Test data analytics — Exploring spatial and test-item correlations in production test data

Abstract

The discovery of patterns and correlations hidden in the test data could help reduce test time and cost. In this paper, we propose a methodology and supporting statistical regression tools that can exploit and utilize both spatial and inter-test-item correlations in the test data for test time and cost reduction. We first describe a statistical regression method, called group lasso, which can identify inter-test-item correlations from test data. After learning such correlations, some test items can be identified for removal from the test program without compromising test quality. An extended version of this method, weighted group lasso, allows taking into account the distinct test time/cost of each individual test item in the formulation as a weighted optimization problem. As a result, its solution would favor more costly test items for removal from the test program.We further integrate weighted group lasso with another statistical regression technique, virtual probe, which can learn spatial correlations of test data across a wafer. The integrated method could then utilize both spatial and inter-test-item correlations to maximize the number of test items whose values can be predicted without measurement. Experimental results of a high-volume industrial device show that utilizing both spatial and inter-test-item correlations can help reduce test time by up to 55%.

Bayesian model fusion: Enabling test cost reduction of analog/RF circuits via wafer-level spatial variation modeling

“…Similar to VP [15]- [20], our proposed BMF framework models the wafer-level spatial variation in frequency domain based on DCT:…”

“…To this end, a number of statistical algorithms and tools, such as virtual probe (VP) [15]- [20] and Gaussian process (GP) [21]- [24], have been developed to model the spatial variation at wafer level. These methods rely on several assumptions that are generally applicable in practice.…”

“…In this case, we only need to measure a small number of dies from a wafer and then use the measurement results to predict the test items of other dies on the same wafer, thereby significantly reducing the test cost. Furthermore, it has been demonstrated that both the spatial correlation and the inter-test-item correlation can be integrated into a unified statistical framework for test cost reduction [20], [24].…”

3-D Probe: Low-Cost Variation Modeling Using Intertest-Item Correlations

“…In silicon testing, multiple items are tested on the same die or wafer, and the results are correlated strongly between test-items because each item is a function of process parameters often shared. In [4], a subset of test items are measured and results of other test items are predicted using a different algorithm from CS. In other words, the method of [4] is not integrated into the CS framework and moderate intertest-item correlations are not utilized.…”

“…In [4], a subset of test items are measured and results of other test items are predicted using a different algorithm from CS. In other words, the method of [4] is not integrated into the CS framework and moderate intertest-item correlations are not utilized. Also, it aims to reduce the test time, not to improve the quality of the prediction.…”