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

For corresponding calculations for long-term statistics, go to Calculations for the gap distribution (long-term statistics) for Calculate Gap Pools.

μGap,ST

Short-term gap mean before allocation

σGap,ST

Short-term gap standard deviation before allocation

Z.LSL(ST)

If only lower specification in the assembly gap is given:
Z.LSL(ST) = (T – LSL) / σGap,ST
If only upper specification in the assembly gap is given:
Z.LSL(ST) = '*'
If neither lower nor upper specification in the assembly gap:
Z.LSL(ST) = T / σGap,ST

Z.USL(ST)

If only upper specification in the assembly gap is given:
Z.USL(ST) = (USL – T) / σGap,ST
Otherwise
Z.USL(ST) = '*'

Z.BenchGap,ST

If neither lower nor upper specification in the assembly gap:
Z.BenchGap,ST = Φ-1(Φ(Z.USL(ST)) – Φ(–Z.LSL(ST)))
If only upper specification in the assembly gap is given:
Z.BenchGap,ST = Z.USL(ST)
Otherwise
Z.BenchGap,ST = Z.LSL(ST)

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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