A Nonparametric Phase I Control Chart for Monitoring the Process Variability with Individual Observations Based on Empirical Likelihood Ratio

TLDR: This work proposes a new nonparametric Phase I control chart for monitoring the scale parameter based on the empirical likelihood ratio test and shows that the proposed chart is more effective than the existing charts in terms of signal probability.

Abstract: Among the statistical process control (SPC) techniques, the control chart has been proven to be effective in process monitoring. The Shewhart chart is one of the most commonly used control charts for monitoring the process mean and variability based on the assumption that the distribution of the quality characteristic is normal. However, in practice, many quality characteristics are not normally distributed. Most of the existing nonparametric control charts are designed for Phase II monitoring. Little has been done in developing the nonparametric Phase I control charts especially for individual observations. In this work, we propose a new nonparametric Phase I control chart for monitoring the scale parameter based on the empirical likelihood ratio test. The simulation results show that the proposed chart is more effective than the existing charts in terms of signal probability. A real example is used to demonstrate how the proposed chart can be applied in practice.