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### System science documentation

1. 1. ARAB ACADEMY FOR SCIENCE &TECHNOLOGY & MARITIME TRANSPORT College of Engineering & Technology Computer Engineering Department Post-Graduate Student System Science & Engineering Documentation By: Eng. Ismail Fathalla El-Gayar Under Supervision Of: Prof.Dr. Mohamed Taher El-Sonni Dr. Ahmed Abou-El-Farag
2. 2. System Science & Engineering Contents Part 1 : System Science & Engineering  Introduction • Motivation & Applications • Report Organization  System Concepts & Definitions  Introduction To System o System Definition o System Classification o System science o System Engineering  System Function, Behavior and Structure o System Patterns o System Structure & Dynamics o System Behavior o System Properties o System Characteristics o System Sustainable o System Life Cycle o System Development Life Cycle  Related System Definitions o Engineering & Scientific Methodology o Integrated Logistic Support o Systematic o Cybernetics o Ergonomics o Systemic  Feedback & Feedback Types o Introduction To Feedback o Feedback Importance o Feedback Types  Introduction To System Modeling  Thinking Process o Analogical o Inductive o Deductive o Abductive  System Modeling • Linguistic • Visualization • Mathematical • Physical
3. 3.  Part 2: Statistics & Probability  Overview Of Statistics & Probability  Basic Concepts on Statistics & Probability o Basic Concepts o Measure Of Dispersions o Causes of not knowing things precisely o Probability & Density Functions o Distributions  Stochastic Process & Markov Chain o Stochastic Process o Markov Chain  Principal Component Analysis ( PCA) o Definition o Applications o Graphical Model o Complete Example Part 3 : Case Study : Dependability  Introduction To Dependability  Dependability Elements o Attributes  Availability  Reliability  Safety  Confidentiality  Integrity  Maintainability o Threats  Fault  Error  Failure o Means  Fault Preventation  Fault Removal  Fault Forecasting  Fault Tolerance
4. 4.  Fault, Error & Failure Classifications o Fault Classes o Error Classifications o Failure Classes  Measuring Dependability o Measuring Dependability Concepts o Fault Tree Analysis Method o Software Tools For Measuring Dependability  Dependability Benchmark o Benchmark & Dependability Benchmark o Elements of Performance & Dependability Benchmarking o Basic Definitions on Dependability Benchmarking Summary & Conclusion List Of References & Figures o List Of References o List Of Figures
5. 5. Part 1System Science & Engineering
6. 6. Chapter 1Introduction
7. 7. System Science & Engineering is one of the most important Courses in our life, Thiscourse has a different felling for anyone who take this course, it depend on how you think andhow you imagine the course , this course learn me a lot of things first of all learned me how tobe a philosopher , how to illustrate what I think in a good way , I learned also the scientificmethodology on thinking how to base my idea & how to think in a good way , therepresentation of the knowledge how to be so simple & in this document , I tried to make thisconcept & trained to be good on it by using system models that I found it so interested as thevisualization ,mathematical , linguistic & physical model , this course that I really enjoyed somuch in learning it and I really want to learn system more & more , I learned also practicalexpressions that benefit me in my work in any system , I learned about how system beReliable , Available , Usable , maintainable ….etc , The dependability was my case study inthis document I learned how system can be dependable & how to measure this dependability?, also I learned the fault , error & failure chain which harm any system and how to detect it &stop it fast before it will be hazard or a Failure of System . Also Another thing which Ilearned about Markov chain & Stochastic process which helps me a lot in analysis of anyprocess also the transforms , probability , statistics ,Principal component analysis , so ILearned a tools which I can benefit from them a lot in my life in analysis any system orproblem I will find in my life . All of this but still more & more Benefits I dont mention yetso as many as I talk, I cant explain this course represents what for me.Motivation & Applications:- System Science & Engineering was a very successful course to me , I have learnedmany topics which will help me in life , all of this topic I have learned from my mastersProf.Dr.Mohamed Taher El-Sunni & Dr.Ahmed Abo El-Farag which I want to thanksThem both for their efforts on this course which was very successful to me, So from thisbeginning point my masters in this course was the first to motivate me to make thisdocumentation to illustrate what I have been learned in this course , I really enjoying makingthis document because its content is what I have learned for 5 months being in this term as atopic & more of this as a methodologies of how I can think & How can I simplify Theinformation & See all things from A holistic view, In my point of view I see that a course likesystem science & Engineering must be learned to all engineers in the world so that they canknow how to deal with a system well, how to control & know the performance of this system,how to develop the system….etc . So this was my second motivate to make this document & Iwill give it to all the engineers I know to be an abstract & a reference to one of the mostimportant courses in the world.This Course Application is too many in any factory, any system in your house as an example :car, refrigerator, television, computer … etc , you will need the basic of system science toknow this system well.
8. 8. Report Organization:The Report Organized in an illustrative flow which makes the reader can imagine &understand the topic well as follow:Part 1: System Science & EngineeringThis Part introduces The Meaning Of System , Characteristics , properties , attributes ,classification & Some definitions that relate to system science & System engineering alsothis chapter has many exciting topics like system like system life cycles & Development lifecycles , System feedbacks & its types , thinking process types & what is meant by systemprocess ? , System modeling & its importance & Types, As We See this part talking generallyabout System Science & its Related Topics.Part 2: Statistics & ProbabilityThis Part introduces probability & statistic Concepts, Importance, Applications. Also talkingabout Joint probability & Distributions Types & Normal Distribution as An Example, AlsoTalked about exciting topics most use this days like Stochastic Processes & Markov chain,Principal Component Analysis…etc.Part 3: Case StudyThe Last Part talking about my Case Study which is the Dependability of Any System as awhole view to the dependability, performance, measures, I also take a look about anotherattributes like Reliability, Availability, Maintainability, Safety, Confidentiality, Integrity alsoI take a look about the threats of dependability which cause dependability failure & minimizethe dependability of a system like the faults, errors & failure chain and the way to preventing,removing, forecasting, tolerance this error , Also talked about dependability Benchmark &Software used for the benchmarking.
