Omega Guide 2

N-Squared - brief guide

ω 2

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Issue 1.0
January 2012


N-Squared - brief guide


  • Originally developed in 1960s – primarily to develop data interfaces
  • Its initial use was to depict data or items that are inputs and outputs of functions in the functional architecture
  • Now recognised as a functional analysis or architecting technique that can provide an effective and efficient means to:
    • Minimise connectivity
    • Maximise cohesion
    • Minimise coupling
  • Connectivity - the extent and complexity of deliberate interaction between functional or physical entities within a system architecture. For example sensor data
    • Minimising connectivity has a near quadratic effect on cost and integration complexity
  • Cohesion – functions with similar characteristics can often be fulfilled by common elements of a system solution using similar technology. For example data storage and display
    • Maximising cohesion reduces development, production and support costs, minimises solution footprint and minimises effect of solution technologies on other Lines of Development. For example training.
  • Coupling – the extent and complexity of the intrinsic relationships between physical entities within the system. For example waste heat, vibration and mutual interference
    • Minimising coupling reduces the likelihood and extent of unwanted emergent properties, thereby reducing integration problems, costs and delays, improving fitness for purpose.

Hints & Tips

  • Arrange in ‘Sequence’ with source nodes at the top and sink nodes at the bottom – this simplifies the flow of outputs to inputs
  • Superimpose the functional hierarchy above the N-squared grid to get started - this provides context and forces a natural order of closely related functions in proximity on the chart – easier to analyse
  • For Data inputs/outputs use the Message Name or Type, or use an index number and list all the data separately
  • Be prepared to ‘re-group’ the functions to get most interactions close to the diagonal
  • Boundary inputs can be shown at top (preferred) or bottom, and boundary outputs at the (right) side
  • Control/Feedback loops can be shown by a super-imposed circle

N-Squared Diagram

N-Squared Diagram

N-Squared Process

  • Select the set of relevant functions
  • Arrange N Functions on the diagonal of an N by N grid – top left to bottom right – mark with rectangles
  • Outputs from Functions are on the Horizontal
  • Inputs to Functions are on the Vertical
  • Mark inputs and outputs with ‘roundtangles’ or ovals
  • Add Boundary inputs and outputs
  • Analyse for completeness
    • For each function – Are all inputs and outputs marked?
  • Re-arrange to show tightly related functional groups, nodal points and critical functions
  • Consider mathematically automating arrangement for optimisation

N-Squared Process

This summary is adapted from material prepared by Chris Lamb of Sula Systems Ltd for INCOSE UK one day event “Back to basics, simple tools”, held on the 3rd March 2010

This leaflet is intended as a working guide to N-Squared analysis

This series of working guides is produced by members of the UK Chapter of INCOSE. For further information, advice and links to helpful websites go to:

Members can download copies of this leaflet and other Systems Engineering resources online at:

For more information about the worldwide Systems Engineering professional community, go to:

Series editor: Hazel Woodcock
Lead author: Chris Lamb (Sula Systems Ltd)
© 2012 INCOSE UK Ltd