There are different calculations for the gap pools depending on whether you have specified shift or drift (variation expansion) factors for the elements and which gap specifications are given.
μ_{Pool} = σ_{Gap,LT}[Z_{p} – Z.Bench_{Gap,LT}]
σ^{2}_{Pool} = 0
μ_{Pool} = σ_{Gap,LT}[Z_{p} – Z.Bench_{Gap,LT}]
σ^{2}_{Pool} = 0
μ_{Pool} = σ_{Gap,LT}[Z.Bench_{Gap,LT} – Z_{p}]
σ^{2}_{Pool} = 0
μ_{Pool} = 0
σ^{2}_{Pool} = σ^{2}_{adj,LT} – σ^{2}_{Gap,LT}*
* where if , then
or else σ^{2}_{adj,LT} is the unique solution to:
μ_{Pool} = 0
μ_{Pool} = 0
σ^{2}_{Pool} = σ^{2}_{adj,LT} – σ^{2}_{Gap,LT} *
σ^{2}_{Pool} = 0 if T=LSL or T=USL and Z_{p}=0
* where if , then
or else σ^{2}_{adj,LT} is the unique solution to:
Term | Description |
---|---|
C_{i} | Diametrical correction of the i^{th} element |
D_{i} | Drift factor for the i^{th} element |
N_{i} | Complexity of the i^{th} element |
S_{i} | Shift factor for the i^{th} element |
σ_{i} | Standard deviation of the i^{th} element |
σ_{adj,i} | Adjusted standard deviation of the i^{th} element |
T | Gap targeted value (if not available, T = μ_{Gap,ST}) |
T_{i} | Nominal value of the i^{th} element |
μ_{i} | Mean of the i^{th} element |
μ_{adj,i} | Adjusted mean of the i^{th} element |
V_{i} | Directional vector of the i^{th} element |
w_{i} | Allocation weight for the mean pool or the variance pool, i^{th} element |
Z.Bench_{Gap,LT} | Benchmark Z (long-term) of the gap |
Z.Bench_{Gap,ST} | Benchmark Z (short-term) of the gap |
Z.Bench_{i,LT} | Benchmark Z (long-term) of the i^{th} element |
Z.Bench_{i,ST} | Benchmark Z (short-term) of the i^{th} element |
Z_{P} | Z-value, which gives desired PPM (right tail) for long-term gap distribution |