Draft #8 of Concepts Needed for System Static Structure

1. Draft #8 of Concepts Neededfor System Static Structure David W. Oliver Version October 9, 2002 Wakefield, R.I.

2. Concept Model for Systems Engineering Semantic Dictionary and Accompanying Model The concept model consists of two interlocking parts. The first part is the semantic dictionary that defines each term. It is currently captured in an Excel spread sheet. The definitions have been written to satisfy the ISO standard for writing definitions that can be found on the BSCW web site. The definitions are an ordered set. Definitions lower in the set use terms found higher in the set. This helps prevent circular definition. Since the definitions are not arranged alphabetically, they are numbered with a reference number to aid in locating them. Definitions according to the ISO standard define kinds of things, composition of things from other things, and associations among things. When one reads ten or more text definitions the usual mind finds it difficult to remember the many relationships implied. Hence a model accompanies the semantic dictionary. The dictionary explains meanings in natural language. The model captures the multitude of relationships in a graphic form so that the relationships can be scanned. The model is written in UML 1.X, with indications of semantics that are missing from the language.

3. C C C C (3) Domain of Interest (2) Category (5) categorizes System View (1) (7) (6) has view Stakeholder Environment SE_Thing exhibits has (4) (8) Interacts with Stakeholder Need satisfied by System (11) (9) allocated to Property Reference System Requirement Property represented by reference for statement of (10) derived from (12) (13) (14) Physical Property Structure Behavior Top Level Concept Model, Figure 1. allocated to budgeted to

4. Top Level Model The model needs to be read with reference to the definitions in the semantic dictionary. It starts with SE_Thing that is any thing on which repeated measurements can be made for the engineering purposes of interest. This is a necessary definition because otherwise it is not possible to verify that a design or implementation meets its requirements. SE_Thing is built from SE_Thing in a hierarchy. The aggregation symbol has a small “C” in it to show that what is meant is a decomposition into all of the parts. The special notation is used because this concept is missing form UML 1.X. The Domain of Interest constitutes all the things of interest to the application. System is a kind of SE_Thing and thus it is built of systems in a hierarchy and it must have measurable characteristics that are repeatable. What makes the System unique is that it has well defined relationships with all of the things with which it interacts. The collection of those things is its Environment. To have a system it is necessary to characterize what is in the system and what is in the environment along with the static and dynamic interactions between system and environment. The Environment contains SE_Things and Systems.

5. Different persons in engineering, manufacturing, maintenance, and management need different sets of information about the system. Manufacturing personnel need to know about all the materials, nuts and rivets that go into the system and how they assemble together. Maintenance personnel need to have diagnostic information and deal with replaceable units of the system. There are a very large number of such useful collections of information, each with its own context. System View provides for the collection of such sets of information, each set in a particular context. An important subset of things in the environment are the Stakeholders. These are all the persons and organizations with a need, preference, or interest in the system. Stakeholders may include manufacturer, owner, user of owner’s services, user of the system, operator, maintainer, government regulator. Stakeholder Need represents their need, preference, interest, etc. in the system. If the System is designed and implemented well, then it satisfies these needs in a manner that is superior to competitive systems. It sells in the marketplace.

6. A Property is a named measurable or observable attribute, quality or characteristic of an se_thing. If you can measure it or observe it it is called a property. Properties have units, values, variances and probability distributions associated with them. They may be looked up in handbooks of properties of standard materials, they may be calculated from the structure of the thing, or they may be measured directly. In general they are tensors and may be a function of time. Because of the multiple ways of arriving at a property and its values, it is important to have a Property Reference that establishes the source of the information. A Requirement is a statement of a Property that a System shall exhibit. The relationship to System is handled by allocating the requirement to the system that shall exhibit that property. This formality allows the engineer to consider alternative allocations to different systems that may fulfill the requirement. It is fundamental to trade-off among solutions. Requirements originate from Stakeholder Needs. As the design proceeds in levels of detail, requirements are derived from other requirements. These “derived from” relationships are preserved as traceability relationships. In a real world problem requirements will be changed from time to time. It is critical to trace from a requirement that has changed to other requirements impacted by that change.

7. It is useful to distinguish among three kinds of properties. • Structure, the description of how a system decomposes into its parts • and how the parts assemble to make the whole. • Behavior, what the system does in response to the things in its • environment. This includes both desired responses that satisfy needs, • and prevention of undesired responses (failures) that can cause injury, • destruction, or loss. • Physical Property includes all the measurable or observable attributes, • qualities or characteristic of an se_thing that cannot be observed • in interaction with the environment. Additional instruments or tools • are required to make the measurement or observation. Mass may • require a scale for weighing, index of refraction may require use of • an optical instrument. • These three kinds of properties are described separately and then • interrelated. This principle supports the consideration of alternatives.

