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
| Term | Description |
|---|---|
| Ci | Diametrical correction of the ith element |
| Di | Drift factor for the ith element |
| Ni | Complexity of the ith element |
| Si | Shift factor for the ith element |
| σi | Standard deviation of the ith element |
| σadj,i | Adjusted standard deviation of the ith element |
| T | Gap targeted value (if not available, T = μGap,ST) |
| Ti | Nominal value of the ith element |
| μi | Mean of the ith element |
| μadj,i | Adjusted mean of the ith element |
| Vi | Directional vector of the ith element |
| wi | Allocation weight for the mean pool or the variance pool, ith element |
| Z.BenchGap,LT | Benchmark Z (long-term) of the gap |
| Z.BenchGap,ST | Benchmark Z (short-term) of the gap |
| Z.Benchi,LT | Benchmark Z (long-term) of the ith element |
| Z.Benchi,ST | Benchmark Z (short-term) of the ith element |
| ZP | Z-value, which gives desired PPM (right tail) for long-term gap distribution |
