Minimax Multivariate Control Chart Using a Polynomial Function

Nowadays one of the most rapidly developing areas of process control is Multivariate Statistical Process Control (MSPC). MSPC refers to process monitoring problems in which several related variables are of interest. The most widely used tool of MSPC is control charting, which may be used efficiently in order to monitor and control processes in a multivariate environment. Till today, the majority of the charts appeared in the literature require the assumption of multivariate normality. In cases, that the multivariate normal is not an appropriate model, the literature on alternative multivariate charting techniques is poor. The aim of this article is to present thoroughly the use of Information Theory to the area of MSPC as well as to introduce some valuable tools for controlling processes which are related to non-normal variables.

Scientia Iranica

In some applications, quality of product or performance of a process is described by some functional relationships among some variables known as multivariate linear pro le in the literature. In this paper, we propose Max-MEWMA and Max-MCUSUM control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression pro les in Phase II. The proposed control charts also have the ability to diagnose whether the location or variation of the process is responsible for out-of-control signal. The performance of the proposed control charts is compared with that of the existing method through Monte-Carlo simulations. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry.

AIP Conference Proceedings

Control charts are the most often technique used in the industry to continuously monitor a process for quality improvement. This paper proposes a variable control chart based on attribute inspection, denoted as Max-, to evaluate the stability of mean and variability processes using a single chart. The main advantage of using the attribute inspection is its ease of use and lower costs required compared to the variable-type inspection that using the actual value. Quality characteristics are monitored using a go/no go gauge with five categories. In practice, a sample with the size of n is taken periodically and each item is allocated to one of five categories with adjusted go/no go boundaries, then a value is generated randomly for each item based on a truncated normal distribution with an upper and a lower limit truncated according to the dimensions of go/no go gauge. The performance evaluation is carried out using the Monte Carlo simulation and shows that Max-chart with the addition of sample size of three items has a better performance in detecting various mean and/or variability processes shifts than chart, another simultaneous control chart based on attribute inspection. Therefore, the proposed Max-chart can be considered as an alternative to control charts with the variable-type inspection. An example with the real case using piston ring data is presented to illustrate the application of Maxchart.

The International Journal of Advanced Manufacturing Technology, 2009

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T 2 and the |S| charts. However, these charts have two drawbacks: (1) the T 2 and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-ofcontrol variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T 2 and |S| charts in signaling processes disturbances.

Computers & Industrial Engineering, 2020

This paper considers adaptive schemes for the simultaneous monitoring of the mean and variability of a multivariate normal quality characteristic. At first, we extend an already existing bivariate nonadaptive simultaneous control chart to a multivariate one. Then, we develop several adaptive schemes, which will cover both previously bivariate and newly multivariate charts. After having designed adaptive schemes for the multivariate chart, eight performance measures are computed based on the run length, time to signal, number of observations to signal and number of switches to signal and evaluated using a new Markov chain model. With the developed performance measures, non-adaptive and adaptive schemes under different mean, variability, simultaneous shift sizes, and different number of quality characteristics are compared. Our scheme is also compared to one of the best methods available in the literature. A numerical example is also provided in order to demonstrate how the adaptive scheme can be implemented in practice.

Quality and Reliability Engineering International, vol. 23 (5), pp. 517-543, 2007

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial least squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal. Copyright © 2006 John Wiley & Sons, Ltd.

2018

Statistical quality control relies heavily on the goodness of control chart limits. The more accurate those limits are, the more likely are to detect whether a process is in control. Various procedures have been developed to compute good control limits. This paper proposes variable control charts based on the percentiles of Exponentiated Lomax distribution (ELD) for mean, range and standard deviation. The percentiles of the distribution of mean, range and standard distribution were developed and are used to construct the control limits. The coverage probability of the control charts of ELD was compared with that of traditional shewhart control chart. The result shows that ELD performs better than the traditional shewhart control chart.

Tecno-Lógica, 2013

The effective simultaneous monitoring of the many quality characteristics of a production process often depends on statistical tools that have become more and more specific. The goal of this paper is to investigate, via an industrial application, whether there are significant differences in sensitivity between the use of Multivariate Cumulative Sum (MCUSUM), Multivariate Exponentially Weighted Average (MEWMA) control charts, and Hotelling T 2 charts to detect small changes in the mean vector of a process. Machining process real data were used. A MCUSUM control chart was applied to monitor these two quality characteristics of this process simultaneously. A MEWMA chart was also applied. The result was compared to that of the application of the Hotelling T 2 chart, which showed that the MCUSUM and MEWMA control charts detected the change sooner. This study was essential to determine the best option between these three charts for the multivariate statistical analysis of this industrial process.

