**Author details**

**A. Appendix**

**In-control ARL**

sqrt (shape)

scale:log (scale)

scale:log (shape)

shape:log (scale)

shape:log (shape)

log(scale): log(shape)

scale:sqrt (shape)

**Table A1.**

**B. Appendix**

**194**

*smoothing constant α = 0.1.*

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>

*Quality Control - Intelligent Manufacturing, Robust Design and Charts*

400. This can be further revised using simulation (**Table A1**).

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

(Intercept) 55.27965623580790 14.50063556867970 35.4751774678155 1.62174314752660 scale �626.65874427126700 �750.65355682164500 �853.0616160220110 �666.97214806267300 shape 54.99181051902600 6.91623162316955 26.9351743566771 �2.52567948128196 log(scale) �8.64992403297571 �8.66215508213318 �8.6812026091707 �8.66460977364899 log(shape) 16.34706116414410 6.99770664515964 12.4345299969720 3.32335746029235

scale:shape �224.25112834314800 �263.89677049308800 �301.0663396807370 �236.64136324217100

**100 200 300 400**

�132.57740079984300 �43.82444799901730 �84.7132341475612 �21.35094544552350

�69.61113437236530 �70.49847595504570 �69.8492890948244 �69.64522997112020

�160.56646815370100 �201.15404356846600 �235.8054471494210 �174.62069894929300

2.19016501325625 2.17689719954047 2.2105503473413 2.20073389465297

�7.97657987867648 4.93365063336234 0.1464213924397 6.88699339675467

�3.19688371718715 �3.19951671299892 �3.1780225086612 �3.20431683519426

795.53717813564600 957.71276755290300 1098.4086506150800 848.24798318601300

*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*

þsqrt shape ð Þ ∗ scale

Ross Stewart Sparks\* and Hossein Hazrati-Marangaloo Data61, CSIRO, Sydney, NSW, Australia

\*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, provided the original work is properly cited.
