Monitoring prespecified changes in linear profiles using control charts with supplementary runs rules

In profile monitoring, some methods have been developed to detect the unspecified changes in the profiles. However, detecting changes away from the “normal” profile toward one of several prespecified “bad” profiles is one possible and challenging purpose. In this article, control charts with supplementary runs rules are developed to detect the prespecified changes in linear profiles. A control chart is first developed based on the Student's t-statistic in t test, and two runs rules are then supplemented to this chart, respectively. Simulation studies show that the proposed control schemes are effective and stable. Moreover, the control schemes are better than the existing alternative charts when the number of observations per sample profile is large. Finally, two illustrative examples indicate that our proposed schemes are effective and easy to be implemented.