A computationally efficient self-starting scheme to monitor general linear profiles with abrupt changes

Abstract

A self-starting monitoring scheme is proposed in this paper for the simultaneous detection of variance and coefficients in linear profiles with unknown error distributions. Based on the global data, we construct a sequential Wald-type charting statistic, obtain the corresponding asymptotical distributions and further provide a recursive algorithm to quickly calculate statistics sequentially. Control limits of our charting statistics are also constructed based on their asymptotical distributions. Finally, we apply our method to analyze both artificial and real data, and numerical results show that our method performs well.