Although enhancing the detection ability of control charts with run-rules scheme is very common, this approach received little attention in profile monitoring in which the quality of a process can be characterized by a relation between a response variable and one or more explanatory variables. In this paper, a new scheme based on a combination of multivariate exponentially weighted moving average control chart and novel run-rules is proposed to improve the performance of the procedures for monitoring simple linear profiles in Phase II. Moreover, the performance of the proposed scheme in monitoring polynomial profiles is also evaluated through simulation runs as well as a real application. The results demonstrate superior performance of the proposed scheme to the existing methods based on average run length criterion for monitoring linear profiles in Phase II especially for small and moderate shifts.

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