How to fit a model with challenging data on Minitab

Hi all!

I have a data about different kinds of cylinders(radius of 1,2, and 3 inches) that are produced from 3D printer. On Minitab, I made the normality plot but it is not normal. I also tried to make Box-Cox transformation, still it doesn't work. Its scatter plot is like an ellipse. I have the data about x and y coordinates, radius and angles. Do you have any idea how can I fit a correct model at first on Minitab? I am open for all advices. If you want, I can also send the data set with mail. Thank you!


TS Contributor
You can attach your data to a post.

Please explain in more detail what you are attempting to do. Why must the data be normal? There are many manufacturing processes that do not produce normally distributed product, and that is perfectly "normal" :D for those processes.

Note: I am a Minitab user, specialize in industrial statistics, and have a Quality background, so I can help.
Yeah, you are right. Thank you for your answer. The data is in the link:

I was first looking for randomness if the order of the data is known and normality, that's why I looked at normality if it is not normal I was trying to do transformation and so on. :D I should find a proper models for these data, first of all 3 different models like AR, MA or ARIMA models, then 1 model for all of data that include 3 kinds of cylinders with radius 1,2 and 3 again like AR, MA, ARIMA models.


TS Contributor
My company firewall prevents access to file storage locations. Please attach the file itself. If the forum prevents you from attaching the *.MTW formal, Excel is fine.
x1 and y1 are coordinates of center of the circles that belong to cylinders, angle is used to describe like x1=r1*cos (angle). The process is 3D printing. Especially the aim is predicting the in-plane errors of cylindrical parts manufactured via stereolithography process(rapid prototyping) that is an additive manufacturing process works by focusing an ultraviolet (UV) laser on to a vat of photopolymer resin.


TS Contributor
The other two cylinders exhibit the same/similar patterns.

How does your sampling span compare with the actual process? Are these samples taken throughout the entire build of one cylinder and reflect movement through the Z-axis?

The process appears to be highly predictable. The real thing is to understand why it does what it does and to minimize the impact.
I think that for the actual process radius should be 1 for first sample,2 for second, 3 for third. It can be the comparison. Also, z-axis is not important in this case, we can think like 2-D because there is no data about height or z coordinate of the cylinders. A cylinder is produced like flashlight. Regression models may be used in my opinion.


TS Contributor
Try regressing radius against x^2 and y^2. Those account for over 99% of the variation in radius for cylinder 1. The residual patterns do look strange, but are extremely small.

I would try to understand why this relationship exists and see whether you can improve it.
I tried this model but I am not sure if it is correct or not. Residual plot seems like normal distributed even if p value is smaller than 0,05. Also, it is recommended that using radius and angle is better for modelling in the given data.
radius1 = M - A * cos(w * angle1 + phi) This formula is applied to nonlinear regression model and M is mean of radius, A is 0,005. w is 2pi/pi=2, and phi is 3,14. A between 0,004 and 0,1, w between 1,9 and 2,2. Equation is
radius1 = 0,995512 - 0,00555637 * cos(1,97029 * angle1 + 3,14). Can it be a right approach?
it is from another one actually, I add it here. Also, we found two models for that, you can see. We want to add x and y if we can do, so prediction may be more precise with more parameters in my opinion. Sorry for this confusing thing. I will wait for your comments.


TS Contributor
The first graph looks like the data are cubic fitted to a quadratic model. However, the real question is whether this predicts close enough for your needs.
I obtained 0,002630 as maximum of residuals from one of the models for cylinder with radius 2. You can see residuals plot and fitted line plot below. Can it be a right model, or should we improve it?