There are different calculations for the long-term statistics depending on whether you have specified shift or drift (variation expansion) factors for the elements and which gap specifications are given.

Shift and drift factors are used to accommodate unexpected errors or movement over time.
  • Drift is a change in the variance over time, while the mean does not exhibit a systematic change.
  • Shift is a systematic change in the mean over time. Typically, a shift of 1.5 sigma accommodates unexpected errors or movement over time.

For calculations for short-term statistics, go to Calculations for the gap distribution (short-term statistics) for Allocate Gap Pools.

Mean shift factor only

One or no gap specification
Both gap specifications
Note

ki = 1 + 8/15 |Si|

Variation expansion factor only

One or no gap specification
Both gap specifications
Note

ki = Di

Both mean shift factor and variation expansion factor

One or no gap specification
Note

ki = max{D, 1 + 8/15 |Si|}

Both gap specifications
Note

ki = max{D, 1 + 8/15 |Si|}

Neither mean shift factor nor variation expansion factor

One or no gap specification
Both gap specifications
Note

ki = 1.8

Notation

TermDescription
CiDiametrical correction of the ith element
DiDrift factor for the ith element
NiComplexity of the ith element
SiShift factor for the ith element
σiStandard deviation of the ith element
σadj,iAdjusted standard deviation of the ith element
TGap targeted value (if not available, T = μGap,ST)
TiNominal value of the ith element
μiMean of the ith element
μadj,iAdjusted mean of the ith element
ViDirectional vector of the ith element
wiAllocation weight for the mean pool or the variance pool, ith element
Z.BenchGap,LTBenchmark Z (long-term) of the gap
Z.BenchGap,STBenchmark Z (short-term) of the gap
Z.Benchi,LTBenchmark Z (long-term) of the ith element
Z.Benchi,STBenchmark Z (short-term) of the ith element
ZPZ-value, which gives desired PPM (right tail) for long-term gap distribution
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