A CUSUM CHART WITH LOCAL SIGNAL AMPLIFICATION FOR DETECTING A RANGE OF UNKNOWN SHIFTS

Abstract

The cumulative sum (CUSUM) control chart is one of the most dominant statistical process control schemes. Despite its simplicity, its performance deteriorates when the actual mean shift is unknown. In this paper, we present an effective alternative approach called the CUSUM chart with local signal amplification (LSA-CUSUM) by amplifying or weakening local signals to improve the power of the traditional CUSUM chart in detecting an unknown mean shift over a range. Additionally, we introduce a measure for evaluating the efficiency of the LSA-CUSUM chart to detect a pre-specified mean shift range and describe a procedure to find an approximately optimal LSA-CUSUM chart over a mean shift range. Comparisons of the simulation results show that the proposed approxmated optimal LAS-CUSUM chart outperforms its traditional counterpart.