A method and system is provided for detecting at risk structures due to mask overlay that occur during lithography processes. The method can be implemented in a computer infrastructure having computer executable code tangibly embodied on a computer readable storage medium having programming instructions. The programming instructions are operable to obtain a simulation of a metal layer and a via, and determine a probability that an arbitrary point (x, y) on the metal layer is covered by the via by calculating a statistical coverage area metric followed by mathematical approximations of a summing function.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method implemented in a computer infrastructure having computer executable code tangibly embodied on a computer readable storage medium having programming instructions operable to: obtain a simulation of a metal layer and a via; and determine a probability that an arbitrary point (x, y) on the metal layer is covered by the via by calculating a statistical coverage area metric followed by mathematical approximations of a summing function. 2. The method of claim 1, wherein the mathematical approximations of the summing function includes engineering approximations to detect structures at risk of overlay error. 3. The method of claim 1, wherein the statistical coverage area metric is computed using a Gaussian distribution for an overlay of the via. 4. The method of claim 3, wherein the statistical coverage area metric is based on equi-probability contours of the via. 5. The method of claim 1, wherein the via can be any shape of choice. 6. The method of claim 5, wherein the shape of the via is a circular shape. 7. The method of claim 1, wherein the steps are of claim 1 are integrated into a rule checking system. 8. The method of claim 1, wherein the statistical coverage area metric comprises determining whether the arbitrary point (x, y) on the metal layer is inside or outside of the via. 9. A system implemented in hardware, comprising an overlay aware optical rule checking module configured to determine a probability that an arbitrary point (x, y) on a metal layer is covered by a via by calculating a statistical coverage area followed by a summing factor. 10. The system of claim 9, wherein the summing factor includes a mathematical approximation. 11. The system of claim 10, wherein the mathematical approximation is a Gaussian distribution. 12. The system of claim 9, wherein the summing factor is provided by an exact distribution. 13. A computer program product comprising a computer readable hardware storage device having readable program code stored on the computer readable storage device, the program code comprising: program code to obtain a simulation of a metal layer and a via; and program code to determine a probability that an arbitrary point (x, y) on the metal layer is covered by the via by: calculating a statistical coverage area metric; and using mathematical approximations of a summing function, computed using a Gaussian distribution for an overlay of the via, wherein the statistical coverage area metric is based on equi-probability contours of the via which are summed after multiplying each area by its probability of being inside or outside of the coverage area, and wherein the arbitrary point (x, y) is defined by an x coordinate and a y coordinate in a cartesian coordinate system. 14. The computer program product of claim 13, wherein the at least one component is operable to determine whether the arbitrary point (x, y) on the metal layer is inside or outside of the via.