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A task requires the use of one or   more tools

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For example, the user can divide the model parameters into any number of subgroups and control the number of iterations to execute in optimizing the values of the parameters of each subgroup.

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Rounding errors which lead to inaccuracy in the Jacobian matrix calculation can cause this behavior near the minimum. This can be resolved by switching to central differences in calculating the Jacobian matrix, adjusting the size of the differentiation steps, or relaxing the convergence criteria.

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In Chapter 6, nonlinear programming is used to determine the statistical variable values at the corners with the maximum probability distance.

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In the rest of this section, single output models are assumed without any loss of generality.

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Other forms of analytical approximations are feasible but will not be discussed here.

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In the rest of this section, the term random number is used in a nondiscriminate manner. One should keep in mind that computer generated random numbers are indeed deterministic pseudorandom numbers.

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These are determined by equipment capabilities, and/or predefined targets (e.g. ).