New measures of testability and test complexity for linear analog failure analysis

The failure analysis of analog electronic systems is characterized by numerous, difficult problems. Assessing the testability and test complexity of a given system is one such problem. In fact, robust, quantitative measures of these important features have not been available to the analog testing community. This paper introduces new measures for both testability and test complexity which: (1) are quantitative, (2) are capable of handling multiple faults, and (3) have a well-defined interpretation. These measures are based upon published results from optimal experiment designs as developed in the discipline of systems identification. Parameter testability is defined in terms of information (in the sense of Fisher) return, while test complexity is functionally related to the experiment time required to achieve specified accuracy with regard to the uncertain parameters of interest. Thus both of the new measures introduced depend, not only upon the specific system at hand, but also upon the experimental conditions used in performing the tests. The results of this approach lead to quantitative measures that have optimality features based upon the Cramer-Rao bound.