Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

An Examination of the Robustness to Non Normality of the EWMA Control Charts for the Dispersion

The EWMA control chart is used to detect small shifts in a process. It has been shown that, for certain values of the smoothing parameter, the EWMA chart for the mean is robust to non normality. In this article, we examine the case of non normality in the EWMA charts for the dispersion. It is shown that we can have an EWMA chart for dispersion robust to non normality when non normality is not extreme.Average run length, Control charts, Exponntially weighted moving average control chart, Median run length, Non normality, Statistical process control

Multivariate Statistical Process Control Charts: An Overview

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 lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

A Nonparametric Multivariate Control Chart Based on Data Depth

For the design of most multivariate control charts, it is assumed that the observations follow a multivariate normal distribution. In practice, this assumption is rarely satisfied. In this work, a distribution-free EWMA control chart for multivariate processes is proposed. This chart is based on equential rank of data depth measures. --

A Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

Application and Use of Multivariate Control Charts In a BTA Deep Hole Drilling Process

Deep hole drilling methods are used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances usually classified as either chatter vibration or spiralling. In this paper, we will focus on the application and use of multivariate control charts to monitor the process in order to detect chatter vibrations. The results showed that chatter is detected and some alarm signals occurs at time points which can be connected to physical changes of the process. --

Monitoring variance by EWMA charts with time varying smoothing parameter

Memory charts like EWMA-S² or CUSUM-S² can be designed to be optimal to detect a specific shift in the process variance. However, this feature could be a serious inconvenience since, for instance, if the charts are designed to detect small shift, then, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to overcome this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper proposes new adaptive EWMA control charts for the dispersion (AEWMA-S²) based on a timevarying smoothing parameter that takes into account the potential misadjustment in the process variance. The obtained control charts can be interpreted as a combination of EWMA control charts designed to be efficient for different shift values. Markov chain procedures are established to analyse and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals

An Assorted Design for Joint Monitoring of Process Parameters: An Efficient Approach for Fuel Consumption

Due to high fuel consumption, we face the problem of not only the increased cost, but it also affects greenhouse gas emission. This paper presents an assorted approach for monitoring fuel consumption in trucks with the objective to minimize fuel consumption. We propose a control charting structure for joint monitoring of mean and dispersion parameters based on the well-known max approach. The proposed joint assorted chart is evaluated through various performance measures such as average run length, extra quadratic loss, performance comparison index, and relative average run length. The comparison of the proposed chart is carried out with existing control charts, including a combination of X and S, the maximum exponentially weighted moving average (Max-EWMA), combined mixed exponentially weighted moving average-cumulative sum (CMEC), maximum double exponentially weighted average (MDEWMA), and combined mixed double EWMA-CUSUM (CMDEC) charts. The implementation of the proposed chart is presented using real data regarding the monitoring of fuel consumption in trucks. The outcomes revealed that the joint assorted chart is very efficient to detect different kinds of shifts in process behaviors and has superior performance than its competitor charts.Deanship of Scientific Research, King Saud University, King Fahd University of Petroleum and MineralsScopu

The Multivariate EWMA Model and Health Care Monitoring

We introduce the construction of MEWMA (Multivariate exponentially weighted movingaverage) process control in the field of bio surveillance. Such introduction will both improve the reliability of data collected in bio surveillance, better interpretation of the results,improvement in the quality of results and standardization of results when more than two variables are involved. We propose sensitivity ratios as a measure of the effects of the mean shift and dispersion shift in processes under study. Using these sensitivity measures, we designed the optimal exponential weighting factor, which is consistent to results reported in control chart applications. Although ARL (average run length) is the usual measure for control chart performance in multivariate process control, it is by no means the only criterion, however, at the moment it is most widely used criterion for decision making. We suggest addition study of other criteria. For example Medial Run Length, Days to Completion, Direction of Eorrors and others