The problem of shift detection in the mean of a sequence of normally distributed random variables in two-way arrays is examined. The problem has applications in the manufacturing industry where the mean level of one or more machines in a process may shift. The goal is to find a model that best describes the data so that a true picture of how the process operates may be obtained. To that end, it is important to detect any shifts that may occur. If the shifts go undetected, the estimates of the process variability may be biased. A diagnostic procedure is developed which estimates the location and magnitude of the shifts. When all shifts are identified, the variability in the process may be estimated by formulating the correct model.

In this dissertation, the problem of shift detection in two-way arrays is examined. In particular, the case when there is large column to column variability is studied. Although large column variability is not very typical in industrial processes, its presence can often cause the shifts to go undetected. The procedure proposed in this dissertation is powerful even in the presence of large column variability. It is therefore a powerful diagnostic procedure which can be applied to industrial data.