# Chapter 10 Introduction To Axiomatic Design

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Chapter 10Introduction toAxiomatic DesignThis presentation draws extensively on materials from [Suh 2001]:Suh, N. P. Axiomatic Design: Advances and Applications. New York:Oxford University Press, 2001. ISBN: 0195134664.

Example: Electrical ConnectorMale connectorCompliant pin(for permanent connection)PlasticovermoldingFemale connectorPlasticovermoldingMultiple layers will be stacked togetherto obtain an entire connector.Figure by MIT OCW.

Axiomatic Design FrameworkThe Concept of Domains{CAs}{FRs}MappingCustomer domain{DP}MappingFunctional domain{PVs}MappingPhysical domainFour Domains of the Design World.The {x} are characteristic vectors of each domain.Figure by MIT OCW. After Figure 1.2 in [Suh 2001].Process domain

Characteristics of the four domains of the designworldDomains CharacterVectorsCustomer Domain{CAs}Functional Domain{FRs}Physical Domain {DPs} Process Domain {PVs}ManufacturingAttributes whichconsumers desireMaterialsDesired performanceFunctionalrequirementsspecified for theproductRequired PropertiesPhysical variableswhich can satisfy oftwareAttributes desired inthe softwareOutput Spec ofProgram codesInput Variables orAlgorithms ModulesProgram codesSub-routines machinecodes compilersmodulesOrganizationCustomer satisfactionFunctions of theorganizationPrograms or Officesor ActivitiesPeople and otherresources that cansupport the programsSystemsAttribute desired ofthe overall systemFunctionalrequirements of thesystemMachines orcomponents,sub-componentsResources (human,financial, materials,etc.)BusinessROIBusiness goalsBusiness structureHuman and financialresourceTable by MIT OCW. After Table 1.1 in [Suh 2001].Process variables thatcan control designparameters (DPs)

Definitions Axiom:Self-evident truth or fundamental truth forwhich there is no counter examples orexceptions. It cannot be derived from otherlaws of nature or principles.Corollary:Inference derived from axioms or propositionsthat follow from axioms or other propositionsthat have been proven.

Definitions - cont’dFunctional Requirement:Functional requirements (FRs) are a minimum set ofindependent requirements that completelycharacterizes the functional needs of the product (orsoftware, organizations, systems, etc.) in thefunctional domain. By definition, each FR isindependent of every other FR at the time the FRs areestablished.Constraint:Constraints (Cs) are bounds on acceptable solutions.There are two kinds of constraints: input constraintsand system constraints. Input constraints areimposed as part of the design specifications. Systemconstraints are constraints imposed by the system inwhich the design solution must function.

Definitions - cont’dDesign parameter:Design parameters (DPs) are the key physical(or other equivalent terms in the case ofsoftware design, etc.) variables in the physicaldomain that characterize the design thatsatisfies the specified FRs.Process variable:Process variables (PVs) are the key variables(or other equivalent term in the case ofsoftware design, etc.) in the process domainthat characterizes the process that cangenerate the specified DPs.

The Design AxiomsAxiom 1: The Independence AxiomMaintain the independencefunctionalrequirements (FRs).Axiom 2:oftheThe Information AxiomMinimize the information content of thedesign.

Example: Beverage Can DesignConsider an aluminum beveragecan that contains carbonateddrinks.Howmanyrequirements mustsatisfy?functionalthe canSee Example 1.3 in [Suh 2001].How many physical parts does ithave?What are the design parameters(DPs)? How many DPs are there?

Design MatrixThe relationship between {FRs} and {DPs} can bewritten as{FRs} [A] {DPs}When the above equation is written in a differentialform as{dFRs} [A] {dDPs}[A] is defined as the Design Matrix given byelements :Aij FRi/ DPi

ExampleFor a matrix A: A11 A12 A13 [ A] A21 A22 A23 A31 A32 A33 Equation (1.1) may be written asFR1 A11 DP1 A12 DP2 A13 DP3FR2 A21 DP1 A22 DP2 A23 DP3FR3 A31 DP1 A32 DP2 A33 DP3(1.3)

Uncoupled, Decoupled, and Coupled DesignUncoupled Design A11 0[ A] 0 A22 000 0 A33 (1.4)Decoupled Design0 A11 0[A] A21 A22 0 A31 A32 A33 Coupled DesignAll other design matrices(1.5)

Design of Processes{DPs} [B] {PVs}[B] is the design matrix that defines thecharacteristics of the process design andis similar in form to [A].