9. 9. Chapter 2System Concept & Definitions
10. 10. Introduction To System:- Definition of SYSTEM:- A set of components integrated together to perform a certain goal surrounded by a certain Environment within a boundary observed by a set of observers Figure .121 Comparing between Some Definitions Of important Organizations & Known Authors in SYSTEM:-Define Components Integration GoalANSI/EIA[1] end products , enabling aggregation To achieve a given purpose. productsIEEE[2] elements and processes A set or arrangement - whose behavior satisfies related customer/operational needs and provides for life cycle sustainment of the productsISO/IEC[3] elements A combination - to achieve one or more stated interacting elements - purposes organizedNASA[4] elements (include all The combination - to produce the capability to meet a hardware, software, function together need. equipment, facilities, personnel, processes, and procedures needed for this purpose)
11. 11. Classification of Systems:  Natural System and Human-Made System:  Natural System – a high degree of order and equilibrium, such as seasons, food chains, water cycle  Human-made system – technology based system  Physical and Conceptual System:  Physical system – in physical form or space  Conceptual system – in ideas, plans, concepts, hypotheses  Static and dynamic System:  Static system – structure without activity  Dynamic system – structural components with activity  Closed and Open System:  Closed system – one that does not interact with its environment  Open system – one that interact with its environmentWhat is SYSTEM SCIENCE:- • Is an interdisciplinary field of science that studies the nature of complex systems in nature, society, and science, It aims to develop interdisciplinary foundations, which are applicable in a variety of areas, such as engineering, biology, medicine and social sciences.What is SYSTEM ENGINEERING:- • is Defined as the art of designing & Optimizing Systems , Starting with expressed needs & ending up with the complete set of specifications for all the system elements (Aslaksin& Belcher 992)
12. 12. System Function, Behavior and Structure:-System Patterns:- A pattern is more than either just the problem or just the solutionstructure: It includes both the problem and the solution, along with the rationale that binds themtogether. A problem is considered with respect to conflicting forces, detailing why theproblem is a problem. A proposed solution is described in terms of its structure, andincludes a clear presentation of the consequences both benefits and liabilities—ofapplying the solution. Types of Patterns:- Low level pattern to solve implementation Idioms specific problems Medium scale pattern to organize sub- Design system functionality in application domain in independent way High Level pattern to help to specify the Architecture fundamental structure of the system Figure .122Architecture Pattern:-Expresses a fundamental structural organization schema for any system .it provides aset of predefined sub-systems, specifies their responsibilities, and includes rules andguidelines for organizing the relationships between them [Buschmann, Meunier,Rohnert, Sommerland]Design Pattern:-Describes a commonly- recurring structure of communicating components that solve ageneral design problem in a particular context [Gamma , Helm , Johnson]Idioms Pattern:-Describes how to implement particular aspects of components or the relationshipsbetween them. [Buschmann, Meunier, Rohnert, Sommerland][*]
13. 13. Note: Each pattern is a three-part rule, which expresses a relation between:- ( a certain context, a problem, and a solution).System Structure & Dynamics:-System Structure: - A graphical representation of the pattern. Classdiagrams and Interaction diagrams may be used for thisSystem dynamics: - is an approach to understanding the behavior of complex over time. It dealswith internal feedback loops and time delays that affect the behavior of the entiresystem. What makes using system dynamics different from other approaches tostudying complex systems is the use of feedback loops and stocks and flows. Theseelements help describe how even seemingly simple systems displaybaffling nonlinearity.System Behavior:-is what the system does to implement its function and is describedby a sequence of states.System Attributes:-The term attributes classifies functional or physical features of a system.Examples include gender; unit cost; nationality, state, and city of residence; type ofsport; organizational position manager; and fixed wing aircraft versus rotor.(Wasson)System Properties:-The term, properties, refers to the mass properties of a system.(Wasson) Examples include composition; weight; density; and size such as length, width, orheight.
