Investigating zero-state and steady-state performance of MEWMA-CoDa control chart using variable sampling interval.

Area of Science:

• Statistical Process Control
• Multivariate Quality Control
• Compositional Data Analysis

Background:

• Traditional control charts use fixed sampling intervals, which can be inefficient for detecting process shifts.
• Variable sampling intervals (VSI) schemes adjust sampling frequency based on process monitoring statistics, offering potential improvements.
• Compositional data, common in industrial processes, require specialized methods for accurate analysis.

Purpose of the Study:

• To propose a novel multivariate exponentially moving average control chart for compositional data (MEWMA-C).
• To optimize chart parameters using zero-state and steady-state average time to signal (ATS).
• To evaluate the statistical performance of the proposed MEWMA-C chart.

Main Methods:

• Utilized isometric log-ratio (ILR) transformation for handling compositional data.
• Developed a methodology for parameter optimization considering both zero-state (Z) and steady-state (SS) ATS.
• Employed a continuous-time Markov chain (CTMC) model for performance evaluation.

Main Results:

• The proposed MEWMA-C chart significantly reduced the out-of-control (OOC) average time to signal (ATS) compared to traditional charts.
• The number of variables (d) negatively impacts the MEWMA-C chart's performance, while subgroup size (n) has a mildly positive effect.
• The MEWMA-C chart demonstrates superior performance, particularly under steady-state conditions, compared to competing charts like EWMA-C and MEWMA.

Conclusions:

• The MEWMA-C chart is an effective tool for monitoring compositional data in industrial processes.
• The variable sampling interval strategy enhances the sensitivity of control charts.
• The proposed method provides a statistically significant improvement in process monitoring accuracy.