The Downside of Using Dependent Variables in a DOE matrix

[#1]

I have been running into this argument for awhile now.

Question:

What are the downsides of using Dependent Variables (Measured Responses) as the Independent Variabels in a DOE?

Example:

For example, I can add an acid or base to achieve different pH. Typically, I would use the amount of acid (g) or amount of base (g) to achieve different pH. Where acid and base amount are the independent variables and the pH is the dependent variable.

Downsides I've Heard:

Typically, the downsides I have seen / heard are the following, are there any others?

1. There can be multiple ways or multiple acid and bases that could be used to achieve a specific pH value. Depending on the source used to achieve pH the reaction could change and obtain different results.

   a. The rebuttal I receive is that it doesn't matter how we get to a specific pH value. The only thing that matters in the reaction is the pH. 

2. It's actually more difficult to adjust to a pH value than to simply add the materials and record the pH. You will get varying pH values, but using the multiple response optimization in JMP one can achieve the pH values of interest as well as other properties.

 a. The rebuttal I receive is that outside the pH values the conditions make it desired run infeasible to run. In theory, one could run a small experiment to see how the acid & base impact pH and design constraints around the acid and base amounts in order to achieve a specific ph.

3. When optimizing to find the ideal pH value, you really don't know exactly what to add to achieve that pH value unless you have a specific row that you recorded the amount of acid / base (g).

 a. The rebuttal that I recieve the individual will adjust until it hits the target using a sequential process. Also, it is mentioned that in a production process they measure the response and add acid / base to achieve a result. Even if experimentally, we were to do the acid and base amounts this doesn't reflect what a production facility would do.

Thank you in advance for your assistance in this matter.

Nate

[#2 · Accepted solution]

Calling pH a dependent or independent variable is relative to how it would be used in the experiment.  If you plan the experiment using specific pH levels, then I really don't care that you are adjusting the ratio of the acid and base to achieve those predetermined pH levels; that's still a dependent variable.  That adjustment is just like turning a knob on a machine.  I say this assuming:

1. You know how to get the desired pH from a known formula as a function of the base:acid ratio

2. pH is going to be used to predict some other independent variable.

Consider speed as an experimental factor.  Speed is probably a knob on a machine, so speed itself is dependent on how far you turn the knob.  I don't think anyone would make the case that the factor in the experiment needs to be "amount of knob rotation" or something like that.  You turn the knob to achieve a certain speed, which is actually the factor you care about.  pH in this example seems no different in that regard.

What it ultimately comes down to is the deliverable.  Lets say ultimately you want to predict something like "hardness."  If it will be more helpful to have predictive model for hardness as a function of pH, then use pH.  If it will be more helpful to know the relationship of hardness as a function of base and acid, then make those your factors (I actually would propose doing acid and base as a ratio rather than an amount assuming there should be some fixed total volume for the mixture).