TABLE OF CONTENTS Our clients often ask if it would be alright to cut down or possibly even eliminate the replication of center points called for by textbooks and associated software for CCDs. In short, the answer is "No!"
Recall from the previous chapter that a good RSM design should provide for testing of lack of fit (LOF). Otherwise you cannot tell how well your model fits the actual response data. This statistic requires a measure of pure error, which comes only from true replication. To achieve any sort of power for the LOF test, three degrees of freedom (df) of pure error are mandatory. If only center points are replicated, then you must do at least four of them to get over this threshold.
With fewer than four df, the lack-of-fit test achieves very little power, in part due to the rapid escalation of critical F-values with such meager samples of data. For example, consider doing a three-factor CCD. For uniform precision we suggest that this design include six center points, but you may be tempted to do fewer. Think again after seeing these critical F-values at the 5 percent risk level as a function of the number of center points ("CPs"):
| CPs | df | F (5,df) for LOF |
|---|---|---|
| 1 | 0 | Not possible |
| 2 | 1 | 230.2 |
| 3 | 2 | 19.30 |
| 4 | 3 | 9.01 |
| 5 | 4 | 6.26 |
| 6 | 5 | 5.05 |
To construct this table we assumed a full quadratic model that...