Axiomatic Design TheoryFunctional Requirement (FR) – ‘What’ we want to achieveA minimum set of requirements a system must satisfy FunctionalDesign Parameter (DP) – ‘How’ FRs will be achievedKey physical variables that characterize design solutionFR1FR11FR111DP1FR12FR112FR121FR122FR1111 FR1112 FR1211 ng{DP}Decomposition – ‘Zigzagging’DP12DP121DP122Process of developing detailedrequirements and concepts by movingbetween functional and physicaldomainDP1111 DP1112 DP1211 DP1212:Independence AxiomMaintain the independence of FRsHierarchical FR-DP structureInformation AxiomMinimize the information content

Design AxiomsIndependence Axiom: Maintain the independence of FRsO DP1 X DP 2 FR1 X FR 2 O FR1 X FR 2 XUncoupledO DP1 X DP 2 FR1 X FR 2 XDecoupledX DP1 X DP 2 CoupledInformation Axiom: Minimize the information contentInformation content for functional requirement i - log2Pi dr DesignRangep.d.f.f(FR)FRCommonRange, ACDPSystem Range,p.d.f. f(FR)FRDPdrldru sr FRFRFRDPDPFRFRFRFRFRFRFRDPDPDPDPDPDPDP

FR must be satisfied within the designrange.Prob.DensityDesignrangeFR

To satisfy the FR, we have to map FRs in thephysical domain and identify DPs.Prob.DensityDesignrangeSystemrangeFR

Design Range, System Range, and CommonRangeProbab.DensityTargetBiasSyst emRang eDesign Rang eArea o fCommonRang e (Ac)Variationfrom t hepeak valu eFR

What happens when there are many FRs?Most engineered systems must satisfy many FRs ateach level of the system hierarchy.The relationship between the FRs determines howdifficult it will be to satisfy the FRs within thedesired certainty and thus complexity.

If FRs are not independent from each other,the following situation may exist.Pro b. De n s i tyPro b. De n s ityDe si g nRa n geDe si g nRa n g eSy ste mRa n g eFR1Syste mRa n geFR2

Coupling decreases the design rangeand thus robustness!!Uncoupled FR1 A11 0 FR2A22 0 FR3 00 FR1 DP1 A11 FR2 DP2 A22 FR3 DP3 A330 DP1 0 DP2 A33 DP3 Decoupled FR1 A110 FR2 A21 A22 FR3 A31 A32 DP1 DP 2 DP3 DP1 DP2 A33 DP3 00 FR1A11 FR 2 A21 DP1A22 FR3 A31 DP1 A32 DP 2A33

What is wrong with conventional connectors?It violates the Independence Axiom, whichstates that“Maintain the independence of FunctionalRequirements (FRs)”.It is a coupled design.

What is the solution?Tribotek connector: A woven connector

Tribotek Electrical Connectors(Courtesy of Tribotek, Inc. Used with permission.)

Performance of “Woven” Power ConnectorsPower density 200% of conventionalconnectorsInsertion force less than 5% ofconventional connectorsElectric contact resistance 5 m ohmsManufacturing costCapital Investment

TMA Projection SystemPhotos removed for copyright reasons.

What are the FRs of a face seal that mustisolate the lubricated section from theabrasives of the external environment?There are many FRs.They must be defined in a solution neutralenvironment.

Is this knob a good design or a poordesign?AAInjectionmolded knobShaftwith flatmilledsurfaceSection A-A

AAInjecti onmolded k nobShaftwith flatmi lledsurfaceSect ion A-A

Which is a better design?M ill ed FlatEn d o f th esh af tSlotM ill ed FlatEn d o f th esh af tAMe talSh af tAIn jec tio nm old ednylo n K n ob(b)(a)Se cti on view A A

HistoryGoalTo establish the science basefor areas such as design andmanufacturing

How do you establish sciencebase in design?Axiomatic approachAlgorithmic approach

ReferencesN. P. Suh, Axiomatic Design: Advancesand Applications. New York: OxfordUniversity Press, 2001N. P. Suh, The Principles of Design. NewYork: Oxford University Press, 1990

