Xia Pan

The quality control chart for monitoring multivariate autocorrelated processes

Previously, quality control and improvement researchers discussed multivariate control charts for independent processes and univariate control charts for autocorrelated processes separately. We combine the two topics and propose vector autoregressive (VAR) control charts for multivariate autocorrelated processes. In addition, we estimate AR(p) models instead of ARMA models for the systematic cause of variation. We discuss the procedures to construct the VAR chart. We examine the effects of parameter shifts and by example present procedures to show the feasibility of VAR control charts. We simulate the average run length to assess the performance of the chart.

Applying State Space to SPC: Monitoring Multivariate Time Series

Monitoring cross-sectional and serially interdependent processes has become a new issue in statistical process control (SPC). In up-to-date SPC literature, Kalman filtering was reported to monitor univariate autocorrelated processes. This paper applies a Kalman filter or state-space method for SPC to monitoring multivariate time series. We use Aokis approach to estimate the parameter matrices of a state-space model. Multivariate Hotelling T 2 control charts are employed to monitor the residuals of the state-space. Examples of this approach are illustrated.

Multivariate Process Control charts and their use in monitoring output quality: a perspective

The authors suggest multivariate methods for the construction of quality control charts for the control and improvement of output of manufacturing processes. By example, they demonstrate the usefulness of Multivariate Process Control (MPC) as compared with univariate or Shewhart style control charts. They illustrate and view an existing production process which indicates how variation is not detected by the use of standard quality control charts. In turn, they detect the changes in the process by use of MPC charts. They indicate that the gap between theory and practice and indicate why this gap should be greatly narrowed.

An alternative approach to multivariate EWMA control chart

Abstract This Paper proposes a multivariate EWMA scheme that is alternative to the traditional EWMA-M. The distribution of the chart statistic is derived from Box quadratic form and the sensitivity of the chart is examined. The average run lengths of the M-EWMA scheme are numerically computed with the integral equation method. The exponential weight of 0.2 is found to be the optimal choice for the sensitive chart to detect assignable causes in the mean vector of processes.

Using Golden Ratio Search to Improve Paired Construction of Quality Control Charts

Our purpose is to indicate a new method for determining the control limits of univariate control charts to show the effectiveness of golden ratios search. We examine a solution to a problem when signals from mean and variance charts differ. Lack of concordance in the signals from mean and variance (or standard deviation) control charts bring confusion to Quality Control managers which in turn may lead to sub optimal management quality practices. To achieve better quality management practice, we provide a solution to the problem of finding different decision signals for in-control processes for quality control charts for mean and variability. We construct the control charts in experimental conditions for in-control average run length using the methods of simulation. Finally, we employ the golden ratio search method to identify the control limit parameters which differ from standard methods for constructing quality control charts. Last, we minimize the length of time in computation in the construction of these new quality control charts.

The Multivariate EWMA Model and Health Care Monitoring

We introduce the construction of MEWMA (Multivariate exponentially weighted moving average) process control in the field of bio surveillance. Such introduction will both improve the reliability of data collected in bio surveillance, better interpretation of the results, improvement in the quality of results and standardization of results when more than two variables are involved. We propose sensitivity ratios as a measure of the effects of the mean shift and dispersion shift in processes under study. Using these sensitivity measures, we designed the optimal exponential weighting factor, which is consistent to results reported in control chart applications. Although ARL (average run length) is the usual measure for control chart performance in multivariate process control, it is by no means the only criterion, however, at the moment it is most widely used criterion for decision making. We suggest addition study of other criteria. For example Medial Run Length, Days to Completion, Direction of Eorrors and others.