Systems Theory

Many systems fail due to improper formulation at interfaces and/or after encapsulation.

Dr Wayne Wymore founder of University of Arizona's Systems and Industrial Engineering Department.

https://en.wikipedia.org/wiki/A._Wayne_Wymore
http://sysengr.engr.arizona.edu/wymore/WWAutobiography.htm

There are now many different types of "System Theory"
https://en.wikipedia.org/wiki/List_of_types_of_systems_theory

Dr Wymore developed a rigorous mathematical formulation for systems; a system is defined as

System Model = (IZ, OZ, SZ, NZ, RZ)

IZ is set of all inputs
OZ is set of all outputs
SZ is set of all states
NZ  is the next state function, NZ(IZ, SZ) --> SZ
In English NZ is a function that maps inputs within context of current states to the next state
RZ is the read / output function, RZ(SZ) --> OZ
In English RZ is a function that maps the current state set to the output set.

Note that each set IZ, OZ, SZ is the set of all inputs, outputs, states across all time.  Additionally IZ, OZ, SZ, NZ, RZ at any time instant can be defined by multidimensional vectors or matrices across time.

Wymore's mathematical systems theoretic definition includes how systems can be encapsulated and how to properly consider coupling between systems.  Google books and Wymore's original books contain complete discussion on how to study systems in a rigorous mathematical basis.

Many systems fail due to ill-defined behavior of the next state function especially with regard to assumptions that are made at interfaces or after encapsulation.