14. 14. System Characteristics:-The term characteristics refer to the behavioral and physical qualities thatuniquely identify each system. (Wasson) - Behavioral characteristics examples include predictability andresponsively. - Physical characteristics examples include equipment warm-upand stabilization profiles; equipment thermal signatures; aircraft radarcross-sections; vehicle acceleration to cruise speed, handling, or stopping;and whale fluke markings.When we characterize system, there are four basic types of characteristics we consider: General Characteristics •stated in marketing brochures where key features are emphasized to capture a client Operating or Behavioral Characteristics •describe system features related to usability, survivability, and performance Physical Characteristics •relate to nonfunctional attributes such as size, weight, color, capacity System Aesthetics •relate to the “look and feel” of a system. Figure .123
15. 15. System Sustainable:- Sustainability refers to a quality and system of life that allows people to meettheir current needs without compromising the resources available for futuregenerations to meet their future needs. Sustainability rests on the belief that we cancoexist with the environment if we work to ensure our actions are not harmful to it.Essentially, it means ensuring that we leave our environment no worse than we foundit.System Life Cycle Development Production Operation Disposal Figure .124
16. 16. System Development Life Cycle Figure .125
17. 17. Related System Definitions:-System thinking:- Is a framework that is based on the belief that the component parts of a systemcan best be understood in the context of relationships with each other and with othersystems, rather than in isolation.Systematic • is a study of systems and their application to the problem of understanding ourselves and the world, – Formal Systematic – Pure Systematic – Applied Systematic – Practical SystematicCybernetics Is the interdisciplinary study of the structure of regulatory systems.Cybernetics is closely related to control theory and systems theory. cybernetics isequally applicable to physical and social (that is, language-based) systemsSystemic To study systems from a holistic point of view. It is an attempt atdeveloping logical, mathematical, engineering and philosophical paradigms andframeworks in which physical, technological, biological, social, cognitive, andmetaphysical systems can be studied and modeled.(Bunge (1979))
18. 18. Ergonomics Is the scientific discipline concerned with the understanding ofinteractions among humans and other elements of a system, and the profession thatapplies theory, principles, data and methods to design in order to optimize humanwell-being and overall system performance.(International Ergonomics Association)Methodology:  "the analysis of the principles of methods, rules, and postulates employed by a discipline"  "the systematic study of methods that are, can be, or have been applied within a discipline" Scientific Methodology: - (deduced from Definition of Methodology)  Is To Analysis by a scientific way ( Methods , Rules ) Engineering Methodology: - (deduced from Definition of Methodology)  Is To Analysis by an Engineering way ( Methods , Rules )Integrated Logistic Support (ILS):- Is the management organization that plans and directs the activities of manytechnical disciplines associated with the identification and developmentof logistics support and system requirements for military systems or equipment / parts
19. 19. Feedback & Feedback Types Introduction to Feedback When the system is part of a chain of cause-and-effect that forms a circuit orloop, then the event is said to "feed back" into itself. Feedback Importance Feedback used to give indicator about the output is the output isgood or we need to change in the input or in the system. It is very important in any system to develop the performance ofthe system feedback methods also used in community systems & societysystems not also the systems related to engineering. Feedback Types Feedback has many types we cant mentioned it all so we will mention as anexample:- Positive & Negative Feedback Positive when the feedback signal can amplify the input signal, leading to more modification. Negative when the feedback signals dampen the effect of the input signal, leading to less modification.Introduction to System Modeling:- System modeling is a technique to express, visualize, analyze and transform the architecture of a system. Here, a system may consist of software components, hardware components, or both and the connections between these components. A system model is then a skeletal model of the system.
20. 20. Thinking Process:- Is any process of estimating or inferring how local policies, actions, or changes influence the state of the neighboring universe It also can be defined, as an approach to problem solving, as viewing "problems" as parts of an overall system, rather than reacting to present outcomes or events and potentially contributing to further development of the undesired issue or problem Analogical Refers to a process of finding and using a known experience or domain to understand an unknown phenomenon or domain. Inductive Moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that its "bottom up" which is the kind of thing the bartender says to customers when hes trying to close for the night!). Deductive Works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. Abductive Starts from a set of accepted facts and infers their most likely, or best, explanations. The term abduction is also sometimes used to just mean the generation of hypotheses to explain observations or conclusions
21. 21. Chapter 3System Modeling
22. 22. Model:-  A model is a simplification of another entity, which can be a physical thing or another model. The model contains exactly those characteristics and properties of the modeled entity which are relevant for a given task. A model is minimal with respect to a task, if it does not contain any other characteristics than those relevant for the task.  A model is a representation of one or more concepts that may be realized in the physical world. It generally describes a domain of interest. A key feature of a model is that it is an abstraction that does not contain all the detail of the modeled entities within the domain of interest. Models are represented in many forms including graphical, mathematical, and logical representations, and physical prototypes.For example, a model of a building may include a blueprint and a scaled prototypephysical model. The building blueprint is a specification for one or more buildingsthat are built. The blueprint is an abstraction that does not contain all the buildingsdetail such as the characteristics of its materials.A model must:  Relates to an entity  be a simplification of that entity  be a related to a task and an objective  may relate to a not yet existing entity
23. 23. Modeling Types:- Modeling Methods Linguistic Visualization Mathematical Physical Modeling Modeling Modeling Modeling Describe by Describe by Describe by Describe by Words Graphs & Mathematical tangible Materials Animations Equations Figure .131Linguistic Modeling:-  It is a method for Modeling by using Language describe our system by language Expressions Example: Description Of A Car:- It is a block in which has 4 tires , it moves forward & Backward , this block consist of a Salon , Engine ,Electrical & Mechanical Sub-systems , Used for traveling distances.Visualization Modeling:-  It is a method for modeling by using a visualize images & Diagrams to express The system idea, relationships, components ….etc
24. 24. As Seen In The Figure (A Periodic Table Of Visualization Method): Figure .132The Table Consist Of category for Visualization (by Colors):- Metaphor Compound Strategy visualization visualization visualization Concept Information Data visualization visualization visualization Figure .133
25. 25. Mathematical Modeling:-  It is a method for modeling by using mathematical equations to express the system as an equation & variables  A representation of the essential aspects of an existing system , which presents knowledge of that system in usable form. (Eykhoff (1974))Example:-Physical Modeling:-  It is a method for modeling by using tangible materials to express the system, can be a physical object such as an architectural model of a building. Uses of an architectural model include visualization of internal relationships within the structure or external relationships of the structure to the environment.Example As An Empty Cup :- Figure .134
26. 26. Part 2Statistics & Probability
27. 27. Chapter 1Overview Of Statistics & Probability
28. 28. In This Part We will go to a journey around probability & statistics & Methodused in system science applications & Computations we will take a look aboutprobability computations & how to analyze data on statistics & classify them bydifferent method & how we can deal with different types of data & variables(Continuous & discrete) also we will learn about markov chain & its application ondependability methods, also we will talk about principal component analysis methodand its role in researches area, we will talk about how we can get another dimensionsby an illustrative exampleImportance Statistics & Probability are very important in this course to simplify theanalysis of the data & help us to improve performance of the system. we can measuresystem performance, availability, reliability, dependability, usability and all theabilities of the system using probability & statistics method which will be illustrate inthis chapter, this chapter will help us to practically apply these definitions & conceptson any system we want.Applications Applications of these chapter varies in many science & situations we meet inour life, we will learn some concepts must be understood well, for solving problemsin our life, we will learn how to measure the meaning by a different methods, we canbenchmarking systems by these methods, these methods is the practical view forsystem science & Engineering course, in which we can develop ourselves & practicethese in our field.
