OK. But I would say that results for MCH and MCHC are different because they are measuring two different things. And I am not so sure that using the "rule of three" or "H&H check fail" to check results is very useful when we can just look to the indices for troubleshooting. For example:
I see the MCH as the Mean Cell Hemoglobin, that is: the total amount of hemoglobin in the cell (NOT the concentration of Hgb). So for high MCVs, the MCH will tend to be high, and for low MCVs, the MCH will tend to be low.
The MCHC, on the other hand, is the Mean Cell Hemoglobin Concentration. Cell size, by itself, does not matter here. However, consider an iron-deficiency anemia where not only are the cells small (low MCV and MCH) but the concentration of Hgb is also low, which will result in a low MCHC.
However, the concentration of Hgb can only be so high (no more than 36 or 37), as it is physically impossible to have a higher density of Hgb beyond that. (Again, the MCV or MHC is not the issue here.) This is why when one has a very high MCHC you have to try to resolve it. Too much lipemia skews hemoglobinometer results upward, resulting in a higher Hgb and no change to the RBC or MCV. Cold agglutinins skew the RBC count downward, with no change in Hgb. In either case, if you do the calculations for MCHC, you get a impossibly high result.
Scott