On an optimization problem in sensor selection for failure diagnosis

We address the following sensor selection problem for failure diagnosis. We assume that a dynamic system is diagnosable when a set Γ of sensors is used. There is a cost c_A associated with each set A of sensors that is a subset of Γ. Given any set of sensors that is a subset of Γ, it is possible to determine, via a test (using a prespecified diagnostic scheme), whether the resulting system-sensor combination is diagnosable. Each “diagnosability test” incurs a fixed cost. For each set of sensors A that is a subset of Γ there is an a priori probability p_A that the system-sensor combination is diagnosable. We determine conditions on the sensor costs c_A and the a priori probabilities p_A under which the strategy that tests combinations of sensors in increasing order of cost minimizes the expected number of tests needed to identify a least costly (sensor-wise) system-sensor combination that is diagnosable