Statistical Process Monitoring for Correlated Data Project

Process monitoring is very important for industries. Statistical methodologies have been used to monitor various production process successfully. The majority of statistical process monitoring techniques assume that the process data are free of correlation. However, this assumption is frequently invalid in many manufacturing processes and other processes. For example, chemical process data and Internet traffic data are correlated or self dependent. Under such conditions, the traditional statistical monitoring methodologies are not effective. The impetus of this project is to develop new statistical methodologies to apply to the self dependent data.

The objectives of this project are:

1. to provide new statistical measures and techniques for process monitoring and control for manufacturing industries, and
2. to perform research in the applications of these techniques to additional areas with one example being the monitoring of Internet traffic.

This project has generated the following publications.

• Zhang, N. F. (2000) " Statistical Control Charts for Monitoring the Mean of a Stationary Process," to appear in Journal of Statistical Computation and Simulation.
• Zhang, N. F. (1999) "Statistical control for autocorrelated data," Proceedings of EUROPT Series: Process and Equipment Control in Microelectronic Manufacturing," Vol. 3742, 65-70.
• Zhang, N. F. (1998) "Comparisons of Control Charts for Autocorrelated Data," 1998 proceedings of the Section on Quality and Productivity of American Statistical Association, 8-12.
• Zhang, N. F. (1998), "Estimating Process Capability Indices for Autocorrelated Data," Journal of Applied Statistics, 25(4), 559-574.
• Zhang, N. F. (1998), "A Statistical Control Chart for Stationary Process Data," Technometrics, 40(1), 24-38.
• Zhang, N. F. (1997), "Detection Capability of Residual Control Chart for Stationary Process Data," Journal of Applied Statistics, 24(4), 475-492.
• Zhang, N. F. (1997), "Autocorrelation Analysis of Some Linear Transfer Function Models and its Applications in the Dynamic Process System," Lectures in Applied Mathematics, 33, 385-399, American Mathematical Society.
• Zhang, N. F and J. P. Pollard (1994), "Analysis of Autocorrelations in Dynamic Processes," Technometrics, 36, 354-368.

The methodologies have been published in several mathematical and statistical journals and have been presented to mathematical and applied statistics societies.  The responses are encouraging. Some methodology has been implemented in industry.

The timelines and milestones for this project are:

• FY94 - Publish the first paper on dynamic processes in Technometrics.
• FY97 - Publish a paper on detection capability of residual control charts and publish a paper on autocorrelation analysis of linear transfer function models.
• FY98 - Publish a paper on process capability indices for autocorrelated data. Publish a paper on control chart for stationary process data in Technometrics.
• FY99 - Make comparisons among the control charts for autocorrelated data.
• FY00 - Publish a paper on the comparisons of control charts for autocorrelated data. Propose to use generalized moving averages of stationary process data to reduce process autocorrelations.