International Journal for Quality Research

Control Charts are one of the most powerful tools used to detect aberrant behavior in industrial processes. A valid performance measure for a control chart is the average run length (ARL); which is the expected number of runs to get an out of control signal. At the same time, robust estimators are of vital importance in order to estimate population parameters. Median absolute deviation (MAD) and quantiles are such estimators for population standard deviation. In this study, alternative control charts to the Tukey control chart based on the robust estimators are proposed. To monitor the control chart's performance, the ARL values are compare for many symmetric and skewed distributions. The simulation results show that the in-control ARL values of proposed control charts are higher than Tukey's control chart in all cases and more efficient to detect the process mean. However, the out-of-control ARL values for the all control charts are worse when the probability distribution is non-normal. As a result, it is recommended to use control chart based on the estimator Qn for the process monitoring performance when data are from normal or non-normal distribution. An application example using real-life data is provided to illustrate the proposed control charts, which also supported the results of the simulation study to some extent.

Proceedings of the 7th Hellenic European Conference on Computer Mathematics and its Applications, Athens, 2005

Woodall and Montgomery [35] in a discussion paper, state that multivariate process control is one of the most rapidly developing sections of statistical process control. Nowadays, in industry, there are many situations in which the simultaneous monitoring or control, of two or more related quality -process characteristics is necessary. Process monitoring problems in which several related variables are of interest are collectively known as Multivariate Statistical Process Control (MSPC).This article has three parts. In the first part, we discuss in brief the basic procedures for the implementation of multivariate statistical process control via control charting. In the second part we present the most useful procedures for interpreting the out-of-control variable when a control charting procedure gives an out-of-control signal in a multivariate process. Finally, in the third part, we present applications of multivariate statistical process control in the area of industrial process control, informatics, and business.

International Journal of Business and Statistical Analysis, 2014

The drawbacks to multivariate charting schemes is their inability to identify which variable was the source of the signal. The multivariate exponentially weighted moving average (MEWMA) developed by Lowry, et al (1992) is an example of a multivariate charting scheme whose monitoring statistic is unable to determine which variable caused the signal. In this paper, the run length performance of multivariate exponentially weighted moving average (MEWMA) chart with application is studied. Industry fertilizers is important one of the chemical industries in Egypt, so that this work concerns the fertilizers industries quality control, especially urea fertilizer with application on Delta fertilizer and chemical industries which is considered on of the leading companies the field of fertilizer production in Middle east with application of multivariate quality control procedures to achieve best one procedure for multivariate quality control.

IEEE Access

A Simultaneous control chart is a well-known tool for monitoring the process mean and process variability with a single chart. In recent decades, many researchers have been interested in developing simultaneous control charts. The Shewhart chart is the most common and simple simultaneous control chart. The Multivariate Maximum control chart (Max-Mchart) is a type Shewhart chart that simultaneously monitors the process of multivariate data. This paper proposes a new transformation using a half-normal distribution to improve the Max-chart performance for subgroup observations. The new proposed chart is called Max-Half-Mchart. The Average Run Length (ARL) results show that the proposed Max-Half-Mchart outperforms the Max-Mchart. Additionally, in real data scenarios, the proposed Max-Half-Mchart is consistent with the statistic in the Hotelling T 2 chart and the Generalized Variance (GV) chart. INDEX TERMS Single control chart, multivariate control chart, simultaneous monitoring, subgroup observations, Max-Half-Mchart.

Revstat Statistical Journal, 2013

• In this paper control charts for the simultaneous monitoring of the means and the variances of multivariate nonlinear time series are introduced. The underlying target process is assumed to be a constant conditional correlation process (cf. [3]). The new schemes make use of local measures of the means and the variances based on current observations, conditional moments, or residuals. Exponential smoothing and cumulative sums are applied to these characteristic quantities. Distances between these quantities and target values are measured by the Mahalanobis distance. The introduced schemes are compared via a simulation study. As a measure of performance the average run length is used.

Production & Manufacturing Research

Ahsan (2019) Residual-based maximum MCUSUM control chart for joint monitoring the mean and variability of multivariate autocorrelated processes,

In this paper, a Multivariate-Multistage Quality Control (MVMSQC) procedure is investigated. In this procedure discriminate analysis, linear regression and control chart theory are combined to control the means of correlated characteristics of a process, which involves several serial stages. Furthermore, the quality of the output at each stage depends on the output of the previous stage as well as the process of the current stage. The theoretical aspects and the applications of this procedure are enhanced and clarified and its performance is evaluated through a series of simulated data. Both in-control (type one error) and out-of-control (type two error) Average Run Length (ARL) studies are made and the performance of the MVMSQC methodology is discussed.