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

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

MULTIVARIATE STATISTICAL PROCESS CONTROL FOR CORRELATION MATRICES

Measures of dispersion in the form of covariance control charts are the multivariate analog to the univariate R-chart, and are used in conjunction with multivariate location charts such as the Hotelling T2 chart, much as the R-chart is the companion to the univariate X-bar chart. Significantly more research has been directed towards location measures, but three multivariate statistics (|S|, Wi, and G) have been developed to measure dispersion. This research explores the correlation component of the covariance statistics and demonstrates that, in many cases, the contribution of correlation is less significant than originally believed, but also offers suggestions for how to implement a correlation control chart when this is the variable of primary interest.This research mathematically analyzes the potential use of the three covariance statistics (|S|, Wi, and G), modified for the special case of correlation. A simulation study is then performed to characterize the behavior of the two modified statistics that are found to be feasible. Parameters varied include the sample size (n), number of quality characteristics (p), the variance, and the number of correlation matrix entries that are perturbed. The performance and utility of the front-running correlation (modified Wi) statistic is then examined by comparison to similarly classed statistics and by trials with real and simulated data sets, respectively. Recommendations for the development of correlation control charts are presented, an outgrowth of which is the understanding that correlation often does not have a large effect on the dispersion measure in most cases

On the Monitoring of Simple Linear Berkson Profiles

[[abstract]]We consider the quality of a process, which can be characterized by a simple linear Berkson profile. One existing approach for monitoring the simple linear profile and two new proposed schemes are studied for charting the simple linear Berkson profile. Simulation studies demonstrate the effectiveness and efficiency of one of the proposed monitoring schemes. In addition, a systematic diagnostic approach is provided to spot the change point location of the process and to identify the parameter of change in the profile. Finally, an example from semiconductor manufacturing is used to illustrate the implementation of the proposed monitoring scheme and diagnostic approach.[[incitationindex]]SCI[[booktype]]電子版[[booktype]]紙

A Comparison Of The Performances Of Various Single Variable Charts.

Control charts are used for process monitoring and improvement in industries. Two charts are usually used in the monitoring of both the mean and variance separately

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. --

Comparison of change-points in multivariate statistical process control using the performance of Lapage-type (nonparametric)

The inability of the Shewhart‟s, the EWMA, and the CUSUM, Hotelling‟s T2 and many other control charts to indicate the time of shift poses great problems in production, Medicine, etc. To overcome the problems the need to identify the period of change (shift) in the process becomes inevitable. The study used Lapage-type Change-point (LCP) to detect the simultaneous shift in both mean and variance. In the study we compare the performance of generalized likelihood ratio change-point (GLRCP) a parametric-base with our proposed method (LCP) at different varying start-ups using real life data. We run the data on Normal, Laplace and Lognormal distributions and also Average Run Length (ARL0) to assess the performance of the methods. Evaluating in-control ARLs (IC-ARLs) for each of the methods at change-point 250 and ARL0 500 indicates the same performance irrespective of the start-up value; LCP and GLR methods have rather a similar performance IC-ARLs at change-point 50 and change-point 100 under the normality assumptions, but under non-normal distributions, LCP has substantially higher IC-ARLs compared to GLRCP at 20. The LCP outperformed the GLRCP when applied to children bronchial pneumonia status. We therefore recommend that new method be used in short-run situations and also when underlying distributions are usually unknown