Model-based systems engineering

730 Pages·1993·260.176 MB·English

by  Wymore, A. Wayne

systems engineering series
Linear Systems Theory
FerencSzidarovszky, University ofArizona
A. Terry Bahill, UniversityofArizona
Engineering Modeling and Design
William L. Chapman, Hughes AircraftCompany
A. Terry Bahill, University ofArizona
A. WayneWymore, Systems Analysis and DesignSystems
Model-Based Systems Engineering
A. Wayne Wymore, Systems Analysis and DesignSystems
The Theory and Applications ofIteration Methods
loannis K. Argyros, CameronUniversity
Ferenc Szidarovszky, University ofArizona
model—based systems
engineering
an introduction to the mathematical theory ofdiscrete
systems and to the tricotyledon theory ofsystem design
A. Wayne/Wymore
@
CRCPress
BocaRaton AnnArbor London Tokyo
LibraryofCongressCataloging-in-PublicationData
Wymore,A.Wayne
Model-basedsystemsengineering:anintroductiontothemathematicaltheoryof
discretesystemsandtothetricotyledontheoryofsystemdesign/byA.WayneWyrnore.
1sted.
—
cm. (Systemsengineeringseries)
. ——
[ndudesbibliographicalreferencesandindex.
ISBN0-8493—8012-X
1. Systemsengineering—Mathematicalmodels. 2. Engineeringmathematics.
3. Systemdesign. I. Title. H. Series.
TA168.W9]2 1993
620’.001’1—dc2O 92-37410
CIP
Thisbookrepresentsinformationobtained fromauthenticand highlyregarded sources.
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DirectallinquiriestoCRCPress,Inc.,20()0CorporateBlvd.,N.W.,BocaRaton,Florida33431.
O1993byCRCPress,Inc.
internationalStandardBookNumber0—8493-8012-X
PrintedintheUnitedStatesofAmerica l 2 3 4 5 6 7 8 9 0
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Contents
Preface ix
1 Systemsengineering 1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Systemrequirements 6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemdesign 18
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemlifecycle 20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises S3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Systems 57
Introduction 57
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discretesystems 57
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemexperiments 63
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemmodeling 70
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemtheoreticpropertiesofsystemmodels 72
. . . . . . . . . . . . . . .
Cartesianproductsandsystemartifacts 76
. . . . . . . . . . . . . . . . . .
Systemparameterizations 85
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises 103
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Systemcoupling 109
Introduction 109
. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
Systemcouplingrecipes . . . . . . . . . . . . . . . . ._ . . . . . . . . . . 110
Taxonomyofsystemcouplingrecipes 114
. . . . . . . . . . . . . . . . . .
Resultantsofsystemcouplingrecipes 118
. . . . . . . . . . . . . . . . . . .
Theoryofsystemcoupling I38
. . . . . . . . . . . . . . . . . . . . . . . . .
Componentsandsubsystems 156
. . . . . . . . . . . . . . . . . . . . . . . .
Exercises 158
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Systemhomomorphisms 167
Introduction 157
. . . . . . . . . . . . . . . . . . . . . . . . - - - - - - - - -
Homomorphisms 163
. . . . . . . . . . . . . . . . . . . . . - - - - - - - - -
Systemisomorphisms 134
. . . . . . . . . . . . . . . . . . . . - . - - - - - -
Homomorphismsofsystemresultants
. . . . . . . . . . . . . . . . . .
Exercises
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi Model-basedsystemsengineering
5 Systemmodes 201
Introduction 201
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemmodes 205
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implementation 227
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemmodesindesign 240
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Systemmodehologenicity 245
. . . . . . . . . . . . . . . . . . . . . . . . .
Exercises 265
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Input/outputrequirements 275
Introduction 275
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thespaceofinput/outputrequirements 278
. . . . . . . . . . . . . . . . .
Satisfactionofinput/outputrequirements 291
. . . . . . . . . . . . . . . .
Thefunctionalityspace 294
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Homomorphismsofinput/outputrequirements 308
. . . . . . . . . . . .
Exercises 310
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Technologyrequirements 317
Introduction 317
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Technologies 318
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buildability 320
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thebuildabilityspace 333
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implementabilityintechnologies 334
. . . . . . . . . . . . . . . . . . . . .
Theimplementabilityspace 351
. . . . . . . . . . . . . . . . . . . . . . . . .
Exercises 355
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Performance,cost,andtrade-offrequirements 361
Introduction 361
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figuresofmerit 367
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Combiningfiguresofmerit .383
. . . . . . . . . . . . . . . . . . . . . . . . .
