Calibration of Probability Density Function

The capability performance index (Cpk) is often used to measure the capability of the production process and to predict yield. However, this Cpk is only defined for the Gaussian distribution. At NXP Semiconductors an on-chip calibration technique is frequently used to reduce the effect of process variations. The resulting distribution has a much flatter peak than a Gaussian density and consequently the Cpk is significantly underestimated. In this chapter we propose two possible approaches to address accurate Cpk calculation for non-normal distributions. One approach is to use the so-called Generalized Gaussian distribution function and to estimate its defining parameters. We propose a numerical fast and reliable method for computing these parameters and a simple formula to calculate the Cpk value from these defining parameters. Another approach is to transform data as a way to deal with non-normal distributions. We show that both approaches significantly outperform the standard Cpk calculation for the non-normal distributions of interest.