A note on CUSUM design for autocorrelated processes

Lee, Jae-June; Lee, Jong-Seon

Journal of Korean Society for Quality Management > Volume 36(4); 2008 > Article

Journal of Korean Society for Quality Management 2008;36(4): 87-.

자기상관 공정에 대한 누적합관리도에서 설계모수 값의 결정

이재준, 이종선

인하대학교 자연과학대학 통계학과

A note on CUSUM design for autocorrelated processes

Jae-June Lee, Jong-Seon Lee

Department of Statistics, Inha University

ABSTRACT

It is common to use CUSUM charts for detecting small level shifts in processes control, in which reference value(k) and decision interval(h) are the design parameters to be determined. To control process with autocorrelation, CUSUM charts could be applied to residuals obtained from fitting ARIMA models. However, constant level shifts in processes lead to varying mean shifts in residual processes and thus standard CUSUM charts may need to be modified. In this paper, we study the performance of CUSUM charts with various design parameters applied to autocorrelated processes, especially focussing on ARMA(1,1) models, and propose how they can be determined to get better performance in terms of the average run length.

Key Words: CUSUM;Autocorrelation;Reference value;ARMA(1, 1);