  Suppose that local characteristics of several independent compound Poisson
and Wiener processes change suddenly and simultaneously at some unobservable
disorder time. The problem is to detect the disorder time as quickly as
possible after it happens and minimize the rate of false alarms at the same
time. These problems arise, for example, from managing product quality in
manufacturing systems and preventing the spread of infectious diseases. The
promptness and accuracy of detection rules improve greatly if multiple
independent information sources are available. Earlier work on sequential
change detection in continuous time does not provide optimal rules for
situations in which several marked count data and continuously changing signals
are simultaneously observable. In this paper, optimal Bayesian sequential
detection rules are developed for such problems when the marked count data is
in the form of independent compound Poisson processes, and the continuously
changing signals form a multi-dimensional Wiener process. An auxiliary optimal
stopping problem for a jump-diffusion process is solved by transforming it
first into a sequence of optimal stopping problems for a pure diffusion by
means of a jump operator. This method is new and can be very useful in other
applications as well, because it allows the use of the powerful optimal
stopping theory for diffusions.
