# Calculations for the gap distribution (long-term statistics) for Calculate Gap Pools

The calculations for the long-term statistics differ, depending on whether you 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 i 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 Calculate 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

ki = Di|

## Both mean shift factor and variation expansion factor

One or no gap specification
###### Note

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

Both gap specifications
###### Note

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

## Neither mean shift factor nor variation expansion factor

One or no gap specification
Both gap specifications

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