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Using linear regression analysis and the Gibbs sampler to estimate the probability of a part being within specification
Author(s) -
Stefano Brenda
Publication year - 1998
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/(sici)1099-1638(199807/08)14:4<237::aid-qre187>3.0.co;2-z
Subject(s) - semiconductor device fabrication , computer science , regression analysis , measure (data warehouse) , linear regression , set (abstract data type) , product (mathematics) , reliability engineering , industrial engineering , wafer , mathematics , data mining , engineering , machine learning , electrical engineering , geometry , programming language
‘In‐line’ or ‘process’ specification limits are used in semiconductor manufacturing processes to provide some level of assurance for the functional performance of product measured at functional testing or probe. However, these limits are not always set in a rigorous manner and may not prove to be an adequate in‐line screening method for good and bad circuits. In this paper an alternative way for engineers to release equipment or product for production will be explored. This approach uses a probability measure to predict how likely it is that the device will be good at functional testing based upon its in‐line measured characteristic. This probability is obtained using the predictions from a linear regression equation. The Gibbs sampler is then used to construct a 100(1−α)% 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 ® system for personal computers can be used to implement this technique. © 1998 John Wiley & Sons, Ltd.