Complexity in Engineering

In designing and operating engineering systems such as products and manufacturing systems, the goal is to reduce complexity so as to make the system robust, guarantee their long-term stability, make the system reliable, and minimize the cost. In the complexity theory presented in this keynote paper, the complexity is defined as the measure of uncertainty in achieving the functional requirements (FRs) of a system within their specified design range. This definition of complexity leads to the existence of four different types of complexity: time-independent real complexity, time-independent imaginary complexity, time-dependent combinatorial complexity, and time-dependent periodic complexity. According to this complexity theory, complexity of any system can be reduced by taking the following actions: (1) minimize the number of functional requirements (FRs), (2) eliminate the time-independent real complexity, (3) eliminate the time-independent imaginary complexity, (4) transform a system with time-dependent combinatorial complexity into a system with time-dependent periodic complexity by introducing functional periodicity and by reinitializing the system at the beginning of each period. The importance of the functional periodicity in reducing time-dependent combinatorial complexity is illustrated using examples.