Distribution Fitting of Skewed Data: An Industrial Case Study

• Activity Number: 206
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Thomas J. Bzik*+
• Companies: Air Products and Chemicals
• Keywords: Distribution fitting ; Statistical standards ; Quantile Estimation ; Right Skew ; Truncated distributions

Abstract

This discusses the results and theoretical implications of an extensive industrial case study that pitted distribution fitting versus alternative statistical methodologies. This application originated in the electronics industry which frequently deals with trace contamination. Observed trace contaminant distributions are almost always non-normal in distribution and often demonstrate substantial right skew. Additionally these distributions may sometimes have substantial observed truncation on the left side due to detection limit issues.

This particular industrial application was primarily focused on estimation of a relatively extreme quantile on of the right hand side of these highly non normal (and sometimes truncated) distributions. It was also focused on testing for when a given estimated upper tail quantile may have changed over time. While the best methodology found via testing with extensive industrial product data was not classical distribution fitting, there were many interesting lessons learned. This effort ultimately culminated in the development of an industrial standard, SEMI C64-0308 - SEMI Statistical Guidelines for Ship to Control.