Final answer:
Sociology is not one of the parts of Deming's 'system of profound knowledge'; the system includes Appreciation for a system, Knowledge about variation, Theory of knowledge, and Psychology.
Step-by-step explanation:
W. Edwards Deming's "System of Profound Knowledge" is a management philosophy that he developed to guide organizations in achieving quality and productivity improvements. The part of Deming's 'system of profound knowledge' that is NOT included in the options provided in the question is 'sociology'. Deming's system is based on four parts: Appreciation for a system, Knowledge about variation, Theory of knowledge, and Psychology. Therefore, 'Sociology' does not constitute one of the parts of Deming's system focused on improving management and operational processes.