How should experimental day be treated in a Custom Design: fixed block or random block?

[#1]

I am planning to create a DOE using Custom Design with 5 factors and 40 experimental runs.
Due to operational constraints, I can conduct up to 20 runs per day, so the experiment will be executed over 2 days.

In this situation, how should the experimental day be treated in the design and analysis?

• Should the experimental day be modeled as a fixed block or a random block?
• My assumption is that there is no scientific interest in the difference between days, and ideally, the day-to-day variation should be treated as a nuisance effect.
• In addition, I would like to use the resulting model for future prediction, where I specify only the 5 experimental factors and do not condition predictions on a specific experimental day.

Given these goals, would it be appropriate to:

• include experimental day as a random block factor in the Custom Design, and
• analyze the data using a mixed-effects model in JMP?

I would appreciate guidance on the recommended best practice in JMP for this type of situation.

[#2]

Factor day is a random effect; in custom DOE, you can assign each day to a “random block” consisting of subplots of different fixed effects in random order. For analysis/modeling, “day” is treated as a random effect using REML.

[#3]

Hi @CoverGazelle271,

Welcome in the Community!

The decision to have fixed or random effects is known during design creation and before the analysis, depending on how you consider these factors:

• If this factor may change the response mean and can be changed/repeated in a reproducible way, then it can be considered as a fixed effect.
• If this factor needs to be accounted for the response variance (different variability in the response for different operators, equipments, days, ...), and only represent a subset/sample of possible values from a population, then this factor can be considered as a random effect.

In your case, and given your prediction objective independently of the day, I would consider this factor as random.
You would then use a mixed model for the analysis.

Note that you can visualize the results before analyzing, and since the experiments will be distributed "homogeneously" between the two days (random blocks), you can check visually that you don't have any significant difference in response mean and variance/variability between the two days. A simple visualization with day as X, response as Y, allow you to check if response mean seems very different between the two days as well as the variability (using box plots and statistics summaries for example).

Hope this answer will help you,