Multidimensional analog test metrics estimation using extreme value theory and statistical blockade

Abstract

The high cost of testing certain analog, mixed-signal, and RF circuits has driven in the recent years the development of alternative low-cost tests to replace the most costly or even all standard specification tests. However, there is a lack of solutions for evaluating the parametric test error, that is, the test error for circuits with process variations, resulting from this replacement. For this reason, test engineers are often reluctant to adopt alternative tests since it is not guaranteed that test cost reduction is not achieved at the expense of sacrificing test quality. In this paper, we present a technique to estimate the parametric test error fast and reliably with parts per million accuracy. The technique is based on extreme value theory and statistical blockade. Relying on a small number of targeted simulations, it is capable of providing accurate estimates of parametric test error in the general scenario where a set of alternative tests replaces all or a subset of standard specification tests.

Adaptive Learning Based Importance Sampling for Analog Circuit DPPM Estimation

“…Then, we choose the initial training set size to be one tenth of the maximum training size (500), shown in the third column of Table 1. Model assessment and relearning rate is calculated using (7). The fourth column shows relearning rates.…”

“…In [6], we used a uniform learning approach, where all system performance parameters of interest were learned equally. A method [7] was published later that uses a similar idea using uniform learning approach. However, each parameter has a different level of difficulty of learning, and a uniform learning approach typically results in excessive simulation time.…”

Estimation of Analog/RF Parametric Test Metrics Based on a Multivariate Extreme Value Model

“…As future work, we expect to develop the MGPD-II model beyond two dimensions which will allow a study of the effet of the number of dimensions in the estimation error. Also, we will be able to compare the use of the MGPD-II approach described here with the technique proposed in [8], where the multidimensional problem has been transformed into a onedimensional problem with the use of a univariate EVT model. This comparison could be done in terms of the number of extreme random variables, the test metrics estimation error and the number of extreme circuit samples required.…”

“…However, it provides a population of extreme circuits from which test metrics can be computed using an estimation of the tail density following a univariate Extreme Value Theory (EVT) model [5] [6] [7]. In [8], a multidimensional problem for test metrics estimation is considered using EVT although it is transformed to a one-dimensional problem and a univariate model is used.…”

Fast Monte Carlo-Based Estimation of Analog Parametric Test Metrics

“…Thus, our method provides the necessary data for evaluating alternative test sets in terms of both fault coverage and yield coverage. The statistical blockade technique was also used in [11] and [28] for generating the data to fit mathematical models for the fault coverage and yield coverage metrics based on extreme value theory and in [29] for enhancing the training set of a classifier used to differentiate functional from faulty circuits.…”