Math, Statistics, and Engineering
In college, Mechanics was a required class from the civil engineering department. This included differential equation.
Luckily for me, I also enjoyed a required course called analytical mechanics for my physics degree. This included using Lagrange and Hamiltonian equations to derived a wide range of formulas to solve mechanisms problems.
In the civil engineering course, the professor did the derivation as the course lectures, then expected us to use the right formula to solve a problem. He even gave us a ‘cheat sheet’ with an assortment of derived equations. We just had to identify which equation to use for a particular problem and ‘plug-and-chug’ or just work out the math. It was boring.
Learning to Understand
Meanwhile, in the physics course, we learned how the math tools of differential calculus worked to help us solve a wide array of problems. This included all the equations worked out in the civil engineering course and more. The difference was being able to make just the right tool vs just picking one up on occasion.
We learned the math and the understanding of how to use it well in the physics course. The engineering course expected us to master addition, subtraction, multiplication, and division, which was about the most difficult math in the course. Or not all that taxing at all.
Reliability and Math
Reliability engineering uses math. Sorry if this new to you, yet calculating a simple average (aka MTBF) is a simplification of just one of the many formulas available for our use.
We use math to provide summaries, reports, tracking, and when possible to reveal insights. We should use math to consider:
- diffusion rates,
- cooling rates,
- relations between equipment settings and wear rates,
- between process stability and field failure rates.
We have data all about us, and we are the engineers expected to make sense of it.
You may not have use calculus lately to derive a cumulative distribution function based on your data described by a novel histogram shape. You may not have employed differential equations to solve a thermal transfer problem. You certainly should understand the equations you (or your computer) are using, though.
Statistics is Just Math
A lot of what we deal with is variability. Holes, even cut by the same drill bit on the same material and machine, differ in diameter. You already know this, everything varies. Our job is to understand this variability and how it impact the reliable performance of the system.
Statistics is the language of variability. It is just math. Basic math mostly, that includes addition, subtraction, etc. Along with a few fancier tools like summation and product. We on occasion may need calculus. We rely on regression analysis to fit a distribution to the data. Statistics is a collection of math tools.
Do The Math
We’re engineers or managers interested in reliability. We have data or should find it as it is there for the analysis. We have been exposed to a broad range of math tools. You may not have realized the value of calculus or statistics during school. If you were lucky to have a professor that helped (forced) you understand the way math work to help you solve problems. Really understand the math. Then you may already be doing the math.
If not. If you are groping to find the simplest formula to get a basic analysis done. To create a summary, maybe even, alas, just the MTBF calculation, because the ‘more difficult’ math has been just out of reach for you. Then it’s time to open the books again. If you sold your college textbooks on math and statistics – get new ones. Learn the math and solve real world problems you have in front of you every day.
Recently, I’ve been buying and reading older textbooks and reference works on quality and reliability engineering. What has struck me is the amount of math in the older works. The newer text includes more pictures to adorn the pages without any practical value. As engineers are we losing our ability to enjoy using math tools?
How does math and statistics play into your day? What was the last formula you used and why did you select that particular formula? Do you understand the math behind the formula including the assumptions required to use it? Let us know how understanding the math has made a difference in your work.