All organizations today dedicate some level of effort on improving their business processes. It's an important component of competitive strategy. Leading organizations invest heavily in improvement with Theory of Constraints (TOC) Lean and Six Sigma activity. There are other areas, such as Systems Thinking, Modelling and Process Mining that also provide advantages in business improvement. For the process improvement professional, these are the main tools. Keep your toolkit full and your tools sharp.
I've worked in process improvement for over 25 years and I know these tools. The best resource, in my experience, has been data.
Your process, or system, is a physical entity. For manufacturers, this physical system operates with cycle times, temperatures, pressures, concentrations, forces, quantities, positions, weights, etc. There are so many variables that play a role in the process and influence the outcome of the process. When the outcome varies excessively or produces something that isn't desired, the detective in you should look through all the data to see which variable(s) correlate best. If you don't have a lot of available data, find a way to get some. Processes communicate through data.
Don't fall into the trap of holding brainstorming meetings (root-cause meetings). These meetings can generate a lot of action items because everyone has an idea or opinion. You end up with a load of work. Brainstorming for problem solving isn't successful often enough to make it a strategy. It is weak because guessing doesn't work. It's one thing to brainstorm for creative ideas. People are creative and can come up with imaginative new product ideas. But problem solving isn't about creativity. It's a scientific endeavour.
You don't need to have a deep understanding of the various tools of applied statistics. Nor do you need a Green or Black Belt. What you do need is curiosity. If you can work your way around Microsoft Excel, you can import data, generate plots, observe trends, correlations, outliers and more. Don't let a lack of statistics training hold you back. If something is interesting in your data, it will be visible in a plot of that data. As you dig into your process data more and more, you'll begin to really understand how the process operates. You'll learn which variables dominate and thereby, which ones to control.