Complexity Metrics for Design

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Complexity Metrics for Design Manufacturability
Analysis
(Shaping the Complexity of a Design)

• Carlos Rodríguez-Toro
• Cranfield University, UK

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Outline of This Presentation

• Designers Sandpit background.
• Manufacturing cost analysis reasons for
  complexity measure.
• Past studies survey review.
• Complexity analyses.
• Theoretical considerations.
• Final discussion conclusions.
• Ongoing work.
• Questions and suggestions.

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The Designers Sandpit

• Assembly-oriented environment written in C.
• Implements DFA as design evaluation tool.
• Incorporates methods for generation and
  evaluation of concept design ideas, manufacturing
  analysis, assembly planning and design advice.

• Website http//eng.hull.ac.uk/research/sandpit/

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DFMA Analysis Steps
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Manufacturing Cost Estimation

• Most factors can be measured, but geometry and
  topology are still subjective,
• Shape complexity affects manufacturing and
  assembly operations

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How to Measure Complexity?
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Past Studies Survey (1)

• Definitions of complexity declare it as ...
• Abstract estimation,
• Context dependent,
• Information management,
• Associated with product flexibility and tendency
  to product mistakes.
• Conceptual definitions design (geometry).
• Quantitative representations and mathematical
  models manufacturing (systems complexity).

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Past Studies Survey (2)

• Geometry.
• Computer graphics and FEA.
• Topology.
• Feature recognition techniques,
• Group technology part codes.
• Assembly analysis.
• Assembly sequence,
• Insertion trajectories,
• Gripping configuration, etc.

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Specific Complexity Measures

• Axiomatic design (Nam Suh, 1999).
• Time independent (imaginary and real complexity).
• Time dependent (uncertainty of future events).
• Systems complexity (Calinescu et al., 2000).
• Entropic measures of information (amount of
  information required to predict state of the
  system).
• Complexity and complicatedness. (Victor tang,
  2001).
• Function of number of parts and their
  interactions.
• Beneficial property, given reduction of
  complicatedness.

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Evaluating Shape Complexity

• 2D objects shape similarity for image
  retrieval.

• Statistical methods.
• Stochastic methods for part orientation yield the
  measure of shape complexity.

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Complexity in the Sandpit

• DFA methodology evaluation of manufacturing
  processes for each component.
• Part count reduction minimises assembly
  operations, but increases component complexity
  (geometry).

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Complexity Analysis Taxonomy
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Component Complexity

• Manufacturing complexity.
• Geometric shape,
• Counterbalance part count reduction.
• Process complexity.
• Difficulty associated with alignment, insertion
  and handling operations on individual parts.
• DFA techniques provide a scoring system to
  evaluate these aspects.

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Assembly Complexity

• Structural complexity.
• Structural breakdown implications in ease of
  assembly (critical paths).
• Subassemblies increase product flexibility
  (parallel processing), but impact part tracking
  (mating conditions, storage and inspections).
• Sequence complexity.
• Number of insertion operations is proportional to
  the number of components.
• Badly defined sequences incorporate unnecessary
  operations.

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Theoretical Considerations

• Complexity related to
• Number of parts,
• Complexity of each part,
• Part count vs. Part complexity (efficiency?)

• Overall complexity as the sum of component and
  assembly complexity.
• Is there a threshold value for the overall
  complexity?
• Spotted - Geometry as the common factor.

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Overall Sandpit Requirements

• Manufacturing cost estimation,
• Establish precise definitions of each type of
  complexity,
• Complexity metrics that can be used in
  conjunction with other metrics,
• Shape similarity comparison (for reduction of
  variance or enhancement of product flexibility)

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Conclusions (1)

• Complexity is a problem of semantics and
  interpretations are only relevant within the same
  context,
• Product design presents challenges for specific
  complexity metrics that need be comparable,

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Conclusions (2)

• The problem is the creation of methods and
  metrics for assessing the impact of design
  decisions on production (product design
  efficiency),
• Shape/geometry is a common factor amongst the
  different types of complexity of a product and
  fundamental for the manufacturing analysis.

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Ongoing Work

• Definition of precise geometric reasoning
  methodology for manufacturability analysis
  (algorithms),
• Definitions of units of measurement,
• Identification of hidden dependencies and
  additional factors to the problem of complexity
  metrics.