Monte Carlo (MC) techniques are widely applied to check a design on its robustness and for estimating the production yield of integrated circuits. Using standard random MC and the sample yield for estimation, a very large number of samples is required for accurate verification, especially if a high yield is desired. This can make MC extremely time consuming, but if the data follows a normal Gaussian distribution a much faster yield prediction is possible by using the well-known C-PK method. We extended this specification-distance-based scheme for the far more difficult general non-normal case by three different means, ending up in a new generalized process capability index named C-GPK. First, we apply parametric modeling only to the specification-sided distribution part. This way any difficulties in distribution parts that actually have little yield impact do not degrade the model fit anymore. Second, to improve the parametric model we introduce a new tail parameter t. Third, to allow modeling of difficult asymmetrical, multimodal or flat distributions we also introduce a new reference location parameter instead of using the mean. An advantage of improving MC this way is that-in opposite to many other MC enhancements (like importance sampling)-the performance of the C-GPK is not negatively impacted by design complexity. We described the formulation of the C-GPK and derived confidence intervals using an advanced bootstrap scheme. We verified the performance against the sample yield and C-PK for a representative set of distributions, including real production data and MC data from the design of a CMOS operational amplifier and other circuits.