Control Chart For Process Dispersion Research Articles

A two-sided SPRT control chart for process dispersion

This paper proposes a two-sided sequential probability ratio test chart for monitoring dispersion of a normally distributed process. Accurate approximate expressions that relate the statistical performance measures of this chart to that of its corresponding one-sided charts are obtained through simulations. An approach to design the chart having the specified in-control performance and the optimal out-of-control performances for detecting the particular upper and lower shifts that are desired to detect as efficiently as possible is provided. It is found through numerical comparisons that the overall statistical performance of the proposed chart is superior to that of the competitor charts in the existing literature. The application of the chart is illustrated through real-data on the thickness of dielectric polyimide coating layer that is applied on a wafer used in an integrated circuit.

The SPRT control chart for process dispersion

AbstractThis paper investigates the statistical performance of a sequential probability ratio test control chart for monitoring the dispersion of a normally distributed process. The expressions for statistical performance measures of the chart are derived using a Markov chain approach. It is shown through numerical comparisons that the overall statistical performance of this chart is superior to that of the existing competitor charts for dispersion. An example illustrating an application of the chart in practice is provided.

CS‐EWMA Chart for Monitoring Process Dispersion

Control charts are the most extensively used technique to detect the presence of special cause variations in processes. They can be classified into memory and memoryless control charts. Cumulative sum and exponentially weighted moving average control charts are memory‐type control charts as their control structures are developed in such a way that the past information is not ignored as it is done in the case of memoryless control charts, like the Shewhart‐type control charts. The present study is based on the proposal of a new memory‐type control chart for process dispersion. This chart is named as CS‐EWMA chart as its plotting statistic is based on a cumulative sum of the exponentially weighted moving averages. Comparisons with other memory charts used to monitor the process dispersion are done by means of the average run length. An illustration of the proposed technique is done by applying the CS‐EWMA chart on a simulated dataset. Copyright © 2012 John Wiley & Sons, Ltd.

An Alternative to the Bivariate Control Chart for Process Dispersion

ABSTRACT In this article, we propose a Shewhart-type control chart for monitoring changes in the process variability of a bivariate process. The sample Gini mean differences based matrix is used as an estimate of the population variance–covariance matrix . The newly proposed control chart, denoted by -chart, is based on the generalized Gini mean differences . For the case of two correlated quality characteristics Y and X, the design structure of the proposed -chart is developed assuming bivariate normality of (Y, X). The performance of the proposed -chart is compared with that of the -chart (a sample generalized variance based control chart).

A Multivariate Synthetic Control Chart for Process Dispersion

A multivariate synthetic control chart for monitoring the covariance matrix of a normally distributed process is proposed in this paper. The proposed chart is a combination of the traditional generalized sample variance |S| chart and the conforming run length chart. The operation, design and performance of this chart are described. Average run length comparisons between some other existing control charts and the multivariate synthetic control chart are presented. It is observed that the multivariate synthetic control chart outperforms the traditional |S| chart for monitoring the covariance matrix of a normally distributed process.

Comparison of Multivariate Control Charts for Process Dispersion

ABSTRACT In this article we compare four multivariate control charts for process dispersion in the retrospective analysis of a historical data set. Among the schemes compared, a new control chart based on a robust estimation of the variance-covariance matrix proved to be very effective in detecting changes in the process dispersion matrix.

Multivariate control charts for process dispersion

The multivariate extension of control charts for process dispersion is not as straightforward as that for the process mean. A general model and techniques that would encompass a wide range of problems encountered in practice is not available. In most cases, particular problems need to be handled in a specific manner. In this paper we consider several special cases of a process displacement affecting the covariance matrix and we develop control charts (both Shewhart-type and CUSUM) to detect these process changes.

Alternatives to the Multivariate Control Chart for Process Dispersion

In this article, we compare the performances of six new multivariate control chart schemes for process dispersion to the standard multivariate process dispersion control chart. The six new schemes are designed by transforming the standard multivariate control chart statistic for process dispersion into a standard scale so that runs rules can be incorporated into these schemes. This article discusses a simple extension for using runs rules in a multivariate control chart for process dispersion. The extension is deemed important since the use of runs rules is always confined to univariate control charts only. The performances of the six control chart schemes together with the standard control chart are based on the computed average run length (ARL) profiles. Five of the six schemes have shown better ARL performances than the standard multivariate process dispersion control chart.

Multivariate Control Chart for Process Dispersion Based on Individual Observations

In this paper, we will discuss a simple way for monitoring shifts in the covariance matrix of a p-dimensional multivariate normal process distribution, N p (μ,Σ). An exact method based on the chi-square distribution for constructing multivariate control limits will also be shown. We will illustrate the proposed procedure at work based on an example.