On evaluating and optimizing weights for weighted random pattern testing

Two problems in weighted random pattern testing are considered: 1) evaluating a set of input weights in terms of the amount of time required to generate a set of test patterns and 2) determining the optimal weights for a given test set. An exact expression for expected test length is derived as a function of input weights. Upper and lower bounds for expected test length are presented. Percentage error of approximation is expressed in terms of the bounds. Based on these results, algorithms are given for approximating expected test length. These algorithms allow the user to tradeoff accuracy and computational complexity. Experiments with some test sets are presented to illustrate the accuracy of the approximation technique. Expected test length is shown to be a convex function of input weights. A simple hill-climbing algorithm is defined to find optimal weights for a given set of test patterns. When hardware constraints, limiting the number of weights to be realized for each input bit, are also specified, a simple modification of the algorithm suffices in yielding optimal weights in the constrained space. Experiments with several circuits yield of the order of 96% to 99% reduction in expected test length over that achieved by current techniques.