Doe and replications

[#1]

Hi
After reading a lot i am bit confused with the replications.
When should I use it? In which case? And how to calculate the number or replications?

Thanks

[#2 · Accepted solution]

Hello @YanivD,

Replications are used in order to estimate more precisely pure error and parameters estimates more accurately. Adding replicates in a design enables you to lower the variance prediction and the variance of parameter estimates in your model.

You may use it in the case of a strong noise in your response, or if you need to achieve a certain level of precision for your predictions. You can also add replicates in a second run of experiments (if you realize your prediction variance is too high for example), by using the platform "Augment Design", specifying your factors and response, and then clicking on "Replicate".

There are no "hard rules" for the number of replications, as this may dependent on the topic, equipment used, precision needed, etc... Please note that you may have two options depending on the DoE platform you use (Classical or Custom Design) :
- You can specify replicates, which is the number of times all experiments will be realized independently in the DoE,
- You can specify replicate runs, which is the independent repetition of one experiment in the design.

Concerning the number of replicates (or replicate runs), I would recommend to try the different designs you have in mind (with/without replicates and different number of replicates) and compare them through the platform "Compare Designs" (in DoE / Design Diagnostics). In the comparison window, you'll have more infos on the impact of replicates on the model precision, and you'll be able to make a choice about the best compromise between experimental budget and precision of your model.

I hope this first answer will help you,

[#3]

Thank you a lot for your great advice!

[#4]

So helpful! Thank you @Victor_G !

[#5]

There are multiple strategies for replication:

1. Completely randomized replicates (CRR):  The purpose is to get an estimate of the random errors while reducing the bias of the estimate.  This estimate can subsequently be used for statistical tests (MSmodel/MSerror).  CRR also likely increases the inference space, but this can compromise the precision (Box's definition) of the design.  This strategy is used when the noise has not been identified.  This typically doubles the size of the experiment.

2. Randomized complete block designs (RCBD): The purpose is to increase the inference space while simultaneously increasing the precision of the design.  In addition, the block and block-by-interaction effects can be assigned which is required for robust design. This also doubles the size of the experiment. If you can identify the noise, this is a more effective and efficient strategy.

"Block what you can, randomize what you cannot" G.E.P. Box

3. Randomized incomplete block designs (RIBD or BIB): Similar to RCBD, but the block is fractionated (like fractional factorials).  In this case, higher order model effects will be confounded with higher order block effects.  This is an efficient strategy to assign the noise effects, increase the inference space while increasing the design precision. It does not require doubling the size of the experiment.  This strategy is more useful in the processing or manufacturing setting rather than in the product or process design setting.