Blocking Factor with Varying Distributions

[#1]

I am a heavy user of DOE with up to 8-factors and one blocking variable.  Each block is subjected to a condition over time.  The problem is the S/N ratio improves over that time.  Assume the distribution is normal and just the width decreases over time.  Another key is the time at which each block is removed from the test is unknown prior to the test and is uncontrolled.  And each block can be removed at different points rather than all at once. 

What is the best way to treat the analysis of the blocking variable?  It seems to me the time to removal of the block is information that would be important for the model

Thanks in advance.

[#2]

A basic assumption of linear regression is constant variance. You can use a 'log-linear variance' model in JMP instead. You can read about them here.

[#3]

@DrRubber , first welcome to the community.  The use of blocking for experimental design is an excellent strategy to handle noise.  There are multiple "schools of thought" on how to block and how to analyze block designs.  There are a couple of alternative approaches for blocking and these are likely dependent on the "general" application (e.g., agricultural vs. industrial). Here are my thoughts regarding industrial application:

1. To clarify the language, blocks are sets or chunks of noise variables (not singular).  You may confound factors with a block, but you don't block on a factor.

2. Typically experimentation includes two types of factors.  Design factors are the factors you are willing to manipulate and manage in the future.  Noise factors are the factors you are not willing to manage in the future, but may be able to manipulate in the short term.  Both sets of factors can causally effect the response variables.  We probably want the model to be made of design factors, but the truth is the truth.  Unfortunately, if you do not have a strategy to handle noise, you can compromise the efficiency and effectiveness of your experiment.  Holding noise constant is always a BAD idea as this decreases the inference space and likely negatively impacts your confidence in extrapolating the results from the experiment.  Allowing to vary randomly during an experiment decreases the precision of the design.

3. Blocks are used so the noise within the block is kept constant and that same noise is explicitly changed between blocks.  Holding the noise constant within block increases the precision of the design.  Changing the noise between blocks increases the inference space and provides an opportunity to assign the noise.

4. If you are capable of identifying all of the noise and managing it over the course of the experiment, you have an opportunity not only assign the block effect, but also block-by-factor interactions.  Block-by-factor interactions are keys to understanding robustness of the design factors (Do the design factors have the same effect over changing noise?).  For example, if you have 3 factors A, B & C and these are run in a 2^3 RCBD, then you have the following model:

15 degrees of freedom

Y =A+B+C+AB+BC+AC+ABC+Block + BlockA+BlockB+BlockC+BlockAB+BlockAC+BlockBC+BlockABC

5. If you are unable to identify the noise, then you are left with treating the noise as a random effect. The model becomes:

Y=A+B+C+AB+BC+AC+ABC+Block+ Error

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