Basically, it was widely used in engineering all the time.
TRIZ itself is a unique tool to solve business and engineering problems. But the thing is that it's hard to find a teacher for that.
TRIZ lessons (divided by levels) only wealthy companies can afford. There are several TRIZ schools in the US (probably the biggest ones), France, Sweden, and some other countries.
According to my experience, most of the courses I saw were just business training, which is not TRIZ itself. But during my work in Power Machines, I saw how the guy, who knows TRIZ helped a worker to make several inventions in real-time. Some of them were implemented after.
So TRIZ itself is a tool, an algorithm that allows you to find a solution, no matter what type of problem you aimed to solve.
P.S. It is also quite hard to find any original Genrich Altshuller 's books right now.
SWOTRIZ is a novel way to enhance and improve the SWOT method and systematically strategic planning by combining it with TRIZ systematic innovation knowledge that I could do it.
See:
Method SWOTRIZ Innovative technique (A novel way to enhance and imp...
Data SWOTRIZ (SWOT+TRIZ) Components and implementation steps
TRIZ is a quite powerful technique. SIT is an elegant simplification of TRIZ, however, due to simplification, some TRIZ advantages were lost. Neither TRIZ nor SIT is a theory. Both are empirically based methods, and so are Lean Production, QFD, Design Thinking, and numerous techniques that hardly can be even listed. The lack of theoretical ground is one of the main obstacles to the dissemination of these methods and a combination on some generalized level.
I believe that the basis for this generalization is Information Theory. We solve our problems by creating tools and organizing processes. Tools and processes solve our problems through the Information they contain. Defining the ways for managing Information content of systems allows uncovering the Problem Solving techniques.
By the way, what do you mean by the 'Innovation theory'?
Russo, D., Spreafico, C., & Duci, S. (2013). On the co-existance of FBS and TRIZ for simplifying design process in an iterative way. In DS 75-2: Proceedings of the 19th International Conference on Engineering Design (ICED13), Design for Harmonies, Vol. 2: Design Theory and Research Methodology, Seoul, Korea, 19-22.08. 2013.
here in eco-design:
Russo, D., Spreafico, C., & Spreafico, M. (2021). A Simplified TRIZ Approach Involving Technology Transfer for Reducing Product Energy Consumption. In Sustainable Design and Manufacturing 2020 (pp. 129-138). Springer, Singapore.
Yes, as Igor Zadesenets mentioned, both TRIZ and QFD are tools, not theories. The relationships and differences among TRIZ, QFD, and another highly relevant also powerful tool Taguchi are listed as attached, fyr.