For all variance components, lower and upper bounds for variance components must not be negative values. If the bounds calculated using the formulas are negative, then they are set to zero.
For all ratios between 0 and 1, lower and upper bounds should also be between 0 and 1. If the bounds are outside the range, they are set to 0 or 1 accordingly.
||the α *100 percentile of the chi-square distribution with nq degrees of freedom |
| Fα(nq, nγ)||the α *100 percentile of the F distribution with nq and nγ degrees of freedom |
|J||the number of operators|
|I||the number of parts|
|K||the number of replicates|
For degrees of freedom:
Part Operator Interaction: n3=(I–1)(J–1)
MSPart = S12
MSOperator = S22
MSPart*Operator = S32
MSReplicates = S42