Axiomatic DesignAxiomatic Design applies to alldesigns: Hardware Software Materials Manufacturing Organizations

Axiomatic DesignAxiomatic Design helps thedesign decision making process. Correct decisions Shorten lead time Improves the quality of products Deal with complex systems Simplify service and maintenance Enhances creativity

Axiomatic Design Axioms Corollaries Theorems Applicationsmanufacturing,--hardware,materials, etc. System design Complexitysoftware,

System integrationStack of modulesS tac k o f mo du l e sTrackRobotLoadingStationStack of modulesMachi ne AS tac k o f mo du l e sMac hi ne BA cluster of two machines that are physically coupledto manufacture a part.

Introduction (cont’d)Example1Xerography-based Printing MachineLightOriginalimageImage iscreated hereSeleniumcoated Al.cylinderPaperFeed RollPaperWiperRollTonercontainerToner is coatedon surfaces ofSelenium withelectric chargesSchematic drawing of the xerography based printing machine.

Who are the Designers?How do we design? What is design?Is the mayor of Boston a designer?Design Process1. Know their "customers' needs".2. Define the problem they must solve to satisfy theneeds.3. Conceptualize the solution through synthesis, whichinvolves the task of satisfying several differentfunctional requirements using a set of inputs such asproduct design parameters within given constraints.4. Perform analysis to optimize the proposed solution.5. Check the resulting design solution to see if it meetsthe original customer needs.

Definition of DesignDesign is an interplay betweenwhat we want to achieve andhow we want to achieve them.

Definition of Design"Whatwe wanttoachieve""Howwe wanttoachievethem"

Example: Refrigerator Door DesignFigure ex.1.1.a Vertically hung refrigerator door.

Ultimate Goal of Axiomatic DesignThe ultimate goal of Axiomatic Design is toestablish a science base for design and toimprove design activities by providing thedesigner with a theoretical foundation basedon logical and rational thought processes andtools.

Creativity and Axiomatic DesignAxiomatic design enhances creativityby eliminating bad ideas early andthus, helping to channel the effort ofdesigners .

Historical Perspective on AxiomaticDesignAxioms are truths that cannot be derived but for whichthere are no counter-examples or exceptions.Many fields of science and technology owe theiradvances to the development and existence of axioms.(1) Euclid's geometry(2) The first and second laws of thermodynamicsare axioms(3) Newtonian mechanics

ConstraintsWhat are constraints?Constraints provide the bounds on theacceptable design solutions and differ fromthe FRs in that they do not have to beindependent.There are two kinds of constraints:input constraintssystem constraints.

Example: Shaping of Hydraulic TubesTo design a machine and a process that canachieve the task, the functional requirementscan be formally stated as:FR1 bend a titanium tube to prescribedcurvaturesFR2 maintain the circular cross-section ofthe bent tube

Tube Bending Machine Design (cont’s)Given that we have two FRs,how many DPs do we need?

Example: Shaping of Hydraulic TubesFixed set ofcounter-rotatinggrooved rollersω1ω1 ω2ω2Tube betweenthe two rollersPivotaxis ω 1ω1 ω2See Example 1.6 in [Suh 2001].ω2Flexible set ofcounter-rotatinggrooved rollersfor bending

Example: Shaping of Hydraulic TubesDP1 Differential rotation of the bending rollers to bend the tubeDP2 The profile of the grooves on the periphery of the bendingrollersFixed set ofcounter-rotatinggrooved rollersω1ω1 ω2ω2Tube betweenthe two rollersPivotaxis ω 1ω1 ω2ω2Flexible set ofcounter-rotatinggrooved rollersfor bendingTube bending apparatus

Example: Van Seat Assembly(Adopted from Oh, 1997)See Example 2.6 in [Suh 2001].Schematic drawing of a van seat that can be removedand installed easily using a pin/latch mechanism

Example: Van Seat AssemblySolutionThe FR of the seat engagement linkage is that thedistance between the front leg and the rear latchwhen the seat engages the pins must be equal tothe distance between the pins, which is 340 mm.The linkages [see Figures E2.6.b and c in Suh2001] determine the FR F. The following tableshows the nominal lengths of the linkages.

