Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)

TL;DR

This paper critiques the incorrect formula used in the economic design of memory-type control charts like EWMA and CUSUM, proposes corrections, and suggests simulation-based optimization as a practical alternative.

Contribution

It identifies the fallacy in the Lorenzen and Vance (1986) formula for memory-type control charts and offers corrected formulas and an alternative simulation-based optimization approach.

Findings

The Lorenzen and Vance formula can significantly deviate from true values.

Corrected formulas for memory-type control charts are derived.

Simulation-based optimization is recommended as a practical solution.

Abstract

The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this formula are accurately computed. Consequently, the use of this formula can result in charts that are not economically optimal. The formula is corrected for memory-type control charts, but unfortunately the modified formula is not a helpful tool from a computational perspective. We show that simulation-based optimization is a possible alternative method.