Stochastic analysis process optimization for integrated circuit design and manufacture

A method comprising:

• defining a hierarchical relationship between a lowest-level system and a highest level system;
• pre-generating an analytic model comprising one or more SAP models to predict system behavior for the lowest-level system;
• and
• recursively using the one or more lowest level SAP models to build the highest level system SAP model.

A system comprising:

• means for receiving an input distribution of one or more parameters of a pre-defined circuit and mutual correlations between the parameters;
• means for normalizing the parameter distributions and decomposing the mutual correlations to generate standardized independent parameter sets;
• means for generating a specific set of input values for sampling of the pre-defined circuit based on the standardized independent parameter sets;
• means for performing pre-defined circuit sampling on the specific set of input values to generate pre-defined circuit output values;
• means for performing orthogonal polynomial fitting on the specific set of input values, the pre-defined circuit output values, and the standardized independent parameter set to generate an SAP model;
• and
• means for using the SAP model to generate an output distribution of the pre-defined circuit.

The system 17 further comprising:

• means for defining the number of the fitting order of orthogonal polynomials;
• means for obtaining the number of parameters;
• means for selecting the higher probability roots of the orthogonal polynomials;
• and
• means for converting the higher probability roots to the specific set of input values for sampling of the pre-defined circuit.