Control charts for the Pareto distribution

• Published in: Applied Mathematics-A Journal of Chinese Universities Vol. 30; no. 4; pp. 379 - 396
• Main Authors: Guo, Bao-cai, Wang, Bing-xing
• Format: Journal Article
• Language: English
• Published: Hangzhou Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.12.2015
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; average run length; Pareto distribution; process control; unbiased control chart; 90B25; 62N05
• ISSN: 1005-1031; 1993-0445
• DOI: 10.1007/s11766-015-3355-y

The Pareto distribution plays an important role in various areas of research. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARL 0 , which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.