선택적 이동평균(S-MA) 관리도의 ARL

Abstract

This paper investigates the average run length (ARL) of a selectively moving average (S-MA) control chart. The S-MA 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 shows that the steady-state ARL performance is still better than the CUSUM chart or the Exponentially Weighted Moving Average (EWMA) chart.