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

by   Amir Ahmadi-Javid, et al.

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.



page 16


Transfer function interpolation remainder formula of rational Krylov subspace methods

Rational Krylov subspace projection methods are one of successful method...

The order of convergence of an optimal quadrature formula with derivative in the space W_2^(2,1)

The present work is devoted to extension of the trapezoidal rule in the ...

Self-Learned Formula Synthesis in Set Theory

A reinforcement learning algorithm accomplishes the task of synthesizing...

Kac-Rice formula: A contemporary overview of the main results and applications

The book develops the fundamental ideas of the famous Kac-Rice formula f...

Introducing MathQA – A Math-Aware Question Answering System

We present an open source math-aware Question Answering System based on ...

Superposition de calques monochromes d'opacités variables

For a monochrome layer x of opacity 0< o_x<1 placed on another monochro...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.