8. C C C (14) Structure (19) (17) (15) Interface Description System Assembly described by Port 1 1 Interconnection (18) (16) Link System Static Structure, Figure 2.

9. Structure Structure is built from System Assembly, Port, and Interface Description. Structure decomposes hierarchically. This forces System Assembly and Port to also decompose hierarchically. System Assembly The System Assembly is simply a part or component list. The name used follows the STEP manufacturing point of view of looking at a part or component and talking about it as an assembly because their job is to assemble it. This is a place where it may be advisable for clarity to use the words component or part as an alias for System Assembly. Port Each System Assembly (part or component) attaches to others at particular locations. These locations are called Ports. This is a familiar idea when one thinks of the port on a power cord that plugs into a port on the wall to get electric power. It also applies to the surface of a bridge, a port, that interacts with wind, a port. In the second case the concept is less intuitive and more formal but it works. Ports connect to ports.

10. Interconnection Interconnection specifies which ports attach to which other ports. Together System Assembly, Port, and Interconnection specify how parts go together to constitute the whole. This description does not include Behavior or Physical Properties. Interface Description Each port has associated with it a description, an Interface Description, that describes the geometry, forces, transferred material or energy or information, protocols, how to assemble to it, and tests that may be required of the port-to-port connection. For two ports to be interconnected their interfaces must be compatible. Structure, Behavior and Physical Property Structure, Behavior and Physical Properties are described separately. Behavior and Physical Properties are allocated or budgeted to System Assembly to complete the description.

11. Behavior Behavior is built from Function, I/O (Input/Output), and Function Ordering as shown in Figure 3. Any SE_Thing may be I/O (Light blue shows an entity comes from Figure 1.). A Function is a entity of transformation that changes a set of inputs to a set of outputs. Function Ordering orders the functions such that it is possible to represent sequence, concurrency, branching, and iteration. There are two major forms of representing Behavior. The continuous form emerged in systems engineering in the 1970’s. It provides for completed functions to enable succeeding functions, for I/O to trigger functions, and for ordering operators to represent sequence, branching, and iteration. The SEDRES model represents this with a Petrie net model. UML 2.0 contributors may be using a Petrie Net model. If so, then these two models need careful comparison. The discrete for of behavior representation emerged from automata theory

12. (1) SE_Thing (12) Behavior (21) (20) (22) C C C C Function Ordering orders Function I/O generates and consumes (4) (24) (23) (6) External Function Internal Function allocated to System Environment allocated to 1 2 generates and consumes Light blue background means this entity comes from Figure 1. Behavior, Figure 3.

13. and has matured into State Charts that provide for state explosion in highly concurrent models. SEDRES has a representation for this and has demonstrated model transfer between Statemate and Teamwork Real Time tools. In the UML community Action Semantics are to provide a basis for state based behavior. These two approaches require careful correlation. The concept model here does not go beyond the very general notion of function ordering, but notes the critical importance of correlation among emerging detailed models. Structure and Physical Properties Physical Property, its relationship to the Structure hierarchy and to analysis is shown in Figure 4. The key concept is that performance, behavior and physical properties of the whole results from the structure, the behavior and physical properties of the parts. They are not related to a class tree.

14. Analytical_representation Parameter_assignment model_parameter_assignment model_representation analytical_representation_name Unit Calculated Property Value Measured Property Value Required/ Budgeted Property Value Target budget Property Value parameter_value assigned_parameter mean variance probability_ distribution histogram Analytical_model name representation_language reference_document parameter source_code Model_parameter C C C type_name unit of measure reference_document parameter_type valid_range default_value (25) assigned to (32) (33) measured in assigned by (13) (26) (31) has Physical Property Property Value modeled by represented by Name ID (34) assigned to (27) (30) (28) (29) (14) Structure declared to have calculated to have working target measured to have (19) (15) (17) Interface Description System Assembly described by Port 1 1 Interconnection (18) Structure and Physical Property, Figure 4.

