By systematically varying CAdj and COpp (Equation \ref{eq:Copp}) along with input variance populations with the same descriptive statistics (mean and standard deviation) are produced but consist of very different individuals. Note that some populations are not producible statistically, for example CAdj and COpp can not both be equal to negative one as no such statistical distribution can exist. For each individual the surface stress profile, true mean stress, and two rapid splitting test values are now known, allowing for comparisons of how well different tests predict each other and the true mean value. Further more, some populations can be removed as unlikely, and from previous experimental work some can be removed not fitting previous experimental evidence. Note plotting and interpolation between the resulting points was conducted in \cite{Team2013} using \cite{Auguie2017,Akima2016,Wickham2016}.
Results
The results produced from the models presented in Section \ref{120042} where the surface stress is constant ( CAdj and COpp are both one, the typical axis-symmetric assumption when dealing with growth stress in a stem), required an input strain mean and standard deviation of \(1442\) and \(597\ \mu\epsilon\) to produce an output population mean and variance of \(1520\) and \(629\ \mu\epsilon\) respectively. The differences indicate that either the testing procedure or the model slightly overestimate surface strain from split opening. Note that because both the predicted opening and the surface stress at a given point are known to machine precision it is assumed there is no measurement error in either the opening or strain gauge measurements, this is in contrast to experimental methods where such measurement error does exist with an unknown magnitude (Chapter 5 attempts to quantify this error). Figure \ref{353734} shows the required input strain standard deviation to give the output population standard deviation of \(630\pm5\ \mu\epsilon\).