Effects of Mixture Distributions on Phase I and Phase II Performance of Shewhart Style Charts

• Activity Number: 421 - Contributed Poster Presentations: Quality and Productivity Section
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Bryce Whitehead* and Austin Brown
• Companies: University of Northern Colorado and University of Northern Colorado
• Keywords: mixture; quality; assumptions

Abstract

For many years, control charts have been utilized to monitor processes, improve quality, and increase profitability. However, most classical control charting techniques assume that the data follow some known, single, parametric distribution, usually the normal distribution. In some instances, data may follow a mixture distribution, thus the performance of the classical control charting techniques may deteriorate. For example, a manufacturer may order different inputs from several different companies. However, these inputs may not necessarily have the same distribution. If the mixture distribution is not taken into consideration during Phase I or Phase II monitoring, then erroneous conclusions may be drawn. This study examines the performance of classical Shewhart control charts when the data follows a mixture distribution of two normal distributions with identical variances, but different means. Different combinations of mixture proportions, of the two normal distributions, as well as different magnitudes of mean differences are considered. Discussion and recommendations are also given.