Abstract
This paper analyzes the sequential decision problem related to failure detection and diagnosis in dynamical systems when an input to the data generating mechanism is available to the decision-maker. The sequential decision rules are augmented by an input design rule. It is shown that some important properties of the decision rules related to the classical case (where no input is available) still hold: The terminal decision rule is a collection of fixed sample size Bayes rules and the problem when the sample size is not restricted can be approximated asymptotically.
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