along with control sample was carried out based on biochemical, physical and sensory parameters during storage in chilled condition at 2°C. Storage stability studies of the optimised sausage samples indicated a shelf life of 14 days under chilled conditions. Multivariate statistical control charts based on T2 and PSE statistics were developed to monitor quality variations during storage.

In constructing any control chart, the sample size and the number of samples taken are important issues. When destructive tests are applied to collect data, the sample size and the number of subsamples are usually limited. Lack of sufficient observations affects parameters estimates. Re‐sampling techniques are always suggested to increase the accuracy of parameters estimates. Also, the presence of outlying observations severely affect re‐sampling and the estimates of the underlying distribution parameters. The limited sample size, limited number of subsamples and presence of outliers are more important in multivariate process analysis. In this study, bootstrap re‐sampling technique and robust estimators of mean vector and variance‐covariance matrix are simultaneously utilized to design a multivariate robust T2 control chart to address the three problems in hand. The performance of the proposed robust T2 control chart is evaluated and compared to the Hotelling T2 control chart by means of average run length (ARL). Simulation results indicate that the suggested robust T2 control chart outperforms the Hotelling T2 in presence of outliers and similarly when there is no outlier. Design of robust control chart for processes generating auto‐correlated data applying bootstrap re‐sampling technique is an area for further research.

Analyzing out-of-control signals of T2 control chart for compositional data using artificial neural networks

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.

[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.

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.

Gower distance-based multivariate control charts for a mixture of continuous and categorical variables