Laneyho regulační diagramy

Abstract

The Laney p'-control chart addresses the limitations of traditional p-charts by adding an adjustment factor, which can reflect true process variability more effectively to enable better monitoring of real-world processes under overdispersion or underdispersion. This study compares the performance of traditional p-charts with Laney p'-charts under real-life scenarios through Monte Carlo simulations. Key parameters such as sample size, number of samples, and probabilities of defects were varied across different scenarios—including stable processes, isolated disturbances, gradual trends, and both periodic and singular cyclical disruptions. The ability of each chart to detect the true process shifts (true-positive probability) vs. false alarms (false-positive probability) was then measured using Western Electric rules. Results showed that traditional p-chart performed efficiently under nearly ideal binomial conditions, i.e., in detecting isolated disturbances. In contrast, Laney’s p'-charts charts performed better in scenarios exhibiting significant overdispersion, particularly in detecting trends and cyclical disturbances. This thesis highlights the importance of selecting appropriate control chart types depending on the nature of the process, suggesting Laney’s approach combined with Western Electric rules for process monitoring under real conditions.

The Laney p'-control chart addresses the limitations of traditional p-charts by adding an adjustment factor, which can reflect true process variability more effectively to enable better monitoring of real-world processes under overdispersion or underdispersion. This study compares the performance of traditional p-charts with Laney p'-charts under real-life scenarios through Monte Carlo simulations. Key parameters such as sample size, number of samples, and probabilities of defects were varied across different scenarios—including stable processes, isolated disturbances, gradual trends, and both periodic and singular cyclical disruptions. The ability of each chart to detect the true process shifts (true-positive probability) vs. false alarms (false-positive probability) was then measured using Western Electric rules. Results showed that traditional p-chart performed efficiently under nearly ideal binomial conditions, i.e., in detecting isolated disturbances. In contrast, Laney’s p'-charts charts performed better in scenarios exhibiting significant overdispersion, particularly in detecting trends and cyclical disturbances. This thesis highlights the importance of selecting appropriate control chart types depending on the nature of the process, suggesting Laney’s approach combined with Western Electric rules for process monitoring under real conditions.