15. Discussion of Figure 4. System Assemblies in the system assembly tree all have Physical Properties such as mass, power consumption, geometry, MTBF, drag coefficient, etc. The Physical Properties are assigned to a particular System Assembly. A Physical Property has a name and an ID that identifies it uniquely. For example, many different System Assemblies have the Physical Property mass. Consequently each of these assigned Physical Properties needs an ID. Each has an associated unit in which it is measured. A Physical Property assigned to a particular System Assembly has values. The value may be expressed as a mean, a mean with variance, a probability distribution, or a histogram. The value goes through a series of versions as the system definition evolves. The System Assembly is declared to have a Required or Budgeted Value. The System Assembly may have a Target Budget Property Value used as a guide or target as designers consider alternatives. A System Assembly, as a whole, may have a Calculated Property Value based on analysis of the properties, behaviors and interactions of its parts. When a System Assembly is built, it may have a Measured Property Value.

16. Discussion of Figure 4. Calculated Property Values - Analytical Modeling Any one assembly is an interconnection of assemblies one tier down in the tree. The emergent properties of any assembly are a result of the properties, interconnection,and interaction of the sub-assemblies from which it is built. The relationships may be very non-linear in the physical world as observed with phenomena like combustion and friction. . The basic relationships for analytical modeling of emergent properties and budgeting of properties are shown in Figure 4. A set of engineering equations or estimates, analytical models, are used by systems engineers to budget properties to the interacting sub-assemblies as a guide to designers at the lower level. When designs for all of the sub-assemblies are available, their individual properties and interactions are better defined. The same equations are used to calculate the emergent properties of the complete assembly. The fidelity of the calculations increases as the work proceeds.

17. A System Assembly, as a whole, may have a Calculated Property Value based on analysis of the properties, behaviors and interactions of its parts. This is accomplished by estimation or by an analysis that solves the relevant engineering equations. This makes it necessary to represent physical properties as parameters in the equations of the relevant analysis model. Model Parameter provides this parameterization. It has an attribute of its of the unit of measure applicable to the analysis. This may be different from the unit assigned to Physical Property. The reference_document attribute specifies the standard document that contains the reference for the Model_parameter. A default value and valid range can be specified when needed. Parameter_assignment assigns parameters to the analytical equations that must be solved, Analytical _representation. Each Analytical_representation may have associated with it several Analytical_models that provide answers at different levels of fidelity and with different efforts of computation.

18. Emergent Properties and Budgeting of Properties Example One may wish to develop a car that can accelerate from zero to sixty miles per hour in 6.5 seconds or less. This is a required emergent property of the car. This behavior is a result of the power of the drive train, the air resistance of the body, the total mass of the car, and the friction of the tires on the road. These parameters are inter-related by a second order differential equation. The differential equation is first used to budget target values of mass, power, drag coefficient, and tire friction to the appropriate components as targets for the designers. When the designs are available with definite property values, the same equations are used to calculate the emergent property, time for acceleration from zero to sixty mph for the car. Note that there may be several distinctly different approaches to the solution of what sub-components to use. Thus it is useful for the assembly to have relationships that indicate if it is an alternative or is selected as a solution, if it meets requirements, and what its regularization function value may be as the basis of selecting a particular solution from among the alternatives.

19. Car Weight, Wc Time to Accelerate 0 to 60 mph, Ta C Body Weight, Wb Drag Coefficient, Dg Chassis Weight, Wch Drive Train Weight, Wdt Power, Pdt Tires Weight, Wb Friction, Tf Electrical Weight, We Engineering Equations Wc = Wb + Wch + Wdt + Wh + We Wc * d2x/dt2 + Dg * dx/dt = Tf *Wc 0 < dx/dt < Pdt/(Tf*Wc) Wc * d2x/dt2 + Dg * dx/dt = Pdt/(dx/dt) Pdt/(Tf*Wc) <dx/dt initial condition: x=o, dx/dt=0 compute: t, Ta, when dx/dt=60 mph Figure 5. Ta is an emergent property of Car. Dg is an assembly property of Body

20. Example of Figure 5. The Table below is a crude map of the equations in Figure 5. Into the concept model defined in Figure 4 for the car example. Only the properties of car have been mapped. Note there are two analytical models. One is very simple and assumes constant traction once the car is in motion and rolling friction applies. The second is of higher fidelity and uses traction vs. Rpm. from actual engine data, including transmission gear changing. It is hoped that reviewers Frisch and Thurman will correct Figures 4. and 5. and this table.

