1. Tague, N. R. (2005). The quality toolbox (2nd ed.). ASQ Quality Press. The section on "Cause-and-Effect Diagram" (p. 247) explicitly states its purpose is to "organize and display the various theories about the potential causes of a problem." This confirms it is an analysis tool, not a design representation.
2. Gomaa, H. (2011). Software modeling and design: UML, use cases, patterns, and software architectures. Cambridge University Press. Chapter 1, Section 1.2, "Software Design," defines software design as the process that "bridges the gap between software requirements and the implementation of the software" (p. 4), which involves creating the system's architecture and structure. This clearly distinguishes it from a cause-and-effect diagram.
3. MIT OpenCourseWare. (2010). 16.842 Fundamentals of Systems Engineering. Fall 2009 - Spring 2010. Lecture 3, "Functional Analysis and Allocation," details the process of decomposing system functions to define the system's architecture. This process is what the question describes, and it is distinct from the problem analysis performed with a fishbone diagram.