Simultaneous monitoring of multivariate time between events and their magnitude using multivariate marked Hawkes point process

Abstract

ABSTRACTIn this paper, monitoring the time between events is discussed. The control chart of the time between events in multivariate mode discusses the conditions under which the Hawkes point process generates the time data. It is also necessary to consider that monitoring time data individually and regardless of the magnitude of an event is not very important. Therefore, in addition to monitoring time data, it is also essential to monitor the magnitude of an event. Because of that, the magnitude of each event is considered along with monitoring the time between multivariate events through data generation with the multivariate marked Hawkes point process. Three statistics are presented for simultaneous monitoring of the time between events and the magnitude. A Max-EWMA, two single EWMA that each of which are used to monitor TBE and magnitude (TSEWMA), and the third statistic, derived from existing literature, is a Shewhart statistic that has been integrated into an EWMA statistic framework (EWMA-Z). These charts have been used for a case study and compared according to different shifts.KEYWORDS: High quality processStatistical Process Monitoring (SPM)multivariate time between eventstime between events and magnitudeHawkes point processAverage Run Length (ARL) Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationNotes on contributorsMohammadreza Mirzaei NovinMohammadreza Mirzaei Novin is a graduated M.Sc. in Industrial Engineering from Shahed University. His research interest is statistical process monitoring.Amirhossein AmiriAmirhossein Amiri is a Full Professor at Shahed University in Iran. He holds a BS, MS, and PhD in Industrial Engineering from Khajeh Nasir University of Technology, Iran University of Science and Technology, and Tarbiat Modares University in Iran, respectively. He is currently serving as the Vice Chancellor of Education in the Faculty of Engineering at Shahed University in Iran and is a member of the Iranian Statistical Association. His research interests encompass statistical process monitoring, profile monitoring, and change point estimation. He has published many papers in the field of statistical process control in esteemed international journals such as European Journal of Operational Research, Quality and Reliability Engineering International, Communications in Statistics, Computers & Industrial Engineering, Journal of Statistical Computation and Simulation, Soft Computing and more. In 2011, he co-authored a book titled ”Statistical Analysis of Profile Monitoring” published by John Wiley and Sons.