Combined Exponentially Weighted Moving Average Charts for the Mean and Variance Based on the Predictive Distribution

Abstract

This article develops combined exponentially weighted moving average (EWMA) charts for the mean and variance of a normal distribution. A Bayesian approach is used to incorporate parameter uncertainty. We first use a Bayesian predictive distribution to construct the control chart, and we then use a sampling theory approach to evaluate it under various hypothetical specifications for the data generation model. Simulations are used to compare the proposed charts for different values of both the weighing constant for the exponentially weighted moving averages and for the size of the calibration sample that is used to estimate the in-statistical-control process parameters. We also examine the separate performance of the EWMA chart for the variance.

Keywords:

• Bayesian analysis
• Combined chart for mean and variance
• Control chart
• Estimated parameters
• Normal distribution
• Predictive distribution
• Run length

Mathematics Subject Classification:

• 62F15
• 62H99
• 62P30

Acknowledgment

The author thanks a reviewer for many very helpful comments that led to an improved article.