**A. Appendix**

The thresholds for the linear model fitted

sqrt hc ð Þ� ð Þ scale <sup>þ</sup> shape <sup>þ</sup> log scale ð Þþ log shape ð Þ <sup>2</sup> þsqrt shape ð Þ ∗ scale

The multiply R-squared for all these models is equal to 1 corrected to the sixth decimal place. The square of the fitted values for these models provides an starting estimate of the threshold for the respectively in-control ARL of 100, 200, 300, or 400. This can be further revised using simulation (**Table A1**).


#### **Table A1.**

*Fitted models for predicting the thresholds when the scale parameter is between 0.02 and 0.046 (inclusive) and the shape parameter ranges from 0.6 to 1.4 (inclusive) for the EWMA statistic used in this chapter with smoothing constant α = 0.1.*

**Author details**

**195**

Ross Stewart Sparks\* and Hossein Hazrati-Marangaloo

\*Address all correspondence to: ross.sparks@data61.csiro.au

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Exponentially Weighted Moving Averages of Counting Processes When the Time between Events…*

*DOI: http://dx.doi.org/10.5772/intechopen.90873*

Data61, CSIRO, Sydney, NSW, Australia

provided the original work is properly cited.
