Complexity Measures for Systems Engineering

Complexity measures are informative indicators that can potentially aid designers and system engineers in decision making process in all system life-cycle stages: problem definition, requirements analysis, conceptual design, configuration design, detail design and optimization, and integration and testing. The guiding principle here is that of 14th Century philosopher, William of Okham. This principle, better known as Okham's Razor, states that "objects may not be multiplied beyond necessity" or simple is better. This is a generally accepted principle, but why is it so? Chaos theory help us explain why simple is better to some extent. In mathematics the simple is synonymous with linear, and complex is synonymous with non-linear. Chaotic systems are over-sensitive systems that are born out of severe non-linearity.

There are many outstanding but basic questions with regards to complexity measure that need investigation:

  1. In systems engineering there are many good reason to believe that simple is better. For example, simpler manufacturing process are less costly, and simpler systems are less subject to unforeseen behaviour. Can complexity measures demonstrate this fact?
  2. What are the criteria for effective complexity measures for each of the system life-cycle stages?
  3. Can complexity measures demonstrate system sensitivity to change, variability, variation, and evolution? Is the cost of system upgrade correlated to its complexity?
  4. What level of modelling is required for a complexity measure to effectively show the above correlations?
  5. Is it possible to establish a relationship between depths of models required for effectiveness of complexity measure?