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 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

The Effect of Median Based Estimators on CUSUM Chart

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts.It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts.This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained.The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the out-of-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes.By minimising the false positives, a sound judgement can be made for any clinical decision

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

An Alternative Q Chart Incorporating A Robust Estimator Of Scale

In overcoming the shortcomings of the classical control charts in a short runs production, Quesenberry (1991 & 1995a – d) proposed Q charts for attributes and variables data. An approach to enhance the performance of a variable Q chart based on individual measurements using a robust estimator of scale is proposed. Monte carlo simulations are conducted to show that the proposed robust Q chart is superior to the present Q chart

On Data Depth and the Application of Nonparametric Multivariate Statistical Process Control Charts

The purpose of this article is to summarize recent research results for constructing nonparametric multivariate control charts with main focus on data depth based control charts. Data depth provides data reduction to large-variable problems in a completely nonparametric way. Several depth measures including Tukey depth are shown to be particularly effective for purposes of statistical process control in case that the data deviates normality assumption. For detecting slow or moderate shifts in the process target mean, the multivariate version of the EWMA is generally robust to non-normal data, so that nonparametric alternatives may be less often required

Method of lines and runge-kutta method in solving partial differential equation for heat equation

Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method