Affiliation:
1. Key Laboratory of Advanced Theory and Application in Statistics and Data Science‐MOE, School of Statistics and Academy of Statistics and Interdisciplinary Sciences East China Normal University Shanghai China
2. School of Statistics and Management Shanghai University of Finance and Economics Shanghai China
Abstract
AbstractThe counting process has abundant applications in reality, and Poisson process monitoring actually has received extensive attention and research. However, conventional methods experience poor performance when shifts appears early and only small number of historical observations in Phase I can be used for estimation. To overcome it, we creatively propose a new online monitoring algorithm under the transfer learning framework, which utilizes the information from observations of additional data sources so that the target process can be described better. By making the utmost of the somewhat correlated data from other domains, which is measured by a bivariate Gamma distributed statistic presented by us, the explicit properties (e.g., posterior probability mass function, posterior expectation, and posterior variance) are also strictly proved. Furthermore, based on the above theoretical results, we design two computationally efficient control schemes in Phase II, that is a control chart based on the cumulative distribution function for large shifts and an exponentially weighted moving average control chart for small shifts. For a better understanding of the more practical applications and transferability matter, we provide some optimal values for parameter setting. Extensive numerical simulations and a case of skin cancer incidence in America verify the superiorities of our approach.
Funder
National Natural Science Foundation of China
National Key Research and Development Program of China