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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. Brief introduction to the Designers’ Sandpit Project – Promote the web page and encourage people to visit it frequently. Website:

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DFMA – Analysis Steps Brief verbal introduction to the concept of The Designers’ Sandpit philosophy

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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). Estimations of complexity are, generally, abstract Complexity can only be attributed to models of specific process – context dependent Complexity of system depends critically upon how it is described – information COMPLEXITY IN DESIGN – Generally considered in relation to component geometry MATHEMATICAL MODELS – Mainly derived for Systems complexity and based on the entropy of the information required to describe the system itself

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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. Time Independent Imaginary Complexity – Lack of understanding Real Complexity – Ratio Functional Requirements (FR) / Design Parameters (DP). Function of information content for satisfying a number of FRs. Time dependent – Uncertainty of future events, not predicted a priori. SYSTEMS COMPLEXITY (Entropic measures of information – Static/Structural and Dynamic/Operational) Amount of information required to predict the state of the system

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**Evaluating Shape Complexity**

2D objects – shape similarity for image retrieval. FEM – amount of volume transformed. 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. Process 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. Manufacturing complexity – As part are combined or eliminated, new parts produced can be more elaborated, adding extra difficulty to the manufacturing process, outweighing the benefits of part count reduction.

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**Assembly Complexity Structural complexity. Sequence 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?) NEW MODEL USED AS THE FOUNDATION OF POSTULATIONS Large number of SIMPLE parts, yields a complex assembly and highly costly Small number of COMPLEX parts, yields also a complex and highly costly assembly 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.

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