Some properties of a linear combination CUSUM statistic for controlling a multivariate mean vector

We develop a class of new multivariate procedures for monitoring quality by detecting a change in the level of a multivariate process. Following the ideas of S.N. Roy, we first consider a linear combination statistic which results from projecting the multivariate observations onto a unit vector and then maximizing a selected univariate statistic over all directions.An application to a sheet metal assembly process is discussed in Section 3. Comparisons are made between one of our new procedures and other major multivariate quality monitoring schemes in Section 4. A small simulation study compares the average run lengths of the different procedures both when the process is in-control and after a shift has occurred. Some large sample properties are discussed in Section 5 and some computational details in Section 6.