29. 29. Chapter 2Basic Concept On Statistics & Probability
30. 30. Basic Definitions:- Probability It is the likelihood—or chances—of something to happened Do we have a better chance of it occurring or do we have a better chance of it not occurring? Types Of Probability:- - Empirical Probability It is determined from repeated experimentation and observation, recording results. - Theoretical Probability It is determined using mathematical computations based on possible results, or outcomes. Statistics Analysis and Interpretation of numerical data A number summarizing a bunch of values Data Collection and compilation of relevant information Data are a bunch of values of one or more variables. Variable A variable is something that has different values Discreet variable Continuous variable Independent Events Two events are called independent if the occurrence of one event does not in any way affect the probability of the other event Random Variable A variable is called a random variable if it takes one of a specified set of values with a specified probability.
31. 31. Measure of Dispersions:-  Measure By Central Tendency :- The Mean* • Arithmetic Average Value The Mode • Most frequently Used Value The Median • Middle value after arranging data Figure .221* The Mean Types:-Arithmetic Geometric Harmonic Figure .222
32. 32. When We Use Each Of The Central Tendency Measures??? Figure .223
33. 33.  Measure By Dispersion :-  Range - (minimum, maximum)  Variance and Standard deviation  xi  x  1 2 - Variance = n 1 n - Standard deviation (  x ) = Variance (Measure of spread) - Standard error =   no Causes of not knowing things precisely Figure .224
34. 34. Probability & Cumulative Density Functions:-The Sample Space:- The space of all possible outcomes of a given process or situation is called the sample space S Figure .225An event:- An event A is a subset of the sample space. Figure .226The Laws of Probability:-  The probability of the sample space S is 1, P(S) = 1  The probability of any event A is such that 0 <= P (A) <= 1.  Law of Addition If A and B are mutually exclusive events, then P (A or B) = P (A) + P (B)  If A and B are not mutually exclusive: P (A or B) = P (A) + P (B) – P (A and B)Union:- Elements in at least one of the two sets: AB = { x | x  A  x  B } Figure .227
35. 35. Intersection:- Elements in exactly one of the two sets: Figure .228Disjoint Sets DEF: If A and B have no common elements, they are said to be disjoint, i.e. A B =  .(Mutual Exclusive) Figure .229Disjoint Union When A and B are disjoint, the disjoint union operation is well defined. The circle above the union symbol indicates disjointedness. Figure .2210
36. 36. Set Difference Elements in first set but not second: A-B = { x | x  A  x  B } Figure .2211Symmetric Difference Elements in exactly one of the two sets: AB = { x | x  A  x  B } Figure .2212Complement Elements not in the set (unary operator): A = {x | x  A} Figure .2213
37. 37.  Conditional Probabilities:- It means that what is the probability of occurring A if B has been already happened.  The conditional probability of A given B is P (A|B) = P (A, B) / P (B)  If A and B are independent then P (A, B) =P (A)*P (B)  P (A|B) =P (A) In general: min(P(A),P(B)  P(A)*P(B) max(0,1-P(A)-P(B)) For example:- If P (A) =0.7 and P (B) =0.5 then P (A, B) has to be between 0.2 and 0.5, but not necessarily be 0.35.Probability Density function:- a probability function that maps the possible values of x against their respectiveprobabilities of occurrence, p(x) P(x) is a number from 0 to 1.0. p X ( x)  P[ X  x] Figure .2214
38. 38. Cumulative Distribution function:- For a given x, there is a fixed possibility that the random variable will not exceed certain value x, it is non-decreasing in x FX ( x)  P[ X  x] x1  x2  F ( x1 )  F ( x2 ) Figure .2215Permutation & Combination:-Permutation: How many different sets of r objects can be chosen from n objects prn  nn  1n  2...n  r  1 n! prn  n  r !
