Year: 2024
Type: article
Abstract: There is no known closed form expression for the average sample number, also known as average run length, of a multivariate CUSUM procedure $N = \min\{ M_1, M_2,\cdots, M_m\}$ for $m\geq 3$, where $M_i$ are univariate CUSUM procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the average run length of $N$ with an elementary proof. A bit surprisingly, we further show that the average run length of $N$ is related to the average run lengths of $M_i$ the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.
Authors: Shangchen Yao, Mohammad Khan
Institution: Kent State University
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4403037166