USING LINEAR-REGRESSION ANALYSIS AND THE GIBBS SAMPLER TO ESTIMATE THE PROBABILITY OF A PART BEING WITHIN SPECIFICATION

'In-line' or 'process' specification limits are used in semiconductor manufacturing processes to provide some level of assurance for the fun ctional performance of product measured at functional testing or probe . However, these limits are not always set in a rigorous manner and ma y not prove to be an adequate in-line screening method for good and ba d circuits. In this paper an alternative way for engineers to release equipment or product for production will be explored. This approach us es a probability measure to predict how likely it is that the device w ill be good at functional testing based upon its in-line measured char acteristic. This probability is obtained using the predictions from a linear regression equation. The Gibbs sampler is then used to construc t a 100(1 - alpha)% credible band around the predicted probabilities. These techniques will be demonstrated using data from a semiconductor wafer anneal process. Also, it will be shown how the SAS(R) system for personal computers can be used to implement this technique. (C)1998 J ohn Wiley & Sons, Ltd.