The ARL of a Selectively Moving Average Control Chart

Lim, Tae-Jin

Journal of Korean Society for Quality Management > Volume 35(1); 2007 > Article

Journal of Korean Society for Quality Management 2007;35(1): 24-.

선택적 이동평균(S-MA) 관리도의 ARL

임태진

숭실대학교 산업.정보시스템공학과

The ARL of a Selectively Moving Average Control Chart

Tae-Jin Lim

Dept. of Industrial & Information Systems Engineering, Soongsil University

ABSTRACT

This paper investigates the average run length (ARL) of a selectively moving average (S-MA) control chart. The S-U chart is designed to detect shifts in the process mean. The basic idea of the S-MA chart is to accumulate previous samples selectively in order to increase the sensitivity. The ARL of the S-MA chart was shown to be monotone decreasing with respect to the decision length in a previous research [3]. This paper derives the steady-state ARL in a closed-form and shows that the monotone property is resulted from head-start assumption. The steady-state ARL is shown to be a sum of head-start ARL and an additional term. The statistical design procedure for the S-MA chart is revised according to this result. Sensitivity study shorts that the steady-state ARL performance is still better than the CUSUM chart or the Exponentially Weighted Moving Average (EWMA) chart.

Key Words: Moving Average;CUSUM;ARL;Control Chart;Adaptive Scheme;Markov Chain;