Discussion
When COpp and CAdj are both equal to one, there is no variation of stress in the stem. Interestingly the input axis-symmetric surface strain of \(1442\) rises to \(1520\ \mu\epsilon\) and the population variance rises from \(597\) (surface) to \(629\ \mu\epsilon\) (splitting test) indicating the rapid splitting test slightly over-predicts the real surface strain. These results suggest the rapid splitting test will predict a surface strain approximately 5% higher than the true value (although this may change depending on the magnitude of the strain). Note that this value is insignificant compared to the errors discussed below. Figure \ref{353734} A shows the relationship between the surface point relatedness and the required input strain distribution standard deviation, B shows the same information but presented as a ratio of the output population strain standard deviation (the input strain is divided by \(630\ \mu\epsilon\)). It can be seen in Figure \ref{353734} that as the correlation between surface points reduces and becomes negative, the required input strain standard deviation increases to provide the same output population statistics. This is important as it provides context for how much surface variation must exist for given surface point relationships to obtain a typical output population. The top contour in Figure \ref{353734} B is the 1:1 contour, where the input strain is equal to the output population strain, it is slightly offset from the top corner due to the bias discussed above. The 2:1 contour is where the standard deviation of the input strain was required to be twice that of the output population strain. Note that on this contour the within stem variance is three times that of the population variance.
Chapter 5 outlined an experimental procedure for predicting the precision of the the splitting test, and particularly the magnitude of change in surface strain which is associated with the arbitrary angle of the cut during the splitting test. Experimentally the correlation between the two quartering tests \(\left(0.89\right)\) and the estimated standard deviation of the difference distribution \(\left(300\ \mu\epsilon\right)\). When the experimental method is compared to the closest theoretical example (Figure \ref{710424}), it is seen that the experimental results both must exist when COpp is grater than \(0\) and CAdj is greater than \(-0.5\). When \citet{Chauhan2010} is repeated within the theoretical framework (Figure \ref{832874}) a similar conclusion can be drawn, however slightly negative COpp and high CAdj populations could also be included. Following this, two population sets will be refereed to, the full population set consisting off all of the populations used to make the above figures, and the limited population set, the set which exists inside the lower bounds suggested by the experimental work in Chapter 5.
When perpendicular splitting test results are compared it can be seen that most populations produce a moderate or higher correlation between two perpendicular tests, when using the limited population set the correlations are markedly improved, Figure \ref{738035} shows the density curves for each population set. While the correlations between perpendicular splitting tests are fairly high, Figure \ref{738035} shows even with the high correlations within the limited population set, there can still be significant standard deviations of the differences between the two tests, implying a high error when attempting to identify individuals as superior. If instead the comparison is made between splitting test results and the true surface strain mean, again Figure \ref{122543} shows the destiny comparisons between the full and limited population sets. Most striking here is the substantial movement toward the higher end of strain correlations of both population sets. This can also be seen in Figure \ref{752700} where the standard deviation of the difference distribution approximately halves for all populations, along with the correlation between splitting test and true surface strain correlations approximately doubling, compared to Figure \ref{710424}. The implication being that the accuracy of the splitting test my be higher than the precision suggested in Chapter 5.