21. Some definitions taken from the report of Frisch and Thurman are captured • on the next three slides. • Model_parameter • A Model_parameter is a formally declared variable of the analytical model provided for an external application to • populate at execution time in a computing environment. • EXAMPLE: In Spice, temperature is a Model_parameter that may be set at the execution time. • The data associated with this application object are the following: • default_value • parameter_type • reference_document • type_name • unit_of_measure • valid_range • default_value • The default_value specifies a value for the parameter. The default_value need not be specified for a particular • Model_parameter. • parameter_type • The parameter_type specifies either a boolean_property_type, a logical_property_type, a physical_property_type, or a • string_property_type for the Model_parameter.

22. reference_document The reference_document specifies either a specific document or an identifier for the standard document that contains the reference for the Model_parameter. type_name The type_name specifies the string used as the human-interpretable type name for the Model_parameter. unit_of_measure The unit_of_measure specifies the string used as the descriptive label for the unit of measure associated with the Model_parameter. The unit_of_measure need not be specified for a particular Model_parameter. The representation of units described in ISO 10303-41 shall be used. Note that the unit used in requirements specification may differ from the unit_of_measure used in analysis valid_range The valid_range specifies the appropriate range of values of the Model_parameter. The valid_range need not be specified or a particular Model_parameter. There may be more than one Coordinated_characteristic for a Model_parameter. The valid_ranges need not be contiguous. NOTE: The prefixes of the valid_range and default_value may be different as long as the base units are the same type. Formal constraints: UR1: The combination of the reference_document and the type_name shall be unique within a population of Model_parameter.

23. Parameter_assignment Parameter_assignment provides actual values for characteristics declared formally by the Model_parameter. The data associated with this application object are the following: assigned_parameter parameter_value assigned_parameter The assigned_parameter declares the formal parameters assigned values by the Parameter_assignment. parameter_value The parameter_value specifies actual values for the Parameter_assignment. Formal constraints: WR1: The type of units of the parameter_value shall be the same as that of the assigned_parameter.

24. Analytical_representation An Analytical_representation is the association of specific properties of specific System Assemblies with an Analytical_model in order to unambiguously characterize the performance of a specific System Assembly. NOTES: 1.This entity accomplishes a function similar to the parameter assignment part of a statement in a Spice netlist, or a function or subroutine call in a computer program. This capability is useful where the parts in the library have many parameters, not all of which apply to each simulation model that could be used for the part. This entity matches up the correct parameter values with the correct model. 2.The properties specified should be in accordance with the capabilities and limitations of the Analytical_model. That is, the mathematical formulations in the Analytical_model apply over limited ranges of real product characteristics and environmental characteristics. 3.This part of ISO 10303 does not standardize qualification of Analytical_representations for an intended usage. The data associated with this application object are the following: analytical_representation_name model_parameter_assignment model_representation analytical_representation_name The analytical_representation_name specifies the string for the human-interpretable identifier for this Analytical_representation. model_parameter_assignment The model_parameter_assignment specifies the role of the Parameter_assignment for the Analytical_representation. There shall be one or more Parameter_assignment for the Analytical_representation. NOTE: For each parameter declared in a model definition, an actual value must be assigned when that model is referenced, unless there is a default assignment included in the source code for the model.

25. model_representation The model_representation specifies the Analytical_model as the basis model for the Analytical_representation. Formal constraints: UR1: The analytical_representation_name shall be unique within a population of Analytical_representation. WR1: Each member of model_parameter_assignment.assigned_parameter shall be a member of model_representation model_parameters. NOTE: Only parameters declared in the model_representation are assigned values. Analytical_model Provides a mathematical description of the properties of a system. An Analytical_model may be a Library_model. NOTES: 1.In this part of ISO 10303 an Analytical_model includes the variable declarations of the mathematical description but may not include the assignment of actual values for the variables declared. 2.This part of ISO 10303 provides support for computer systems to verify type consistency between product data defined in this part of ISO 10303 and product data captured by Analytical_models. 3.This part of ISO 10303 describes the interfaces (ports) to an Analytical_model and provides support for type checking of the units used for the parameters that may be assigned values for an Analytical_model.

