The surveillance of several processes with different change points

Abstract

A statistical surveillance situation which involves the simultaneous surveillance of several processes is treated. Some recently suggested multivariate methods are discussed together with a new method based on the likelihood ratio. The emphasis in the discussion is put on different ways to combine information from each time point. The methods treated represent different approaches in this aspect to the construction of multivariate surveillance methods. Shewhart type methods are used to handle the information over time. Comparisons of these methods are made when two processes, which are observed through bivariate normal variables, are surveilled for sudden shifts in the means with known and constant covariance structure. Also, the effects of different change points for the variables are considered. Generalisations to the multivariate case of the ARL and the probability of a successful detection are suggested. The main difference in performance between the compared methods is shown to be between methods based on the marginal and joint distributions of the variables. It is also shown how the choice of method depends on both on the correlation between the variables and when the time when a second change point can be expected.