Statistical Test Compaction Using Binary Decision Trees

Abstract

In this work, we use binary decision trees (BDTs) for statistical test compaction, because they have the following properties. First, decision trees require no assumption on the type of correlation (if any) that exists between T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">red</sub> and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kept</sub> . This makes it possible to derive a more accurate representation of F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kept</sub> ) from the collected test data. Also, deriving a decision tree model for F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kept</sub> ) simply involves partitioning the T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kept</sub> hyperspace into hypercubes, which is a polynomial time process of complexity O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> timesk <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), where n is the number of tests in Tkept, and k is the number of parts in the collected data. Therefore, the computation time required for creating a decision tree can be considerably less than the time required for training a neural network. Our Proposed methodology can eliminate an expensive mechanical test for a commercially available accelerometer with little error. Moreover, it's possible to completely eliminate the error (for failing parts) using specification guard banding. But the same result could not be achieved for the equivalent mechanical test executed at an elevated temperature. Techniques such as specification guard banding and drift removal can reduce error, but more research is needed. More importantly, techniques are needed for incorporating this and similar methodologies into a production test flow