Two-Sided EWMA Charts for Monitoring Double Bounded Processes

TL;DR

This paper evaluates two-sided EWMA charts for monitoring double bounded processes like rates and proportions, analyzing their design, performance, and robustness across different statistical models using individual data points.

Contribution

It introduces tailored EWMA chart designs for double bounded data modeled by Beta, Simplex, and Unit Gamma distributions, including robustness analysis and practical example.

Findings

Charts perform well across models with proper design parameters.

Performance is sensitive to control limit choices not based on the true model.

The methodology is applicable to real-world rate and proportion monitoring.

Abstract

In this work, we study the performance of two-sided EWMA charts for monitoring double bounded processes using individual observations. Specifically, the term double bounded refers to observations in the interval (0, 1) and thus, these charts are suitable for monitoring rates, proportions and percentages. There are several models that can be used to describe this kind of data (and the respective processes, as well) such as the Beta distribution, the Simplex distribution and the Unit Gamma distribution. For each of these three models, we provide the statistical design and the performance of the proposed EWMA charts. Also, apart from providing the appropriate values for the design parameters of each chart, we investigate how much the performance of the EWMA schemes is affected by using the values of control limits which have not been calculated under the true model. Finally, an illustrative example is also presented.