Beta regression control chart for monitoring fractions and proportions

TL;DR

This paper introduces the beta regression control chart (BRCC), a new method for monitoring fraction and proportion data related to control variables, addressing limitations of standard regression control charts with non-normal data.

Contribution

The paper proposes the BRCC, a novel control chart that models mean and dispersion of beta-distributed data using regression, suitable for fractions and proportions.

Findings

BRCC shows good average run length (ARL) performance in simulations.

Two real data applications demonstrate practical usefulness.

Addresses limitations of traditional control charts for non-normal data.

Abstract

Regression control charts are usually used to monitor variables of interest that are related to control variables. However, for fraction and/or proportion data, the use of standard regression control charts may not be adequate, since the linear regression model assumes the normality of the interest variable. To work around this problem, we propose the beta regression control chart (BRCC). The BRCC is useful for monitoring fraction, rate and/or proportion data sets when they are related to control variables. The proposed control chart assumes that the mean and dispersion parameters of beta distributed variables are related to the exogenous variables, being modeled using regression structures. The BRCC is numerically assessed through an extensive Monte Carlo simulation study, showing good performance in terms of average run length (ARL). Two applications to real data are presented, evidencing the practical applicability of the proposed method.