39. 39. Combination: Without regard to order of drawing. • Number of n things taken r at a time. crn     r!nn r ! n r !Distributions:Some Examples on Distributions:- Bernouli Binomial Poisson Distribution distribution distribution Negative Normal binomial Distribution distribution Figure .2216Normal distribution: A continuous random variable X is said to have a normal distribution with parameters  and  , where       and 0   , if the pdf of X is 1 2 2 f ( x)  e ( x   ) /(2 )   x    2
40. 40. Figure .2217 Figure .2218Mean or Expected ValueVariance: The expected value of the square of distance between x and itsmean
41. 41. Coefficient of VariationCovariance Measures the strength of the linear relationship between two variables E[(x   x )( y   y )] N σ xy   ( xi   x )( yi   y ) P( xi , yi ) i 1 cov(X,Y) > 0 X and Y are positively correlated cov(X,Y) < 0 X and Y are inversely correlated cov(X,Y) = 0 X and Y are independentCorrelation Coefficient: normalized value of covariance The correlation always lies between -1 and +1Joint Probability:- The joint CDF of X and Y is:
42. 42. Chapter 3Stochastic Process & Markov Chain
43. 43. Stochastic Process Is a Series of variables represent a process that goes through time and has some random component  To model any variable over time, we need an algorithm or formula that tells us how the variable changes from one period to the next.  We calculate the variable by applying the formula to an initial value to get the second value, applying it to the second value to get the third, etc.Start with a deterministic process: 0, 2, 4, 6, 8… The deterministic process is to add the value of 2 to the previous value., we could describe this algorithm as: X t 1  X t  2, X0  0Stochastic Process is similar to deterministic process, except that they add a chance elementto each change.A simple example: Flip a coin. If (heads) add 1 & If (tails) subtract 1. Here are the results from my home experiment: T, H, T, H, H, H, H, T, H, H which produces -1, 0, -1, 0, 1, 2, 3, 2, 3, 4 Coin Toss Process 6 4 Value 2 0 -2 1 2 3 4 5 6 7 8 9 10 Flips Figure .231
44. 44. So We Can Define stochastic process as an another definition as a collection of random variables indexed on a set; Usually the index denotes time. Continuous-time stochastic process: Discrete-time stochastic process: First order to n-order distribution can characterize the stochastic process. First order: Second order: Strict stationary For all n, k and N
45. 45. Markov Chain Is an example of mathematical model to model a system Probability P(t, t+1) State State t t+1 Figure .232 Convenient to give transition probabilities in matrix formAs an Example:- The Following markov chain with a representation on matrix form of state A, B, C, D 0.95 0.2 0.5 0.2 0.05 0.3 0.8 1 Figure .234 Figure .233
46. 46. Another Example on Markov Chain:- This is an illustrative example of markov chain for CPU in which the states & the process are illustrated with their probability and the corresponding representation using matrix form. WAIT 0.99 IDLE LOOP STATE S0 USER SYSTEM 0.01 SUPERVISOR SUPERVISOR 0.02 0.90 SUPERVISOR 0.02 STATES S1 S2 0.01 0.92 0.01 0.01 0.04 0.09 PROBLEM STATE S3 USER 0.98 PROGRAMS Figure .235 Figure .236
47. 47. Chapter 4Principal Component Analysis(PCA)
48. 48. Principal Component Analysis ( PCA) The Principal components method summarizes data by finding the major correlationsin linear combinations of the observations. Reduce the dimensionality of a data set by finding a new set of variables, smaller thanthe original set of variables — — PCA is a statistical method to transform the data to a new coordinate system.* Little information lost in process, usuallyApplicationsUsed Scientifically in Compression & Classification of data in this Application: ◦ Face Recognition ◦ Voice Recognition ◦ Image Compression ◦ Pattern Recognition ◦ Handwriting Analysis ◦ Lip Reading ◦ Marketing ◦ Social Science Researches ◦ And many more other fields.
49. 49. Graphical Model Figure .241Complete Example 1- Get Some Data: First we will gather some data that can be represented in 2 dimensions. Figure .242
50. 50. 2- Substract The mean: we have to subtract the mean from all the data3- Calculate the covariance matrix4- Calculate Eigenvector and Eigen values of the covariance matrix
51. 51. 5- Choosing components and forming a feature vector Figure .243We then choose the eigenvector with the highest eigenvalue 6- Deriving the new dataset
52. 52. Final Data = Feature Vector x Data Adjusted. Figure .244Shown Example by using Matlab Function:- Figure .245
53. 53. Part 3Case Study: Dependability
54. 54. Chapter 1Introduction To Dependability
55. 55. Definition Of Dependability:- • Is a value showing the reliability of a person to others because of his/her integrity, truthfulness, and trustfulness, traits that can encourage someone to depend on him/her. • The collective term used to describe the availability performance and its influencing factors: reliability performance, maintainability performance and maintenance support performance. [Belcher][1] • Is the system property that integrates such attributes as reliability, availability, safety, security, survivability, maintainability. Performance Concept Diagram:- This Diagram illustrate the relation between the Quality Of Service (QOS) & The Dependability (which depend on Availability, Reliability, Maintainability) Figure .311
56. 56. Dependability and Survivability are the same as shown that TheGoals of Each others are common:Dependability Goal1) Ability to deliver service that can justifiably be trusted2) Ability of a system to avoid failures that are more frequent or more severe, andoutage durations that are longer, than is acceptable to the user(s)Survivability GoalCapability of a system to fulfill its mission in a timely mannerAlso As we will see in the threats we will find that Dependability &survivability has same meaning also:Dependability Threats:1) Design faults (e.g., software flaws, hardware errata, malicious logics)2) Physical faults (e.g., production defects, physical deterioration)3) Interaction faults (e.g., physical interference, input mistakes, attacks, includingviruses, worms, intrusions)Survivability Threats:1) Attacks (e.g., intrusions, probes, denials of service)2) Failures (internally generated events due to, e.g., software design errors, hardwaredegradation, human errors, corrupted data)3) Accidents (externally generated events such as natural disasters)
57. 57. Chapter 2Dependability Elements
