Quantile-Based Metrics Applied to Process Performance

Commonly used metrics are usually evaluated under the assumption that the data have a more-or-less normal distribution. However, often the data are actually skewed. Some metric expressions evaluated under the normality assumption can contain substantial errors. Normality is a special case for distributions in general.

Standard statistical software packages will often automatically generate key quantile values sufficient to aid in expressions that properly characterize distributions and accurately evaluate performance metrics. This leads to better evaluation of incremental process improvements. This article shows how quantile-based metric evaluations can be applied to all process specification variables to assess their relative performance. Sample size calculations are also more accurate when quantile-based expressions are used.

Keywords:

• Quantile
• Normality
• Coefficient of skew
• Coefficient of total variation
• Coefficient of stability
• Process capability index
• OC curves
• Relative accuracy
• Variable skip-lot actual distribution sample size.

Additional information

Notes on contributors

Ben F. Houston

Ben F. Houston has been the factory statistician at Retractable Technologies, Inc. in Little Elm, Texas, since February 2002. He received B.S. and B.A. degrees in chemical engineering and mathematics, respectively, at Lamar University, in Beaumont, Texas, in 1961. Graduate degrees were an M. S. in chemical engineering from The University of Texas, Austin, Texas, in 1963 and a Ph.D. in statistics from Texas A&M University, College Station, Texas, in 1968. He has been an applied statistician in the chemical, petroleum, aircraft, and medical products industries for 35 years