Specificationofperformance,cost,andtrade—offrequirements 404
. . . .
Designofaservicedeliverysystem 408
. . . . . . . . . . . . . . . . . . . .
Exercises 432
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Systemtestrequirements 437
Introduction 437
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thesystemlifecycleandsystemtestrequirements 438
. . . . . . . . . . .
Testability 442
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Developmentofsystemtestrequirements 452
. . . . . . . . . . . . . . . .
Systemdesignproblems 467
. . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises 468
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix1: Systemdesignlanguage 473
Introduction 473
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sets 473
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Therealnumbers 485
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , _
Contents
vii
Alphanumerics 488
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vectors 489
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions 496
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Orders 531
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standardcombinationsoffunctions 566
. . . . . . . . . . . . . . . . . . . .
Appendix2: T3SDnotation 579
Appendix3: Examplesofsystems 591
Appendix4: Examplesofsystemparameterizations 641
Appendix5: Examplesofsystemcouplingrecipes 653
Appendix6: Examplesofinput/outputrequirements 657
Appendix7: Examplesofinput/outputrequirement
parameterizations 677
Appendix8: Examplesoftechnologies 681
Appendix9: Examplesofsystemdesignproblems,system
designs,andimplementablesystemtestitems 685
Bibliography 593
Index 697

Preface
This textbook is intended fora two—semestercourseforstudentsofsystems
engineering. The material in the text was chosen to attain three principal
objectives:
0 toprovidethesystemtheoreticfoundationsnecessarytothestudyand
practiceofsystemsengineering,
0 toexplicatemathematical system theoryasthebasisforthedevelop-
mentofmodelsanddesignsoflarge-scale,complexsystemsconsisting
ofpersonnel,machines,andSoffwafe,and
0 to introduce the student to the tiicotyledon theory ofsystem design
(T3SD)andtotheconsiderationsinvolvedinapplyingthetheorytothe
designofrealsystems.
The introductory chapter informally discusses definitions of systems
engineering,systemdesign,systemanalysis,systemlifecycle,systemrequire-
ments,systemfunctionalanalysis,physicalsynthesis,andtheworkproducts
of systems engineering. Chapter 1 provides motivation for the study of
mathematicalsystemtheoryandsystemdesignmethodology.
Chapter 2 introduces the discrete system as a mathematical construct
consistingofasetofstates,asetofinputs,asetofoutputs,anextstatefunction,
and a readoutfunction. Alsodiscussed aretheconceptsoftimescale,input
trajectory,statetrajectory,outputtrajectory,andsystemexperiments.Stand-
ardnotationisestablishedforalltheseconcepts
Thediscretesystemwaschosenasthebasisforthisdevelopmentprimar-
ily for pedagogical reasons: more general system constructs (see Wymore,
1977) require more mathematical considerations (for example, topological
considerationsoftherealline);theobjectiveoftheworkissystemsengineer-
ing,notnecessarilysystemtheory;thus,thediscretesystemallowstheshortest
linetobedrawnfromsystemtheorytosystemsengineeringwithoutsacrific-
ingrigororevenverymuchmodelingpower.
Chapter 3 discusses the mathematical theory of system coupling: how
systemscanbeputtogetherbyinput/outputrelationshipstocreatehierarchi-
calmodelsofmorecomplexsystems.Thisdiscussionrequirestheconceptsof
I Model-basedsystemsengineering
inputports,outputports,connectablesetsofsystems,connectivityfunctions,
couplingrecipes,andsystemresultantsofcouplingrecipes.Theusualclassi-
fication ofcoupling recipes into conjunctive, cascade, feedback and mixed
categoriesisdiscussed.Theconceptsofsystemcomponentandsubsystemare
defined.
ThehomomorphicrelationshipbetweensystemsisthesubjectofChap-
ter4.Therelatedconceptsofisomorphismandsimulationarealsodiscussed.
Theseconceptsareessential tounderstandingand applyingsystemdesign
methodology, fortheyarethekeystoconsistentelaborationand consistent
simplificationofsystemmodels,tothedeterminationofwhentwomodelsare
essentiallythesame,andtotheessenceofimplementation.
InChapter5,theconceptofsystemmodeisintroducedtomodelidenti-
fiable”modesofbehavior”ofagivensystemsuchasfailuremode,nonfailure
or operational mode(s), and transient modes. The system mode conceptis
comparedandcontrastedtotheconceptsofcomponentandsubsystem.The
importanceofthesystemmodeconceptinsystemdesignanddevelopmentis
demonstratedthroughexamples.Survivalofsystemmodesofcomponentsto
determinesystemmodesofresultantsisdiscussed.
