Hello to anyone reading this post. I hope you're having a great day!
Question Context: I am a junior engineering student and have built DOE with 3 discrete numerical factors at two levels and one response and then conducted trials. Then with JmpPro will use linear regression to develop a model including all interactions for my results. (This is the assignment)
However there was an issue during data collection and one of these factors is off by a constant depending on a different factor.
Question: I believe this can be easily corrected and have a couple of ideas but need to discover an accepted correction method to fix this before proceeding. So I'll write down some of my ideas and open the floor to anyone with more expertise who cares to discuss this with me.
DOE Set-Up: I have three discrete numeric factors at two coded levels (Nominal Pipe Size, Tube Flow Velocity, and Steam Pressure).
The issue is that when conducting trials, there was a blunder with the target factor levels causing the wrong tube flow velocities to be used. The blunder was that the wrong pipe diameters were used to calculate target flow rates.
I have recalculated the measured values for my factors and will show a comparison between what is desired and what I'm working with.
Here is the table representation that better illustrates my dilemma.
| Factor IDs |
Target
NPS ["]
|
Target
v_t [m/s]
|
Target
P_s [psig]
|
|
Measured
v_t [m/s]
|
| +++ |
1/4 |
2.5 |
20 |
|
4.297 |
| ++- |
1/4 |
2.5 |
5 |
|
4.297 |
| +-+ |
1/4 |
1.5 |
20 |
|
2.578 |
| +-- |
1/4 |
1.5 |
5 |
|
2.578 |
| -++ |
1/8 |
2.5 |
20 |
|
1.456 |
| -+- |
1/8 |
2.5 |
5 |
|
1.456 |
| --+ |
1/8 |
1.5 |
20 |
|
0.873 |
| --- |
1/8 |
1.5 |
5 |
|
0.873 |
The measured Tube Flow Velocities are off by a constant which relates to the Nominal Pipe Size.
@NPS = 1/4 ["] Constant ≈ 0.582, @NPS = 1/8 ["} Constant ≈ 1.718
Idea 1: My initial idea to correct this was to introduce another discrete numeric factor with 2 levels named "Scale Factor" and develop an incomplete factorial design where the level would coincide with the factor levels for NPS and then replace all instances of v_t with sf*v_t.
However, this method is pretty crude and was not approved by my professor. (Who encouraged me to refer to JmpPro's youtube account or JmpPro documentation for a solution).
Idea 2: My next idea was to change the number of levels for tube flow velocity to be 4 instead of 2 and then develop an incomplete DOE, however I felt that this was unsatisfying and that surely I could do better considering that there is a clear relationship between the measured velocity levels and the desired velocity levels.
Idea 3: My latest idea is to establish that v_t has two levels but is dependent on NPS. I was considering making v_t a covariate factor dependent on NPS but am uncertain on exactly how to set this up as it seems that covariate factors are more like uncontrolled factors, which does not quite fit my circumstances.
I would greatly appreciate any advice or suggested resources I could use to correct my model.
Thanks in advance.
