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 distr...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 ARLo, 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.展开更多
基金Supported by Foundation of Ministry of Education of China(13YJC910005,13YJC910010,12YJA910005)Zhejiang Provincial Natural Science Foundation of China(LY16G020003)+2 种基金the Philosophy and Social Science Research Project in Zhejiang Province of China(13NDJC055YB)the National Natural Science Foundation of China(11371322)the Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)
文摘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 ARLo, 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.
