On the Efficient Monitoring of Multivariate Processes with Unknown Parameters (original) (raw)
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International Journal of Production Research, 2017
Multivariate monitoring of industrial or clinical procedures often involves more than three correlated quality characteristics and the status of the process is judged using a sample of size one. Majority of existing control charts for monitoring process variability for individual observations are capable of monitoring up to three characteristics. One of the hurdles in designing optimal control charts for large dimension data is the enormous computing resources and time that is required by simulation algorithm to estimate the charts parameters. This paper proposes a novel algorithm based on Parallelised Monte Carlo simulation to improve the ability of the Multivariate Exponentially Weighted Mean Squared Deviation and Multivariate Exponentially Weighted Moving Variance charts to monitor process variability for high dimensions in a computationally efficient way. Different techniques have been deployed to reduce computing space and execution time. The optimal control limits (L) to detect small, medium and large shifts in the covariance matrix of up to 15 characteristics are provided. Furthermore, utilising the large number of optimal L values generated by the algorithm enabled authors to develop exponential decay functions to predict L values. This eliminates the need for further execution of the parallelised Monte Carlo simulation.
Application of Multivariate Control Charts for Monitoring an Industrial Process
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.
Multivariate statistical process control charts: an overview
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.
Short Run Multivariate Control Charts for Process Mean and Variability
2013
Statistical process control methods for monitoring short-run processes with multivariate measurements are considered and new multivariate short-run control charts to monitor process mean and variability are proposed. To monitor the process mean the influence function of mean is proposed and to investigate process variability control charts based on the influence function of eigenvalues are suggested. The proposed techniques are general, and the influence functions may be used to build up short-run multivariate control charts relative to either nominal values or estimates. The method is further illustrated with real datasets, from a flexible job shop manufacturing system producing spare parts for classical cars.
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.
Malaysian Journal of Fundamental and Applied Sciences, 2014
In manufacturing process, it is very important to control and monitor the stability of a process such that a high quality product will be produced. The most common statistical tool used for monitoring the stability of a process is the control chart. In recent applications of control charting methods, there is a need to construct a control chart that is able to represent the behaviour of a multivariate process since in many manufacturing processes; quality of a product is determined by the joint-level of several quality characteristics. For this reason, in this paper, a new control chart is introduced for monitoring the stability of multivariate process in terms of the process variability. The proposed method is based on charting each of the eigenvalues of a covariance matrix. To show the efficiency of the proposed method, we conduct a simulation study and compare the performance of the proposed method with the existing method. A real example will be presented to illustrate the advan...
Design and application of integrated control charts for monitoring process mean and variance
Journal of Manufacturing Systems, 2005
This article presents an integrated control chart system for monitoring process shifts in mean and variance in a multistage manufacturing system. This chart system consists of several X&S charts, each of which monitors one of the critical quality characteristics (for example, dimensions) of a product. The design algorithm optimally allocates the detection power of the system among different stages as well as between the X chart and S chart within each stage. Consequently, the performance characteristics of the system as a whole can be considerably improved and the product quality will be further enhanced. Such improvement is achieved without requiring additional cost and effort for inspection. Furthermore, floor operators can implement and understand the integrated chart system as easily as the conventional 3-sigma system. Some useful guidelines have also been brought forth to aid designers in adjusting the control limits of the charts in a system.
On the performance of a multivariate control chart in multistage environment
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.
A transformation-based multivariate chart to monitor process dispersion
The International Journal of Advanced Manufacturing Technology, 2009
Multivariate monitoring techniques such as multivariate control charts are used to control the processes that contain more than one correlated characteristic. Although the majority of previous researches are focused on controlling only the mean vector of multivariate processes, little work has been performed to monitor the covariance matrix. In this research, a new method is presented to detect possible shifts in the covariance matrix of multivariate processes. The basis of the proposed method is to eliminate the correlation structure between the quality characteristics by transformation technique and then use a S chart for each variable. The performance of the proposed method is then compared to the ones from other existing methods and a real case is presented.
Capability index-based control chart for monitoring process mean using repetitive sampling
Communications in Statistics, 2017
A new process capability index (PCI) control chart for monitoring the process mean using repetitive sampling is presented. The design of the proposed control chart is based on an unbiased estimator 4 s c of the process standard deviation for a normally distributed quality characteristic. The formulae for the in-control and out-of-control average run length and the standard deviation of the run length (SDRL) are derived. Tables of in-control and out-of-control average run length (ARL) and standard deviation of the run length (SDRL) for various shifts, are presented. The proposed control chart outperforms existing control chart in detecting relatively small process mean shifts in terms of ARLs and SDRLs. Numerical example is presented to demonstrate the application of the proposed chart.