Aggregation levels when the time between events is Weibull distributed
- Quality Engineering
- April 2021
- Volume 33 Issue 2
- pp. 348-360
- Sparks, Ross, Hazrati-Marangaloo, Hossein
The copyright of this article is not held by ASQ.
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.