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

Multivariate Control Charts for Attribute Data

In this paper the use of multivariate control charts for attribute data is proposed. These charts are based on chi-square statistics. Data from various categories can be summarized into a multivariate statistic, i.e., the chi-square statistic, and then the process can be monitored by plotting this statistic on a control chart. A numerical example is provided

An Application of Univariate and Multivariate Control Charts in Monitoring Water Quality

Control chart is a tool for detecting an out-of-control signal in statistical process control (SPC). It is widely used in process monitoring in order to detect changes in process mean or process dispersion. This study aims to illustrate the application of multivariate control charts in monitoring water quality at one of the water treatments plants in Kota Kinabalu, Sabah. The tested water quality variables in this study are turbidity, pH value, dissolved oxygen (DO) and concentration of ferum. Two multivariate control charts, Hotelling’sT2 and MCUSUM control charts are constructed under the violation of the multivariate normality assumption. The purpose is to study the effect of non-normal data upon the monitoring process using the selected multivariate control charts. By comparing the monitoring process between the two types of control charts, the consistency of the results is studied. All the univariate and multivariate control charts produced out-of-control signals from different points, hence inconclusive results obtaine

Data Analytics and Managing Health and Medical Care

The purpose is to introduce the demand for the quality movement practice in problems associated with public health diagnostic testing and other health related problems We examine problems involving 1 Multivariate control charts which simultaneously monitor correlated variables 2 we explain why the scale on multivariate control charts is unrelated to the scale of the individual Variables control charts and 3 discover that out of control signals in multivariate charts do not reveal which variable or combination of variables causes the signal and application of quality monitoring New methods provide methods for MPC charts focus on the average run length as the decision factor We indicate that other decision criteria in multivariate control charts are availableand these methods can be useful in evaluating the design and implementation of multivariate charts in special circumstance

Testing Rationality of Subgroups in Multivariate Control Charts

In this study a method will be developed to test whether the subgroups formed for T^2 control charts, a multivariate process control tool, are rational. In an earlier work we suggested that a comparison of the mean square successive difference variance to the usual variance could be used to test the rationality of the subgroups in the univariate control charts. The method proposed in this paper is a multivariate extension of testing the equality of two variance estimators

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. --

On some multivariate control charts

To maintain the quality of a product or to improve the reliability of a process, all industries need to monitor several parameters about their production process. Control charts are some visualization tools for monitoring processes statistically. In this work, we propose a few control charting schemes to monitor several characteristics of a process at the same time and to detect when it goes out of control. Our objective is to reduce the false alarms (the scheme detects a problem when actually there is none) as well as to quickly detect the correct out-of-control situation. The novelty of the proposed schemes are that they do not depend on commonly assumed Normal distribution of the process variables and is applicable for a much wider range of data distributions. At first, we make a detailed literature review of some univariate and multivariate control charts. We perform a comparison study of the commonly used multivariate control charts when the underlying distribution is not normal and show that they perform poorly giving a very high false alarm rate. Next we propose some nonparametric multivariate control charts based on the lengths of the multivariate rank vectors. The ideas are similar to the ones proposed by Liu (1995), however, we show that our proposed methods are computationally simpler in any dimension. We propose some more multivariate versions of Shewhert type, CUSUM and EWMA control charts based on spatial sign vectors and signed rank vectors. We also discuss several design parameters in the construction of these charts. None of the proposed charts depend on the assumption of underlying distribution or estimation of distributional parameters

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. --