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