In the past, I’ve implemented Euler’s totient function for shits and giggles. It’s not a hard exercise by any means, but it can be if you haven’t had education in math at a level to understand the formula.

$$\varphi(n) =n \prod_{p\mid n} \left(1-\frac{1}{p}\right)$$

Admittedly, I had to google what the hell is going on. Technically, that’s just the framework, there are more details that follow in the form of rules. However, it was definitely a fun exercise to implement it. I think today I’m going to commit to downloading the latest version of rust and compiling that old code to see how much data I can generate. It’s really about all I can do to keep myself from going insane having to watch this robot perform the same tasks over and over until it gets them right. Yes, I have to intervene occasionally, but most of these debugs are very “hands off”.

In my job, I work with a ton of unit vectors. While tracking things in three dimensions can be tricky, it helps to start breaking down as many aspects of the dimensions to their base components. I’m sure we’re all familiar with common spatial axis labeling. You get X, Y, and Z. Their application isn’t uniform. Some machine uses X for the vertical axis, some might use Z. What you might not yet be familiar with would be the orientations of objects in space. Yes, you can track the cartesian coordinates rather handily with XYZ, but that will only tell you the position of those objects. It won’t tell you the direction they’re facing, and for that we use unit vectors labeled IJK. They’re typically values between -1 and 1, and they can define rotation completely.

Statistical Analysis of Variance. Using standard deviations six times higher and six times lower than your target, determine whether your process is “in control” or “out of control”. Good stuff.

It’s also part of the framework for determining the reproducibility and repeatability of gaging. I’ve discovered that Minitab is one of the best software suites for achieving what you need in calculating ANOVA for your GR&R. It’s a great deal faster than laying out your own Excel spreadsheet, and it allows you to completely automate the process. Doing capability studies, GR&R’s, and X̅&R charts becomes a task that requires seconds, rather than having to deal with irritating Excel spreadsheets or plotting by hand. I’ve learned a ton about statistical process control. I’ve also learned a ton about what works, and what doesn’t.