Statistical process monitoring of correlated binary and count data using mixture distributions

Statistical Process Monitoring (SPM) is used quite extensively in semiconductor manufacturing, particularly in the areas of yield enhancement and contamination (particles) reduction. These variables are typically measured at the Integrated Circuit (IC)-level, and then summarized to the wafer and lot levels. Due to the batch nature of semiconductor processing, ICs residing in the same wafer are normally processed simultaneously. This tends to induce a positive correlation among the measurements taken at the IC level. It is known that within subgroup correlation affects the performance of control charts. In particular, it tends to induce higher than expected false alarm rates. In this paper we present 3-sigma Shewhart charts, for both yield and particle data, and CUSUM monitoring charts for yield data. These charts use mixture distributions to take into account the inherent correlation in the data; thus reducing the false alarm rate. A SAS/AF(R) application has been developed to deploy the use of our SPM schemes. The application allows the engineers and analysts to seamlessly: (1) estimate the parameters of these mixture distributions (beta-binomial for yield data and negative binomial for particle data) using SAS/IML(R) optimization routines, and (2) produce the corresponding customized control charts using SAS/GPLOT(R) and SAS/SHEWHART(R).