670 – Advances in Statistical Process Control
Xbar Chart with Estimated Parameters: New Formulas to Guarantee a Conditional In-Control Performance
Felipe S. Jardim
PUC-Rio
Subhabrata Chakraborti
University of Alabama
Eugenio K. Epprecht
PUC-Rio
Recently, to design control charts with estimated parameters, a new perspective has emerged where the usual chart performance measure, the average run length (ARL), is recognized as a random variable that depends on the parameter estimates. In this context, a recent idea is to measure the chart performance with the probability of the ARL be greater than a specified value. This is called the exceedance probability criterion (EPC). In recent years, bootstrap method and approximate formulas were proposed to adjust the Xbar chart under normality to guarantee an in-control performance in terms of the EPC. These methods provide accurate, but not exact, results. Given this, in this paper, we present a summary of two recent papers written by us, under review, where we propose the use of an equation in which exact adjustments can be quickly calculated with a software such as RStudios. Furthermore, realizing the complexity of all these methods for a regular user, in these papers, we also derive a new simpler approximate formula which depends only on the well-known chi-square distribution. We show that this new simpler formula provides accurate results compared to the already existing ones.