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Adaptive control limits for risk-adjusted Bernoulli CUSUM charts
Journal of the Korean Data & Information Science Society 2020;31:1-13
Published online January 31, 2020;  https://doi.org/10.7465/jkdi.2020.31.1.1
© 2020 Korean Data and Information Science Society.

Heewon Jung1 · Minjae Choi2 · Jaeheon Lee3

123Department of Applied Statistics, Chung-Ang University
Correspondence to: Professor, Department of Applied Statistics, Chung-Ang University, Seoul 06974, Korea. E-mail: jaeheon@cau.ac.kr
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2017R1D1A1B03029035).
Received September 30, 2019; Revised October 31, 2019; Accepted November 3, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
When using general control charts, we assume that quality characteristic monitored is identically distributed during the in-control period. However, when we monitor the surgical performance such as the surgical outcomes, this assumption is not satisfied because of variability in pre-operative risks of different patient populations. It was proposed that the risk-adjusted Bernoulli CUSUM chart that involves adjusting for each patient’s pre-operative risk of surgical failure using a logistic regression model and then applying a Bernoulli CUSUM chart. However, it is difficult to determine the control limits satisfying the specified in-control performance. In this paper, we propose the method for determining adaptive control limits of risk-adjusted Bernoulli CUSUM charts based on the corrected diffusion (CD) approximation. And we evaluate the in-control performance of the proposed method by using the average run length, the standard deviation of run length, and percentiles.
Keywords : Bernoulli CUSUM chart, control limits, corrected diffusion approximation, risk-adjustment.