Estimating manufacturing yield by means of Jacobian of transformation

It has been known for many years that the Jacobian of transformation method could, at least in principle, be applied to the yield estimation problem. The fact that it has not, in the past, been applied to this problem is because its implementation requires the determination of multiple solutions to nonlinear equations. Recently, several methods of finding multiple solutions to nonlinear equations have appeared in the literature, and in this paper it is shown how these methods can be used in conjunction with the Jacobian of transformation method in order to estimate manufacturing yield. As a technique for yield calculation, the method is found to be generally inferior to Monte Carlo simulation. Some approaches to improving the efficiency of the technique are described, but the improvements do not allow the technique to approach the efficiency of Monte Carlo. The technique does, however, have attributes which indicate that it could be a useful tool in statistical design. These attributes are discussed in the paper.