58. 58. Dependability can be thought of as being composed of three elements:- Attributes •A way to asses (to measure) the Dependability of a system Threats •An understanding of the things that can affect the Dependability of a system Means •Ways to increase the Dependability of a system prevention, fault tolerance, fault removal and fault forecasting. Figure .321Collecting Together As A Tree Called (Dependability Tree) :- Figure .322
59. 59.  Attributes Of Dependability:- Attributes are the qualities of a system. Which can be assessed to determine its overall dependability using Qualitative or Quantitative measures. The following is The Dependability Attributes:-Availability • readiness for correct service.Reliability • continuity of correct service.Safety • absence of catastrophic consequences on the user(s) and the environment .Integrity • absence of improper system alterationMaintainability • ability to undergo modifications and repairs .Confidentiality • i.e. the absence of unauthorized disclosure of information Figure .323
60. 60.  Availability:-  Will be up and running and able to deliver useful services at any given time?  The availability of a system is the probability that it. Reliability:-  The reliability of a system is the probability, over a given period of time, that the system will correctly deliver services as expected by the user.  continuity of correct service Safety:-  The safety of a system is a judgment of how likely it is that the system will cause damage to people or its environment?  Absence of catastrophic consequences on the user(s) and the environment Confidentiality-  Absence of unauthorized disclosure of information. Integrity:-  absence of improper system alteration  Integrity is a pre-requisite for availability, reliability and safety Maintainability:-  ability to undergo modifications and repairs
61. 61.  Threats Of Dependability:- Are things that can affect a system and cause a drop in DependabilityThere are three main terms that must be clearly understood: Figure .324
62. 62.  Fault: A fault is a defect in a system. The presence of a fault in a system may or may not lead to a failure, for instance although a system may contain a fault its input and state conditions may never cause this fault to be executed so that an error occurs and thus never exhibits as a failure. Fault Activation Error Figure .325 * Activation of Fault Leads to Error
63. 63. Error: An error is a discrepancy between the intended behavior ofa system and its actual behavior inside the system boundary. Errorsoccur at runtime when some part of the system enters anunexpected state due to the activation of a fault. Since errors aregenerated from invalid states they are hard to observe withoutspecial mechanisms, such as debuggers or debug output to logs. 1 2 3 4 Fault Activated Error Observer Figure .326* Assume (1, 2, 3&4) is The Processes of the System.* If a Fault has happened (Activated)  The Process will go to theError State (invalid State).* An Observer inside the Boundary of the System (e.g: Debugger)
64. 64.  Failure: A failure is an instance in time when a system displays behavior that is contrary to its specification. An error may not necessarily cause a failure, for instance an exception may be thrown by a system but this may be caught and handled using fault tolerance techniques so the overall operation of the system will conform to the specification. Error Propagate Failure Figure .327 * When the Error propagate it will causes Failure
65. 65. It is important to note that Failures are recorded at the system boundary.They are basically Errors that have propagated to the system boundaryand have become observable. Faults, Errors and Failures operateaccording to a mechanism. This mechanism is sometimes known as aFault-Error-Failure chain. As a general rule a fault, when activated, canlead to an error (which is an invalid state) and the invalid state generatedby an error may lead to another error or a failure (which is an observabledeviation from the specified behavior at the system boundary).Once a fault is activated an error is created. An error may act in the sameway as a fault in that it can create further error conditions, therefore anerror may propagate multiple times within a system boundary withoutcausing an observable failure. If an error propagates outside the systemboundary a failure is said to occur.* A failure is basically the point at which it can be said that a service isfailing to meet its specification. Since the output data from one servicemay be fed into another, a failure in one service may propagate intoanother service as a fault so a chain can be formed of the form: Faultleading to Error leading to Failure leading to Error, etc. Figure .328
66. 66.  Means Of Dependability:- Since the mechanism of a Fault-Error-Chain is understood, it is possible to construct means to break these chains and thereby increase the dependability of a system.Four means have been identified so far: Fault Removal • How Can Be Removed? Fault Preventation • How Can We Prevent? Fault Forecasting • How Can We Forecast? Fault Tolerance • How Can We Tolerant? Figure .329
67. 67.  Fault Removal: - can be sub-divided into two sub-categories:  Removal During Development  Removal During Use. -Removal during development: requires verification so that faults can be detected and removed before a system is put into production. Once systems have been put into production a system is needed to record failures and remove them via a maintenance cycle. -Removal during Use: happen after system put into production.  Fault Prevention: - deals with preventing faults being incorporated into a system. This can be accomplished by use of development methodologies and good implementation techniques.  Fault Forecasting: - predicts likely faults so that they can be removed or their effects can be circumvented.  Fault Tolerance: - deals with putting mechanisms in place that will allow a system to still deliver the required service in the presence of faults, although that service may be at a degraded level.*Dependability means are intended to reduce the number of failurespresented to the user of a system. Failures are traditionally recorded overtime and it is useful to understand how their frequency is measured sothat the effectiveness of means can be assessed.
68. 68. Chapter 3Fault, Error & Failure Classifications
69. 69. Fault Classes:-Represented as follow:- Figure .331Persistence Domain:- • Transient fault: – E.g. hardware components which have an adverse reaction to radioactivity. • Permanent fault: – E.g., a broken wire or a software design error. • Intermittent fault: – E.g. a hardware component that is heat sensitive, it works for a time, stops working, cools down and then starts to work again.