Example: Van Seat AssemblyTraditional SPC Approach to Reliability and QualityThe traditional way of solving this kind of problem has been to dothe following:(a) Analyze the linkage to determine the sensitivity of theerror.Table a Length of linkages and sensitivity analysisLinksL12L14L23L24L27L37L45L46L56L67Nominal Length .00334.70Sensitivity (mm/mm)3.293.746.321.486.555.9411.7210.1712.063.71

Decomposition, Zigzagging and 1Functional Physical DomainZigzagging to decompose in the functional and the physical domains and createthe FR- and DP hierarchiesFigure by MIT OCW. After Figure 1.3 in [Suh 2001].

Identical Design and Equivalent DesignEquivalent Design:When two different designs satisfy the same setof the highest-level FRs but have differenthierarchical architecture, the designs aredefined to be equivalent designs.Identical Design:When two different designs satisfy the same setof FRs and have the identical designarchitecture, the designs are defined to beidentical designs.

Example: Refrigerator DesignFR1 Freeze food for long-term preservationFR2 Maintain food at cold temperature forshort-term preservationTo satisfy these two FRs, a refrigerator with twocompartments is designed. Two DPs for thisrefrigerator may be stated as:DP1 The freezer sectionDP2 The chiller (i.e., refrigerator) section.

Example: Refrigerator DesignFR1 Freeze food for long-term preservationFR2 Maintain food at cold temperature for short-termpreservationDP1 The freezer sectionDP2 The chiller (i.e., refrigerator) section. X 0 DP 1 FR 1 0 X DP 2 FR 2

Example: Refrigerator DesignHaving chosen the DP1, we can now decomposeFR1 as:FR11 Control temperature of the freezersection in the range of -18 C /- 2 CFR12 Maintain the uniform temperaturethroughout the freezer section at thepreset temperatureFR13 Control humidity of the freezer section torelative humidity of 50%

Example: Refrigerator DesignFR11 Control temperature of the freezer section in the range of -18 C /- 2 CFR12 Maintain the uniform temperature throughout the freezer section at the preset temperatureFR13 Control humidity of the freezer section to relative humidity of 50%DP11 Sensor/compressor system that turn on andoffthe compressor when the air temperature ishigher and lower than the set temperature inthefreezer section, respectively.DP12 Air circulation system that blows air into thefreezer section and circulate it uniformlythroughout the freezer section at all timesDP13 Condenser that condenses the moisture in thereturned air when its dew point is exceeded

Example: Refrigerator DesignSimilarly, based on the choice of DP2 made, FR2may be decomposed as:FR21 Control the temperature of thechilled section in the range of 2 to 3 CFR22 Maintain a uniform temperaturethroughout the chilled section within 1C of a preset temperature

Example: Refrigerator DesignFR21 Control the temperature of the chilled section in the range of 2 to 3 CFR22 Maintain a uniform temperature throughout the chilled section within 1 C ofa preset temperatureDP11 Sensor/compressor system that turn onand off the compressor when the airtemperature is higher and lower than theset temperature in the chiller section,respectively.DP12 Air circulation system that blows air intothe freezer section and circulate ituniformly throughout the freezer sectionat all times

Example: Refrigerator DesignFigures removed for copyright reasons.See Example 1.7 in [Suh 2001].

Example: Refrigerator DesignThe design equation may be written as: FR12 XOO DP12 FR11 XXO DP11 FR13 XOX DP13 Equation (a) indicates that the design is a decoupled design.FR22FR21DP22DP21XX0X

Full DM of Uncoupled Refrigerator DesignDP2DP1DP12 DP11 DP13 DP22 DP21FR21 X0000FR1FR11 XX000FR13 X0X00FR2 FR22 000X0FR21 000XX

Full DM of Uncoupled Refrigerator DesignDP2DP1DP12 DP11 DP13DP22DP21FR12X0000FR1FR11XX000FR13X0X00FR2 FR22X0000FR21000X0/X

AnalysisWhen do we perform analysisduring the design process?

Requirements for Concurrent Engineering[A ][B][C] [A] {B]1. Bot h d iago n al[\ ][\ ][\]2. D i ag x Fu ll[\ ][X][X]3. D i ag x tria n g .[\ ][LT][LT]4. Tri a. x Tri ang[LT][LT][LT]5. Tri a. x Tri ang[LT][U T][X]6. Fu l l x Fu ll[X][X][X]Table 1.3 The characteristic of concurrent engineering matrix [C].

