Order statistics from non-identical exponential random variables and some applications
Computational Statistics & Data Analysis
Proceedings of the 39th annual Design Automation Conference
Finding a Small Set of Longest Testable Paths that Cover Every Gate
ITC '02 Proceedings of the 2002 IEEE International Test Conference
First-order incremental block-based statistical timing analysis
Proceedings of the 41st annual Design Automation Conference
Correlation-preserved non-gaussian statistical timing analysis with quadratic timing model
Proceedings of the 42nd annual Design Automation Conference
Variation-aware performance verification using at-speed structural test and statistical timing
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Statistical multilayer process space coverage for at-speed test
Proceedings of the 46th Annual Design Automation Conference
Statistical path selection for at-speed test
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Critical path selection for delay fault testing based upon a statistical timing model
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Robust Extraction of Spatial Correlation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Delay-fault test generation and synthesis for testability under a standard scan design methodology
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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Although order statistics have been studied for several decades, most of the results are based on the assumption of independent and identically distributed (i.i.d.) random variables. In the literature, how to compute the mth order statistics of n correlated random variables is still a problem. This article proposes a recursive algorithm based on statistical min/max operations to compute order statistics for general correlated and not necessarily identically distributed random variables. The algorithm has an O(mn) time complexity and O(m + n) space complexity. A binary tree-based data structure is further developed to allow selective update of the order statistics with O(nm2) time. As a vehicle to demonstrate the algorithm, we apply it to the path selection algorithm in at-speed testing. A novel metric multilayer process space coverage metric is proposed to quantitatively gauge the quality of path selection. We then show that such a metric is directly linked to the order statistics, and our recursive algorithm can thus be applied. By employing a branch-and-bound path selection algorithm with these techniques, this article shows that selecting an optimal set of paths for a multimillion-gate design can be performed efficiently. Compared to the state of the art, experimental results show both the efficiency of our algorithms and better quality of our path selection.