70. 70. Phenomenological Cause • physical faults - Which are due to adverse physical phenomena, • human-made faults - Which result from human imperfections.Nature of fault • accidental faults - Which appear or are created fortuitously; • intentional faults - Which are created deliberately, with or without a malicious intention.Phase of creation • Development faults - Which result from imperfections arising either a) During the development of the system (from requirement specification to implementation) or during subsequent modifications b) During the establishment of the procedures for operating or maintaining the system • Operational faults - Which appear during the system’s exploitation.System boundaries • internal faults - Which are those parts of the state of a system which, when invoked by the computation activity, will produce an error,
71. 71. • external faults - Which result from interference or from interaction with its physical (Electromagnet perturbations, radiation, temperature, vibration, etc.) Or human Environment.Combined FaultIts Used by Laprie, he used to make the faults classes in which we can represent anytype of faults, in which may faults has many types of classes so he illustrate this faultsby the intersection of the classes with each otherMatrix Representation:- Figure .332
72. 72. More combinations may be identified in the future. The combined fault classes asshown belong to three major partially overlapping groupings:• Development faults that include all fault classes occurring during development.• Physical faults that include all fault classes that affect hardware.• Interaction faults that include all external faults.As An illustrative example on this Diagram as shown in:Natural Fault: The fault caused by nature must be hardware fault (physical fault), it cant besoftware fault.Human-made Fault: The fault caused by human-made may be software, hardware orexternal ------------------------------------------------------Error:  An error is detected if its presence is indicated by an error message or error signal. Errors that are present but not detected are latent errors.Whether or not an error will actually lead to a service failure depends on twofactors: 1. The structure of the system, and especially the nature of any redundancy that exists in it: • Protective redundancy, introduced to provide fault tolerance, that is explicitly intended to prevent an error from leading to service failure; • Unintentional redundancy (it is in practice difficult if not impossible to build a system without any form of redundancy) that may have the same presumably unexpected — result as intentional redundancy. 2. The behavior of the system: the part of the state that contains an error may never be needed for service, or an error may be eliminated (e.g., when overwritten) before it leads to a failure.Error Classifications:  A convenient classification of errors is to describe them in terms of the elementary service failures that they cause: o content vs. timing errors
73. 73. o detected vs. latent errors o consistent vs. inconsistent errors when the service goes to two or more users o Minor vs. catastrophic errors. In the field of error control codes  Content errors are further classified according to the damage pattern: single, double, triple, byte, burst, erasure, arithmetic, track, etc., errors.  Some faults (e.g., a burst of electromagnetic radiation) can simultaneously cause errors in more than one component. Such errors are called multiple related errors. Single errors are errors that affect one component only. -----------------------------------------------------Failure classes: Figure .333Domain ClassesContent (value) failures: - The content of the information delivered at the service interface (i.e., the service content) deviates from implementing the system function;Timing failures: -The time of arrival or the duration of the information delivered at the service interface (i.e., the timing of service delivery) deviates from implementing the system function.
74. 74. Figure .334Perception by several usersConsistent failures: - The incorrect service is perceived identically by all system users.Inconsistent failures: - Some or all system users perceive differently incorrect service (some users may actually perceive correct service).Consequence of environmentMinor failures - Where the harmful consequences are of similar cost to the benefits provided by correct service delivery;Catastrophic failures - Where the cost of harmful consequences is orders of magnitude, or even incommensurably, higher than the benefit provided by correct service delivery.
75. 75. Chapter 4Measuring Dependability
76. 76. Measuring Dependability Varies by the type of system & What used for, many types of methods used to measuring dependability, As an example:-  Measuring By Attributes of Dependability ( Reliability, Maintainability, Availability, safety, Confidentiality …etc)  Measuring Using Fault Tree Analysis Method.  Measuring Using Stochastic Petri-nets Method & Markov Chain.I will talk in this chapter about some methods & concepts used in DependabilityMeasurements. -------------------------------------------Some Concepts we use to measure dependability:- As we learn in the dependability elements is the dependability attribute which we try to use them to find equations for computing dependability of a system.  Only Availability and Reliability are quantifiable by direct measurements whilst others are more subjective.
77. 77.  Safety cannot be measured directly via metrics but is a subjective assessment that requires judgmental information to be applied to give a level of confidence; while Reliability can be measured as failures over time. While Reliability can be measured as failures over time. Reliability = Failure / Time Applying security measures to the appliances of a system generally improves the dependability by limiting the number of externally-originated errors. When Measuring Reliability and Availability Time from an initial instant to the next failure event Typical measures: – MTTF: mean time to failure – MTBF: mean time between failures – MTTR: mean time to repair – MFC: mean failure cost Availability = MTTF / MTBF Ratio of service time to elapsed time Computing Mean Time Between Failure:- MTBF = MTTF + MTTR As it is usually true that MTTR is a small fraction of MTTF, it is usually allowed to assume that MTBF ≈ MTTF.
