Adaptive CUSUM for Steady State Normal Data

This chapter deals with monitoring plans that exploit temporal predictable trends by adjusting the cumulative sum (CUSUM) plan to be efficient for their early detection. The adjustment involves changing the amount of memory the chart retains to detect persistent changes in location early. The focus is on steady-state situations when either the shift size is known in advance or when it is unknown. Several options are explored using simulation studies, and an example of application is considered

Exponentially Weighted Moving Averages of Counting Processes When the Time between Events Is Weibull Distributed

There are control charts for Poisson counts, zero-inflated Poisson counts, and over dispersed Poisson counts (negative binomial counts) but nothing on counting processes when the time between events (TBEs) is Weibull distributed. In our experience the in-control distribution for time between events is often Weibull distributed in applications. Counting processes are not Poisson distributed or negative binomial distributed when the time between events is Weibull distributed. This is a gap in the literature meaning that there is no help for practitioners when this is the case. This book chapter is designed to close this gap and provide an approach that could be helpful to those applying control charts in such cases