D4686-91 – Standard Test Method Technical Guide

The ASTM D4686-91 (Reapproved 2003) standard provides a practical framework for identifying common frequency distributions and selecting appropriate data transformations. Published under the jurisdiction of Committee D13 on Textiles, this guide serves as a rudimentary key for practitioners needing to stabilize variance or normalize skewed data for further analysis.

📊 Guide Overview and Scope

This guide is designed for applied use rather than rigorous theoretical derivation. It focuses on the most common distributions encountered in textile testing and quality control: the Binomial, Poisson, and Normal distributions. The terminology aligns with ASTM E 456 and D 4392, ensuring consistency across related standards. For definitive distribution identification, users are directed to advanced procedures such as those described by Shapiro (ASQC Basic References in Quality Control, Vol. 3).

📈 Core Distributions and Probability Functions

Three cornerstone distributions are mathematically defined in the standard. The Bernoulli distribution is treated as synonymous with the binomial distribution. The following table summarizes their probability functions and key parameters, forming the basis for the identification key provided in Section 5.