Forundergraduatesinathree-semestercreditcourse,thefirstsemester
mightendatthispoint.ThesecondsemesterbeginswithChapter6.
Chapters6through9areconcerned withthemathematicalstructureof
systemrequirementsbasedontheconceptofsystemdevelopedinChapters
2through5andwiththeimplicationsofthatstructureforsystemdesign.
Chapter 6 introduces T3SD and the structure of the statement of the
problemofthedesignofasystemasconsistingofsixmathematicalartifacts:
0 theinput/outputrequirement,
0 thetechnologyrequirement,
0 theperformancerequirement,
0 thecostrequirement,
0 thetrade—offrequirement,and
0 thesystemtestrequirement.
InChapter6,theinput/outputrequirementisdiscussedindetail,asare
theconceptsofsatisfactionofaninput/outputrequirementbyasystem.The
spaceoffunctionalsystemdesigns (alsocalledthefunctionalitycotyledon),
transferfunctions,andthestructureofthefunctionalitycotyledonaredefined
andtheimplicationsoftheseforsystemdesignarediscussed.
Chapter7discussesspecificationoftheavailabletechnologyaspartofthe
statementoftheproblemofthedesignofasystem.Theconceptofasystem
buildableinagiventechnologyisintroducedandthespaceofallbuildable
systemdesigns(alsocalledthebuildabilitycotyledon)isdefined. Asystem
is implementable in a technology if there exists a system buildable in the
Preface xi
technologywhichimplementsthegivensystem.Thespaceofimplementable
systemdesigns,alsocalledtheimplementabilitycotyledon,isdefinedasthe
setofsystems,eachsystemofwhichsatisfiestheinput/outputrequirement
andisimplementableinthetechnology.
ThestatementofasystemdesignprobleminT3SDrequiresthedefinition
of three orders, one each over the functionality, the buildability, and the
implementabilitycotyledons,representingthemathematicalstructuresofthe
performance requirement, the cost requirement, and the trade-off require-
ment,respectively.Chapter8isdevotedtotheproblemsassociatedwiththese
definitions and to their implications. Orders, trade-offorders, performance
indices, finite probability density functions, and figures ofmerit and their
thresholdsarethebasicconcepts.Standardcompositionsandstandardscor-
ingfunctionsarediscussedasamethodofcombiningseveralfiguresofmerit
into a single figure ofmerit. The designofa class ofsystems called service
deliverysystemsisdiscussedtoillustratetheconcepts.
The plan by means of which the real, final system will be tested is
considered to be part of the statement of the problem in T3SD. Chapter 9
establishes a structure for the system testplan appropriatetoits roleinthe
statementoftheproblem.Definedanddiscussedaretheconceptsoftestable
system representations, testablecomponentrepresentations,implementable
test items, test tolerance orders, testing functions, and system test require-
ments. The objectives ofthe system testrequirementare to definehow the
system is to be observed for testing purposes, to define compliance of the
system with the system requirements, to defineconformance ofthe system
withthemodel (design)onthebasisofwhichitwasbuilt,andtodefinethe
criteriaforacceptanceofthesystem.
Chapters6through9aresummarizedattheendofChapter9intheformal
definition ofthe system designproblem. Thisproblemconsists ofproperly
relatedmathematicalconstructsrepresentinganinput/outputrequirement,
atechnologyrequirement,aperformancerequirement,acostrequirement,a
trade-offrequirement, and a system testrequirement. Thisstatementofthe
problemofthedesignofasystemistheobjectiveofPhase1ofthesystemlife
cycle,requirementsdevelopment.
TodesignasysteminT3SDmeanstochooseapointintheimplementa-
bilitycotyledon,preferablyoptimalwithrespecttothetrade-offrequirement.
One strategyfordefiningsuchapointisaprocesscomposed oftworelated
butdistinctsubprocesses:systemfunctionalanalysislandphysicalsynthesis.
These processes are the principal tools of Phase 2 of the system life cycle,
concept development. Explication of the mathematical theory underlydng
{T
1Thesystemsengineeringtechniquehereincalledsystemfunctionalanalysisisnotthesameas
themathematicalfieldofstudyknownasfunctionalanalysis.Thatiswhytheprocessdiscussed
hereiniscalled”systemfunctionalanalysis”insteadoftheshorter"functionalanalysis,"which
mightbemisconstrued.