26. Analytical_model • An Analytical_model provides a mathematical description of the properties of a system. An Analytical_model may be a • library model. • NOTES: • In this part of ISO 10303 an Analytical_model includes the variable declarations of the mathematical description but may • not include the assignment of actual values for the variables declared. • This part of ISO 10303 provides support for computer systems to verify type consistency between product data defined in • this part of ISO 10303 and product data captured by Analytical_models. • This part of ISO 10303 describes the interfaces (ports) to an Analytical_model and provides support for type checking • of the units used for the parameters that may be assigned values for an Analytical_model. • EXAMPLE: consider the case where actual values are not included: the Analytical_model for a resistor that is coded in • pseudocode. When the Analytical_model is referenced by an analytical_representation, literals will be supplied for items • declared in the interface; both connections and their parameters, and the simulator will ensure that types are compatible. • NOTES: • Usually the system is exercised in experiments to evaluate the usefulness of the system in the intended application. • The language, syntax, and internal semantics of an Analytical_model are not specified by this part of ISO 10303. • This part of ISO 10303 provides complete support for exchange of units, including SI units, derived units, and user • declared units.

27. This part of ISO 10303 provides complete support for prefixes of units. • The data associated with this application object are the following: • access_mechanism • name • parameter • reference_document • representation_language • source_code • access_mechanism • The access_mechanism is an inverse relationship that specifies that the existence of the Analytical_model is dependent • on the existence of the Analytical_model_port that specifies the Analytical_model as its accessed_analytical_model. • There shall be one or more Analytical_model_port for an Analytical_model. • name • The name specifies the string that is the identifier for the Analytical_model. • parameter • The parameter specifies the role of the Model_parameter for the Analytical_model. There shall be one or more • Model_parameter for a particular Analytical_model. Figure am illustrates the use of parameters. • NOTE: Parameters of a model are separated from their connections to support the nodal formulation.

28. reference_document The reference_document specifies the role of the document for the Analytical_model. The reference_document includes interface specifications for Analytical_models of interest to the enterprise. representation_language The representation_language specifies the Language_reference_manual that defines the semantics and syntax of the computer interpretable strings in which the Analytical_model will be encoded. Figure am illustrates how the representation_language is specified and coded. NOTE: Only representation_languages that use characters from the ASCII code are supported by this part of ISO 10303. source_code The source_code specifies the role of ths specification for an Analytical_model. The source_code contains the source code for the Analytical_model. Figure am illustrates how a source_code is specified and coded. Formal constraints: UR1: The combination of the name and the reference_document shall be unique within a population of Analytical_model. UR2: The combination of the name and the source_code shall be unique within a population of Analytical_model.

29. Allocation of Requirements Depending upon their content, requirements are allocated to different parts of the information model. Requirements describing functions are allocated to functions, etc. This is a useful way of classifying requirements for the purpose of creating a logically consistent model or description of a system. Within systems engineering there is no single standardized way of classifying requirements and many different classifications for different purposes are in use. The classification given in Figure 6. Is defined as shown because it is useful for the purpose allocating or assigning requirements. It is not possible to enforce any process with an information model and AP233 is intended to support both pest practices and other practices in use. Hence, any collection of requirements may contain compound requirements, contradictory requirements, and non-feasible requirements. Consequently the generalization/specialization of Figure 6. Is non-exhaustive and inclusive.

30. A Requirement Classification, needed to show how requirements are allocated to Behavior & System Structure (10) System Requirement User Defined non-exhaustive inclusive based on content and allocation Effectiveness Measure Functional Requirement Temporal Requirement Physical Property Requirement Interface Requirement (35) (42) (38) (36) (37) Imposed Design Requirement Reference Requirement (39) (40) Classification of Requirements for the Purpose of Allocation, Figure 6.

31. C C C C C Property Requirement Allocations, Figure 7. Behavior System Static Structure Physical Property assigned to assigned to consume generate Function Ordering order Port System Assembly Interface I/O Function allocated to bound to assigned to assigned to (28) Reference Source Interface Requirement assigned to Physical Property Requirement assigned to points to assigned to Functional Requirement Temporal Requirement Reference Requirement Imposed Design Effectiveness Measures used in based on allocation non-exhaustive inclusive has Regularization Function has (45) Optimization Direction Requirement_S Weight used in optimizes (44) (43)

32. Summary of Allocation Relationships • Functional Requirements are assigned to to functions • Temporal Requirements are assigned to functions • Function is allocated to System Assembly (red used because of line crossings) • I/O is bound to ports (red used because of line crossings) • Interface Requirements are assigned to Interfaces • Physical Property Requirements are assigned to System Assembly • Imposed Design is assigned to the System Assembly on which it is imposed • Reference Requirements point to a Reference Source that may contain • requirements of all the kinds in the classification

33. Physical Property and Time • Figure 8. Shows draft models for Physical Property and Time. Physical Property • and System Assembly are under study by a team member and improved models • are expected for Figure 8. and Figure 4. • The model for time in Figure 8. is preliminary and needs discussion. • Continuous Time is a dimension along with three spatial dimensions used by science • and engineering to describe reality using math. It has no past, present or future. • Present Time recognizes a standard of year, month, week, day, hour, minute, and • second to represent past, present, and future. It is the basis of plans and schedules. • Time Interval provides a time duration that may be assigned to a task or function to • represent how long the task will take for completion. • Start Time is a Present Time that states where in Present Time a Time Interval • begins. • Stop Time is a Present Time that states where in Present Time a Time Interval • ends.

