Statistical Test Compcation for Non-Digital Devices Using Binary Decision Trees

Sounil Biswas

Project

To reduce test cost, we propose to eliminate tests whose pass/fail results can be predicted using measurements from other "kept" tests (i.e., specification tests that cannot be accurately predicted) [1]. Tests that can be accurately predicted are called redundant tests and the process of identifying them using statistical interpretation of test data is called statistical test compaction. In this work, we use decision trees [2] for statistical test compaction. Decision trees are especially advantageous since no assumption about the type of correlation that may exist between the redundant and kept tests is required. As a result, a more accurate prediction model for redundant tests can be derived (in theory) from collected test data. However, statistical test compaction applied to a commercial part requires a level of accuracy that cannot be achieved with a simple decision tree. We therefore employ several enhancements that adjust the data and the decision tree to improve prediction accuracy. An overview of our methodology is shown in Figure 1. The decision tree model is derived test measurements (called the training data set) is filtered (for example, parts failing kept tests are removed), treated for outlier elimination and drift removal, and transformed with principle components. The specification boundary of a redundant test under consideration is perturbed to create two data sets; one with tightened boundaries and another with relaxed boundaries. This is a form of specification guard banding. These two data sets are used to construct two separate decision tree models for the suspect redundant test. If the predictions from the two models agree, we have higher confidence in the prediction and accordingly classify the part as passing or failing. However, if the predictions disagree, the part is relegated to a guard-band region where further analysis is deemed necessary to determine the pass/fail status of the part with respect to the redundant test.

Selected Highlights

To demonstrate viability, we analyzed test data from a high volume production MEMS accelerometer. Test measurements from over 70,000 parts are utilized; 80% of the parts were used for constructing the decision tree and 100% of the data was used to quantify prediction accuracy. We attempted to eliminate two mechanical tests (i.e., tests aimed at checking the mechanical portions of the accelerometer). The tradeoff between prediction accuracy and the percentage of guard banded parts is shown in the ROC (Receiver Operating Characteristics) plot of Figure 2. From Figure 2, we observe that prediction accuracy can be improved using guard banding. Specifically, to improve the prediction accuracy for failing accelerometers to 95% for the two tests requires 32% and 37%, respectively, of all fabricated parts to be guard banded. Our current work is focused on reducing the number of guard banded parts while simultaneously improving prediction accuracy.