Aggregation levels when the time between events is Weibull distributed

Abstract

Practical applications always require an assessment of an aggregation process that is best for early detection of any outbreak of events including sales, warrantee claims or disease outbreaks. This article provides a means of deciding on the level of temporal aggregation that best suits the needs of whoever aims to monitor a process or a service. This article aims to achieve a practical aggregation level for monitoring events when the in-control time between events (TBE) in the targeted process or service follows a non-homogeneous Weibull distribution. We analyze the impact of various aggregation levels on early detection of outbreaks with different magnitudes using several monitoring schemes including an adaptive exponentially weighted moving average (EWMA) plan and several simultaneous EWMA plans with differing amounts of temporal memory for TBE data. We also consider monitoring the related counting processes to address the problem of deciding on the temporal aggregation level. To the best of our knowledge, the effect of various levels of temporal aggregation on detecting outbreaks in TBEs, when they are Weibull distributed, is not studied thoroughly.

Keywords:

• Adaptive EWMA
• Phase I analysis
• statistical process control
• time between events
• Weibull distribution

Additional information

Notes on contributors

Ross Sparks

Ross Sparks is a Statistician with over 40 years research and teaching experience at universities and research at CSIRO. He is currently based in Data 61, CSIRO, Sydney, Australia and been with CSIRO for over 29 years. His role is in leading strategic and tactical research projects in Data61, CSIRO in the area of multivariate spatio-temporal monitoring and spatio-temporal modeling. He has published over 100 papers in refereed journals and conferences, 12 book chapters, 22 papers in conference proceedings and 10 articles in trade magazines. While working at CSIRO, he has carried out research contract work for most Australian large companies and several international companies operating within Australia. Ross has lectured at the University of Natal, University of Cape Town and University of Wollongong in Statistics and Applied Mathematics before joining CSIRO Australia. He has made a number of research contributions in the areas of (multivariate) process monitoring, spatio-temporal modeling and the handling of (partially) missing data. Specifically, he has contributed to topics in the variable selection in multivariate regression models, outlier detection in regression models, model validation and assessment, quality control and assurance, cluster analysis, dimension reduction methods, and disease surveillance.

Hossein Hazrati-Marangaloo

Hossein Hazrati-Marangaloo is currently a PhD Student in Industrial Engineering at Iran University of Science and Technology in Tehran, Iran. He holds a BSc degree and a MSc degree in Industrial Engineering from Isfahan University of Technology (2012) and K.N. Toosi University of Technology (2014), respectively. He has also been working with CSIRO’s Data61 during 2020. His research interests include modeling and monitoring relational (network) data structures, applications of machine learning to high-dimensional data analysis, and statistical quality control.