Circuit Rare-Failure Prediction Using Modified Sigma Scaling
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Solution Overview
Problem
Existing scaled sigma sampling (SSS) approaches struggle to accurately predict rare failure events in circuits due to significant errors in extrapolated failure probabilities, especially for low-probability events like 6-sigma and beyond, despite using curve-fitting and Monte Carlo simulations.
Innovation Solution
A modified SSS approach introduces an additional term (g·s) in the probability scaling relation (ln Pf(s) = a + b·ln s + c·s + g·s) to improve accuracy in predicting rare failure probabilities, utilizing a distribution enlargement ratio s and fitting parameters a, b, and g.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard Monte Carlo simulation is used to predict rare failure events, then the method is simple to implement, but the prediction accuracy is insufficient for low-probability events
Solution Approach 1:
The patent modifies the probability scaling relation by adding an additional term (g·s) to the equation ln Pf(s) = a + b·ln s + c·s + g·s. This parameter change in the mathematical model improves the accuracy of predicting rare failure probabilities by better capturing the relationship between the distribution enlargement ratio and failure probability, especially for 6-sigma and beyond events
Solution Approach 2:
The patent performs preliminary curve-fitting to determine the fitting parameters (a, b, c, and g) before using the scaled sigma sampling method. This preliminary action establishes the optimized probability scaling relation that will be used for subsequent predictions, ensuring accuracy is built into the methodology from the start rather than attempting corrections later
2Productivity
If distribution enlargement ratio is increased to improve sampling efficiency, then more failure events are captured, but extrapolation errors increase significantly
Solution Approach 1:
The patent uses curve-fitting with multiple data points at different distribution enlargement ratios to determine the fitting parameters. This feedback mechanism allows the model to learn from multiple sampling scenarios and adjust the probability scaling relation accordingly, reducing extrapolation errors even when individual sampling runs use large enlargement ratios
Solution Approach 2:
The patent combines multiple sampling results at different distribution enlargement ratios into a unified probability scaling relation. By composite the information from multiple sampling scenarios and fitting them to the extended model, the method achieves both sampling efficiency and extrapolation accuracy that neither approach could achieve alone
Data Source
AI summary
A computer-implemented method that includes identifying statistical parameters in a model set that affects a given figure of merit for a circuit. The method further includes selecting a set of distribution enlargement ratio values. The method further includes, for each of the set of distribution enlargement ratio values: for each identified statistical parameter, maintain a nominal value and increase a standard deviation; generating sets of random samples using standard deviation enlarged statistical distributions and performing a Monte Carlo simulation with N runs; and among N figure-of-merit values, count the number of figure-of-merit values that fall into a failure region, and calculate a failure probability value of the Monte Carlo run with N events. The method further includes fitting a logarithm of failure probability values for the failure region to a curve defined by a probability scaling relation and extrapolating the curve to predict a rare failure probability for the circuit.