Multivariate Quality Control Chart for Autocorrelated Processes.

Area of Science:

• Industrial Engineering
• Statistical Quality Control
• Time Series Analysis

Background:

• Classical statistical process control (SPC) methods assume independent observations, which is often violated in modern automated systems due to high sampling rates leading to autocorrelation.
• Autocorrelation in data significantly degrades the performance of traditional control charts, compromising process monitoring accuracy.
• Monitoring the mean vector of processes exhibiting autocorrelation is crucial for maintaining quality and efficiency.

Purpose of the Study:

• To address the limitations of traditional SPC methods in the presence of autocorrelation.
• To propose a novel control chart for monitoring the mean vector of processes modeled as a first-order vector autoregressive (VAR(1)) process.
• To develop a method that not only detects deviations from the in-control state but also aids in diagnosing the root cause.

Main Methods:

• The study models process observations using a first-order vector autoregressive (VAR(1)) process.
• A new control chart, termed the Z-chart, is proposed.
• The Z-chart is based on the single-step finite intersection test, a robust statistical procedure for detecting changes.

Main Results:

• The proposed Z-chart effectively monitors the mean vector of VAR(1) processes.
• The Z-chart demonstrates the capability to detect when a process is out of statistical control.
• A key advantage is the Z-chart's ability to identify specific variables contributing to the out-of-control status.

Conclusions:

• The Z-chart offers an effective solution for statistical process control in the presence of autocorrelation.
• This method enhances diagnostic capabilities by pinpointing variables responsible for process deviations.
• The Z-chart provides a valuable tool for quality control in automated manufacturing and data-intensive processes.