34. Physical Property and Time • Discrete Time is time represented by clock pulses of negligible duration. • In this approximation events occur on each clock pulse. • Time is one of the most accurately measured quantities that we have. Current • accuracy of measurement is about one part in 10 -13. Research underway may • extend this to 10 -17. Many properties now have primary standards based in • part on time.

35. uses Measurement Infrastructure Measurement Method measures Physical Property Name Unit Mean Value Variance Probability Distribution Value Range (13) Refined Decomposition for Physical Property and Time, Figure 8. Time Unit Mean Value Variance Probability Distribution Continuous Time Present Time Time Interval Discrete Time Start Time Stop Time

36. Systems Engineering Management Three Models follow that are important to systems Engineering Management. The models for verification and validation are at first draft level and need discussion. The model for Risk was discussed with the Risk Working Group at the INCOSE 2002 symposium. AP233 is waiting for there corrections and changes. The existing model is based on information from the risk working group, NASA Goddard Risk Attributes in SLATE ‘GPM’ Data Base March 7,2002 (Dave Everett), and from NASA JPL Risk Process Diagram

37. System Requirement Verification Requirement Category Verification Event Risk Verification Procedure Verification Configuration Issue Organization (10) categorized by categorized by traces to (47) (48) performed with satisfied by (46) causes causes has scheduled by specified by uses Verification Requirement Status (50) specified by (54) (53) Verification Plan (52) (49) causes causes assigned to (51) generates

38. System Requirement Validation Requirement Category has Validation Event Validation Requirement Status Risk Validation Procedure Validation Infrastructure Issue Organization (10) (7) (8) Stakeholder Need Stakeholder represented by has involves derived from traces to categorized by categorized by (56) (57) (55) performed with satisfied by causes causes (60) schedules specifies uses (58) (59) specifies Validation Plan causes causes assigned to generates

39. Related Risk R-R Title R-R ID Risk Title Risk ID Select Rule Category Name Status Status Title Status ID Risk ID Risk Title Status Names: Submitted Retired Approved Impact Risk Title Risk ID Affected_Thing_Title Affected_Thing_ID Severity Consequence Risk Title Risk ID Type: a,b,c Consequence number Probability_ Distribution Lessons Learned Lesson Title Lesson ID Lesson Date Lesson Description Lesson Category Risk Window_open Window_closed Risk_Handling Time Frame Priority Contingency Plan Plan ID Triggers Date Applied Date Closed Closed by Closing_Rationale Mitigation_Effects _Description Likelihood Risk Title Risk ID Type: a (%),b,c Probability Distribution: Name Mean Variance Individual Risk Risk Title Risk ID Context Risk Owner Originator Date found Date updated AP233 Draft Concept Model for Risk March 20, 2002 combine to incorporate implements Approach Strategy Strategy ID Description/Assumptions Approach: None assigned Accept Watch Mitigate Prevent Transfer drive Inputs Technology Program Plan Schedule/Cost Constraints Risk Management Plan drive has implies resolves likelihood of has n

40. Category The decomposition tree for System Assembly is more than a simple parts tree. At any node one may introduce a category of parts. For example, an automobile may have several different engines that can be used in the automobile, each providing a different level of economy and performance. Categories are a grouping of elements into a set based on defined properties that serve as selection criteria for which elements of all those in the universe belong in that set Explanation: It is categorization that enables us to define alternatives and create taxonomies for libraries. This is one of the forms of generalization/specialization. Note that this is NOT INHERITANCE as found in object-oriented software languages. Physical elements, matter and energy, do not inherit their properties. Rather they posses the properties of themselves and can be identified by measurement of those properties. For a discussion of these issues in computer science see the work of Barbara Liskov and her CLU language. Note: the subcategories may be exclusive or inclusive and the subcategories may exhaust the super category or not there are four such possibilities Category is the basic concept in the physical world to support specialization - generalization.