Multivariate Extensions of CUSUM Procedure

In quality control, to use the recent history data of the process, Page(1954) introduced the CUSUMprocedure in the univariate case. It has been proved(Moustakides,1986)that (when the process is out of control) the CUSUMprocedure has the smallest expected run length among all procedures with the same in-control ARL. In this dissertation, we investigate the multivariate extension of Page's CUSUMprocedure. The expectation and the variance of the run length for various multivariate distributions are studied. Both analytical and simulation results of the ARLand variance are given. The exact expression for the ARLof a trinomial model for any decision intervals are given. Computer programs computing the ARLand variance for any given decision intervals are also given. Advisors/Committee Members: Khan, Mohammad Kazim.