Improved Control Charts for Attributes

Abstract

The classic control charts for attribute data (p-charts, u-charts, etc.,), are based on assumptions about the underlying distribution of their data (binomial or Poisson). Inherent in those assumptions is the further assumption that the “parameter” (mean) of the distribution is constant over time. In real applications, this is not always true (some days it rains and some days it does not). This is especially noticeable when the subgroup sizes are very large. Until now, the solution has been to treat the observations as variables in an individual's chart. Unfortunately, this produces flat control limits even if the subgroup sizes vary. This article presents a new tool, the p′-chart, which solves that problem. In fact, it is a universal technique that is applicable whether the parameter is stable or not.

Keywords:

• Attribute control chart
• p-chart
• u-chart
• Individuals chart
• Batch-to-batch variation

Acknowledgments

My thanks to Larry Aft (Southern Polytechnic State University), Forrest Breyfogle (Smarter Solutions, Inc.), Roger Hoerl (General Electric), Keith Johnson (BellSouth), Thomas Pyzdek, John Ramberg (University of Arizona), Donald Wheeler (SPC, Inc.), and William Woodall (Virginia Polytechnic Institute and State University) for their helpful suggestions and encouragement in this work.