System Analysis and Identification: Objects, Relations and Clusters

The use of Abstract Relation Types (ART) in the analysis of system structure and system component clustering is the primary focus of this paper. Two basic system definitions are presented along with two, object-clustering definitions which were obtained from a literature search. The ART analysis approach is applied to classical N-Squared Charts and Design Structure Matrices (DSM), with specific emphasis on clustering methods, types and meaning. The primary structuring relationship associated with N-Squared ART and DSM ART are evaluated and discussed. Multiple DSM ART solution approaches and techniques are detailed. Introduction: For the purposes of this paper, a system is defined in two, complementary ways: a construction-rule definition and a function-rule definition. The construction-rule definition of a system is “A system is a relationship mapped over a set of objects.” The function-rule definition for a system is “A system is a constraint on variation.” The construction-rule system definition is the foundation of a number of classical system engineering graphical analysis and representation techniques including N-Squared Charts, Automated N-Squared Charts and Design Structure Matrices. The function-rule definition explores specific system configurations and determines whether these configurations are feasible, optimal and/or applicable to a specific system and deployment context. The construction-rule definition is applied to both the system objects and the system organizing relationship in a concurrent fashion. The constraints associated with the function-rule definition may be applied to the objects only, the relationship only, or to a combination of both the objects and the relationship. The function-rule definition is mainly applied to the analysis of the system object sequence represented on the matrix diagonal of the examples presented in this paper. Clustering, or the activity of creating clusters, is one key focus of this paper. Clusters are defined in two complementary ways: object-based and space-based. The first definition of clustering is taken from Robert Tryon and Daniel Bailey for cluster analysis: “objectively group together entities on the basis of their similarities and differences.” This object-based definition requires that the objects in the system be identified and evaluated using a common set of factors. The activity of object-based clustering identifies objects of interest, analyzes and groups the identified objects’ with similar factors, and generates a space populated with the object clusters. The second definition of a cluster is taken from John Warfield and J. D. Hill as “a cluster is a set of entities that lie in a closed connected subspace of some space.” This space-based definition of clustering starts with the contextual space, locates a subspace of that contextual space and then identifies the objects in the subspace as a cluster. The activity of space-based clustering requires three steps: (1) identify the controlling contextual space, (2) identify a subspace within the controlling contextual space, and (3) enumerate the entities (or objects) that are located in the subspace. Figure 1 captures a notional view of the two, complementary definitions of cluster. Working Paper Not to be used for reference or redistribution Sole use of this document is to encourage the discussion, analysis and evaluation of the concepts and content, to provide feedback to the authors to support an improved final document. © 2013 System Concepts LLC Page 2 of 21 Object-Based Cluster Space-Based Cluster Identify, analyze objects 1 Identify analysis space using global system relation 1 Determine cluster dimensions 2 Identify subspace(s) of interest 2 Analyze object clusters 3 Enumerate objects in subspace 3 © 2012 System Concepts LLC ◊◊