Construction of Tolerance Interval Based on Small Data Sets

• Activity Number: 372
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Yuanyuan Duan* and Lanju Zhang and Jorge Quiroz
• Companies: AbbVie and AbbVie and AbbVie Pharmaceutical Research & Development
• Keywords: Tolerance Interval ; Sample Size ; Normality Test ; Nonparametric ; Skewness

Abstract

A tolerance interval (TI) is statistical interval which, with a certain confidence level, includes at least a proportion p of the population. TI is an important tool often utilized in manufacturing, engineering, and quality control. A closely related problem faced by scientists, engineers and researchers is the selection of intervals for a set of observations from an unknown population. Popular software used by scientists and engineers such as Minitab provides both normal and nonparametric TI and the selection is based on a normality test. In practice, data are usually obtained from a very small sample size such that the distribution test, including the normality test, have very limited power and thus are not reliable. In this study, we compared the performance of normal TI, nonparametric TI, and adaptive TI based on normality test. We simulate data from several different distributions (symmetrical and right/left skewed) with different sets of parameters. The result shows that with a small sample size, normal TI always performs better than nonparametric and adaptive TI; and the performance of normal TI may depend on the skewness of data.