CUSUM Schemes for Monitoring Prespecified Changes in Linear Profiles

Because of the characteristics of a system or process, several prespecified changes may happen in some statistical process control applications. Thus, one possible and challenging problem in profile monitoring is detecting changes away from the ‘normal’ profile toward one of several prespecified ‘bad’ profiles. In this article, to monitor the prespecified changes in linear profiles, two two‐sided cumulative sum (CUSUM) schemes are proposed based on Student's t‐statistic, which use two separate statistics and a single statistic, respectively. Simulation results show that the CUSUM scheme with a single statistic uniformly outperforms that with two separate statistics. Besides, both CUSUM schemes perform better than alternative methods in detecting small shifts in prespecified changes, and become comparable on detecting moderate or large shifts when the number of observations in each profile is large. To overcome the weakness in the proposed CUSUM methods, two modified CUSUM schemes are developed using z‐statistic and studied when the in‐control parameters are estimated. Simulation results indicate that the modified CUSUM chart with a single charting statistic slightly outperforms that with two separate statistics in terms of the average run length and its standard deviation. Finally, illustrative examples indicate that the CUSUM schemes are effective.