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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
As with the ¯ and s and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [4] Thus, the R chart is examined before the x ¯ {\displaystyle {\bar {x}}} chart; if the R chart indicates the sample variability is in statistical control, then the x ¯ {\displaystyle {\bar {x}}} chart is examined to ...
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Sampling (running) the model at a number of points in its input space. This requires a sample design. Selecting a type of emulator (mathematical function) to use. "Training" the metamodel using the sample data from the model – this generally involves adjusting the metamodel parameters until the metamodel mimics the true model as well as possible.
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
As regards weighting, one can either weight all of the measured ages equally, or weight them by the proportion of the sample that they represent. For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement, then one might weight the first measurement twice that of the second.
As with the ¯ and R and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [5] Thus, the s chart is examined before the x ¯ {\displaystyle {\bar {x}}} chart; if the s chart indicates the sample variability is in statistical control, then the x ¯ {\displaystyle {\bar {x}}} chart is examined to ...
If r is fractional with an even divisor, ensure that x is not negative. "n" is the sample size. These expressions are based on "Method 1" data analysis, where the observed values of x are averaged before the transformation (i.e., in this case, raising to a power and multiplying by a constant) is applied.