Apr 7, 2006 - 2006 Joseph J Simpson, Mary J Simpson. 2. Overview. System and ... Moore. ⢠Wymore. Abstraction Frames. Abstraction Stacks. Summary ...
CSER 2006 – Conference on Systems Engineering Research Formal System Concepts Joseph J. Simpson Mary J. Simpson April 7, 2006
Overview System and Meta-System Applications Functional & Contruction Rules in Design & Discovery (Simpson & Simpson) An Applied Science to Solve Complex Problems (Hall) System Complexity Management & Control (Warfield)
Sequential Forms Moore Wymore
Abstraction Frames Abstraction Stacks Summary © 2006 Joseph J Simpson, Mary J Simpson
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System Modes A Mapping Context for Complexity (Does Not Address System Boundary Directly )
Design Mode
Design Objects
Design Objects
Increasing Complexity
(Know Relationships)
Discovery Mode (Know Objects)
Discover Relationships
‘Real’ Objects © 2006 Joseph J Simpson, Mary J Simpson
Discover Relationships
‘Conceptual’ Objects 3
A.D. Hall, Cycle for Scientific Method, Model Building
alm e l R ed) a rm el Fo mod C (
Theory C C
C
Deduction
C
Predictions
C Confirm, Verify
Modify
Induction
P
P′
Compare
Data, Observations alm e l R e”) a u ct atur a F “n (
~ Error in Model, Theory
Where © 2006 Joseph J Simpson, Mary J Simpson
C
Data, Observations
Confidence Limits of Model or Theory
= Concepts 4
Warfield – Poly-Loop Model
C
Act on the Theory
Set of Processes
Act on the Process Set
2-Loop
B Theory 3-Loop
1-Loop
One Process Plan
Act on the Foundations E
Foundations 4-Loop
© 2006 Joseph J Simpson, Mary J Simpson
D
Act on the Problem 0-Loop A
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Moore Type Sequential Machine Moore type sequential machine quintuple: M = (S, I, O, δ, λ)
δ
I I = Set of Inputs (finite, non-empty)
δ = Next state function (transition function) δ : S x I→S
O O = Set of Outputs (finite, non-empty)
λ
λ = Output Function of λ : S →O
S
S = Set of States (finite, non-empty)
© 2006 Joseph J Simpson, Mary J Simpson
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Wymore – Model-Based Systems Engineering Discrete system quintuple: Z = (SZ, IZ, OZ, NZ, RZ)
NZ
IZ IZ = Set of Inputs of discrete system Z
RZ
SZ
© 2006 Joseph J Simpson, Mary J Simpson
N = Next state function of discrete system Z
OZ OZ = Set of Outputs of discrete system Z
RZ = Readout Function of discrete system Z
SZ = Set of States of discrete system Z
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Abstraction Frame Sequencing Abstraction Frame (n-1)
Abstraction Frame (n)
Abstraction Frame (n+1)
Δaf n
Δaf n+1
Overall Environment Δaf n-1 © 2006 Joseph J Simpson, Mary J Simpson
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CCFRAT Approach – Phases, Hierarchies, Content Meta Process Applies to:
Content Phases
• Technical • Management • Programmatic
• Over time • Over products • Over events
Hierarchies • Abstraction • Meta-levels • Levels of detail
Pick One Aspect from Each Axis © 2006 Joseph J Simpson, Mary J Simpson
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Abstraction Stacks A House Consists of: Use Abstraction ‘Stacks’
Atoms
*“… house consists of several thousand pounds of carbon, some complex polymers, abount 5000 bricks, two bathrooms, and 13 ceilings…”
Molecules
Lumber, Bricks
Floors, Walls, Ceilings
Rooms * From Chapter 12, What do Classes Represent?, The C++ Programming Language, 2nd Edition, Bjarne Stroustrup, 1991.
© 2006 Joseph J Simpson, Mary J Simpson
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Systems Engineering Conceptual Context T n-1
Tn
T n+1
Customer System Rule Based Interaction
System Design System Rule Based Interaction
System Under Design
© 2006 Joseph J Simpson, Mary J Simpson
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Summary Sequential machines and systems provide a powerful conceptual pattern for system description and design. When vectors/groups of systems are used as inputs into a “sequential system,” each system abstraction level must be clearly defined. System abstraction frames and system abstraction stacks are used to help define and control system levels. The combination of meta-systems, system abstraction frames and system abstraction stacks provide the necessary context for the development of an executable systems engineering and design language.
Provides context for objects and operations. Provides framework for inter-relationship mapping © 2006 Joseph J Simpson, Mary J Simpson
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Questions
© 2006 Joseph J Simpson, Mary J Simpson
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