Process monitoring for mean shifts for multiple stage processes

A monitoring scheme for detecting a mean shift in a multistage manufacturing process for a gamma distributed response and/or a mixture of normally and non-normally distributed variables (and gamma distributed responses) is presented. The procedure is based on a deviance residual obtained from a generalized linear model (GLM). The deviance residual is shown to be a likelihood ratio statistic for detecting a mean shift in many cases for distributions in the exponential family. The advantages over the use of a control chart based on individual observations and the T2 chart based on U statistics are demonstrated by a simulation study. The possibility of modelling the process variation for multistage processes based on a GLM is also discussed.