Ideal Design, Redundant Design, and CoupledDesign - A Matter of Relative Numbers of DPs and FRsDepending on the relative numbers of DPs and FRs the designcan be classified as coupled, redundant and ideal designs.Case 1:DesignNumber of DPs Number of FRs: CoupledWhen the number of design parameters is less than thenumber of functional requirements, we always have acoupled design. This is stated as Theorem 1.Case 2: Number of DPs Number of FRs: RedundantDesignWhen there are more design parameters than the functionalrequirements, the design is called a redundant design. Aredundant design may or may not violate the IndependenceAxiom.

The Second Axiom: The InformationAxiomAxiom 2: The Information AxiomMinimize the information content.Information content I is defined in terms of the probability ofsatisfying a given FR.I log21 log2 PPIn the general case of n FRs for an uncoupled design, I may beexpressed asnn1I log 2 log 2 PiPii 1i 1

Design Range, System Range, and Common RangeProbab.Den sityTar getBi a sSyst emRang eDesign Rang eArea o fCom m onRang e ( Ac)Varia tionfrom t hepe a k valu eFRDesign Range, System Range, and Common Range in a plot of theprobability density function (pdf) of a functional requirement. The deviationfrom the mean is equal to the square root of the variance. The designrange is assumed to have a uniform probability distribution in determiningthe common range.

Measure of Information Content in Real SystemsThe probability of success can be computed by specifying the DesignRange (dr) for the FR and by determining the System Range (sr) that theproposed design can provide to satisfy the FR.AsrI log 2Acr(1.9)where Asr denotes the area under the System Range and Acr is the area ofthe Common Range.Furthermore, since Asr 1.0 in most cases (since the total area of theprobability distribution function is equal to the total probability, which isone) and there are n FRs to satisfy, the information content may beexpressed asnI log 2i 11Acr(1.10)

Example: Buying a HouseFR1 Commuting time for Prof. Wade must be in the range of 15to 30 minutes.FR2 The quality of the high school must be good, i.e., more than65 % of the high school graduates must go to reputablecolleges.FR3 The quality of air must be good, i.e., the air quality must begood over 340 days a year.FR4 The price of the house must be reasonable, i.e., a four bedroom house with 3,000 square feet of heated space must beless than 650,000.

Example: Buying a HouseThey looked around towns A, B, C and collected the followingdata:Tow nABCFR1 Comm.time [min]20 to4020 to 3025 to45FR2 Qualityof school [%]50 to7050 to 7550 to80FR3 Qualityof air [days]300 to 320340 to 350350 and upFR4 Price [ ]450k to 550k 450k to 650k 600k to800kWhich is the town that meets the requirements of the Wadefamily the best? You may assume uniform probabilitydistributions for all FRs.

Example: Buying a HouseSolutionProb.Dist.Design RangeCommonRangeSystemRange10203040FR1 Commuting Time (min).Probability distribution of commuting time

Example: Buying a HouseProb.Dist.Design RangeSystem RangeCommon Range20406080Quality ofSchool (%)Probability distribution of the quality of schools

Example: Buying a HouseThe information content of Town A is infinite since it cannot satisfyFR3, i.e., the design range and the system range do not overlap atall. The information contents of Towns B and C are computedusing Eq. (1.8) as follows:TownABCI1I2I3[bits][bits][bits]1.02.0 Infi nite01.3202.01.00I4ΣI[bits][bits]0Infini te01.322.0 5.0

1.8 Common Mistakes Made by Designersi.Coupling Due to Insufficient Number of DPs(Theorem 1)ii.Not Recognizing a Decoupled Designiii.Having more DPs than the number of FRsiv.Not creating a robust design -- not minimizing theinformation content through elimination ofbias andreduction of variancev.Concentrating on Symptoms rather than Cause -Importanceof Establishing and Concentrating on FR.

Constraints (Cs) are bounds on acceptable solutions. There are two kinds of constraints: input constraints and system constraints. Input constraints are imposed as part of the design specifications. System constraints are constraints imposed by the system in which the des

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