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Math Details¶

How the sweep is built and what each level is. What the report shows is on Tolerance Allocation, and every control is on Options.

What is swept, and what is not¶

Only a Normal or a continuous Uniform input has its spread swept, and only when that spread is a finite number greater than zero. Every other input is held at its own distribution for the whole sweep and carries no curve, and the report names the reason rather than leaving a blank.

The input's nominal spread is the quantity the multipliers act on:

Distribution	Nominal spread
Normal	the standard deviation
continuous Uniform	the half-width

The seven levels¶

You give three percentages, ascending, distinct, each above 0 and below 100. They become seven multipliers of the nominal spread, smallest first, by taking each percentage as a fractional step down and the same percentage as a step up, with 1 in the middle.

With the defaults 10, 25 and 50 the seven multipliers are

\[ 0.5,\; 0.75,\; 0.9,\; 1.0,\; 1.1,\; 1.25,\; 1.5 \]

so the middle level is the input's own spread and the other six sit symmetrically around it as proportions of it, not as absolute amounts. An input with a standard deviation of 2 is swept at 1, 1.5, 1.8, 2, 2.2, 2.5 and 3.

What each level is¶

The centre is held and only the spread moves. At every level the input is rebuilt with its spread multiplied and its middle unchanged:

Distribution	What changes	What is held
Normal	the standard deviation is multiplied	the mean
continuous Uniform	the half-width is multiplied	the midpoint

A level is one ordinary simulation. The whole model is run at that level with every other input at its own distribution, so the number of simulations the sweep performs is seven times the number of inputs it found it could vary.

The seed¶

All seven levels of every input share one seed. The differences between levels are therefore differences of the spread and not of the sampling, so a curve that rises or falls does so because the spread changed.

This is a departure from the previous version, which did not share the seed, and it is the reason a v18 number will not reproduce a v17 number exactly even on the same model.

When the sweep is refused¶

Condition	Why
fewer than two inputs	there is nothing to allocate between
past either size cap	the sweep would run more simulations than the cap allows
the three percentages are not ascending, distinct, above 0 and below 100	the seven multipliers cannot be formed