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

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

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

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. --

The blockage ratio effect to the spray performances

Nozzle sprays are used in wide range of application. The used of nozzle application is depend on the spray characteristics, by which to suit the particular application. This project studies the effect of the air blockage ratio to the spray characteristics. This research conducted into two part which are experimental and simulation section. The experimental was conducted by using particle image velocimetry (PIV) method, and ANSYS software was used as tools for simulation section. There are two nozzles were tested at 1 bar pressure of water and air. Nozzle A (with blockage ratio 0.316) and nozzle B (blockage ratio 1.000). Both of the sprays performances generated by the nozzles was examined at 9 cm vertical line from 8 cm of the nozzle orifice. The validation result provided in the detailed analysis shows that the trend of graph velocity versus distance gives the good agreement within simulation and experiment. From result, nozzle A generated a wider spray angle and higher water droplet velocity which are 31.41 degree and 37.317 m/s compared to nozzle B which has produced 27.13 degree of spray penetration angle and 16.49 m/s water droplet velocity. As a conclusion, blockage ratio has affected the spray system by increasing the velocity of air inside the spray system. This is happened at a condition of 1 bar air pressure