78. 78.  Measuring Maintainability which is a function of time representing the probability that a failed system will be repaired in a time less than or equal to (t). Which can be estimated as: M (t) = 1 - exp-μt (Where μ being the repair rate) Applying security measures to the appliances of a system generally improves the dependability by limiting the number of externally-originated errors.  Security is the concurrent existence of:- a) Availability: for authorized users only, b) Confidentiality c) Integrity: with ‘improper’ meaning ‘unauthorized’. Informally, the security of a system is a judgment of how likely it is that the system can resist accidental or deliberate intrusion.  Measuring Security by : MTTD (Mean Time to Detection) MTTE (Mean Time to Exploitation)
79. 79. Fault Tree Analysis Method:- • Developed in 1962 by Bell Labs • Using probabilities in analysis:- - Assignment of probabilities to specific events - Computation of probabilities for compound events • Basic Structure Of The Fault Tree is : And Gate OR Gate Basic Event Compound Event Transfer Figure .341
80. 80. Fault Tree Structure As Shown In Figure:- Figure .342Fault Tree Calculation As An Example:- Figure .343
81. 81. An Example Of Analysis Of Dual-Core Computer:- Figure .344An Example Of Heart – Pulse Mechanism:- Figure .345
82. 82. When Trigger Fails: it Fails As The Following Tree:- Figure .346* Fault trees can be used to analyze security issues and it called attacktreesSoftware Tools Using For Measuring Dependability: Figure .347
83. 83. Chapter 5Dependability Benchmark
84. 84. Benchmarking:- Is the act of running a computer program, a set of programs, or other operations, inorder to assess the relative performance of an object, normally by running a number ofstandard tests and trials against it. The term benchmark is also mostly utilized for thepurposes of elaborately-designed benchmarking programs themselves. Benchmarking isusually associated with assessing performance characteristics of the System.Dependability Benchmarking:- Is a specification of all elements required to assess certain measures related tothe behavior of a System in the presence of faults. Is performance benchmarking extended to dependability aspects.The main elements of a Performance benchmark are: SUT: System under Test WL: Workload PM: Performance Measures Performance Benchmark Dependability Extensions Dependability Benchmark Workload Faultload Workload Faultload Performance Measures + Dependability Measures = Performance Measures Pricing Information Pricing Information Dependability Measures Pricing Information Full Disclosure Rules Full Disclosure Rules Full Disclosure Rules Figure .351
85. 85. To extend a performance benchmarking into the dependability domain, afault load has to be provided.The main elements of Dependability benchmark are:SUB: System under BenchmarkIFL: Interaction Fault LoadDM: Dependability MeasuresFMD: Failure Mode DetectorFMC: Failure Mode ClassesWL: WorkloadPM: Performance Measures Figure .352Some Definitions:-FMD: Failure Mode Detector:- Identifies and classifies the failure modes in adependability benchmark experiment,SUB: System under Benchmark:- Is a system where the measures applyDBT: Dependability benchmark target:- The SUB could be larger than the component or subsystemthat the benchmark user wants to characterizeDBE: Dependability Benchmarking Experiments:- Benchmarking is performing tests on the SUB.DBC (dependability benchmark configuration):- Is the implementation of the benchmark elements and theexperimental setup.
86. 86. Workload: Is the entire load explicitly or implicitly applied to the Systemunder Benchmarking. • User Workload • Operator Load • Background Load* The workload must be: Scope Oriented Portable Representative Figure .353Performance Measures • tmpC: transactions per minute • \$/ tmpC • Response TimeDependability Measures • Conditional probability of occurrence of failure mode classes. • Availability • Mean Down Time
87. 87. Summary
88. 88. In These Document We Take a Tour around Definition of Systemwhat it means, by different definitions, its structure, patters we knownow what is system science we imagine the word of system we candistinguish its component, their relations, the interaction with theenvironment also we knows the types of models & visualizations we candistinguish when we use each model to describe something, we knowsthe type of feedbacks and the importance of feedbacks, we know moreabout thinking process types, also the probability part has a very highpriority in our documentation because this part serves the course wellby learning probability & statistics methods , deterministic & stochasticprocess, principal component analysis & how to simplify data , markovchain also has a big role in my documentation because also its one ofmethods that used for measuring dependability which is my case studywhich I illustrate its importance, elements which used for measuring itwhich called attributes , threats which used to less its performance likefault, error & failure ,also its means which used for preventing less ofdependability like fault tolerance, forecasting, removing & preventive ,in measuring dependability, illustrating some concepts of measuring & amethod like fault tree analysis was so important for the reader to knowa practical method for representing dependability , all of us now knowsthe importance of system science & Engineering course, Im very proudthat I make a documentation to this course that all of my friends canread and can understand the importance of this course in all practicalfields in our life,
89. 89. Conclusion
90. 90. Conclusion of This Documentation That I introduced a good topicwhich is good for a beginner engineer who has no idea about systemscience to know this field which will benefit him much in his life & willmake him has an imagination & measurements more that anybody forknowing the performance of the system & this will help him fordesigning a new better system or maintain this system , I thought thatthis value is the most important in this book beside a new knowledge ina field which is not known enough in our Arab country, So I hope thatthis documentation will be good enough to benefit all the engineers &can found themselves developed in that field , Also another conclusionthat I knew more in this course when I write this documentation & revisemy information that I have been read for a five months, I really benefit alot from this course,& I hope that I will continue learning & researches Inthis area of science.
91. 91. List Of References & Figures
92. 92. References[1] "Processes for Engineering a System", ANSI/EIA-632-1999, ANSI/EIA, 1999[2] "Standard for Application and Management of the Systems Engineering Process -Description", IEEE Std 1220-1998, IEEE, 1998.[3] "Systems and software engineering - System life cycle processes", ISO/IEC, 2008.[4] "NASA Systems Engineering Handbook", Revision 1, NASA, 2007*5+ “System engineering principles & practice” , William Sweet - & Kossiakoff*6+ “System Engineering & Analysis” , Blanchard & Walter 1998.*7+ “The web of life: a new scientific understanding of living systems” ,Capra (1996).*8+ “GENERAL SYSTEMATICS” , J.G. Bennett (1963) .[9] “Introduction to Cybernetics”, W. Ross Ashby (1956).*10+” A world of systems” , Mario Bunge (1979).*11+ “What is Ergonomics” , International Ergonomics Association(2008).[12] "System Engineering", Erik Aslaksin & Rod belcher , 1992[13] Muller, "System Modeling and Analysis: a Practical Approach", 2009[14] wikipedia, "Systems_Modeling_Language"[15] Lecture Notes , "http://www.ict.kth.se/courses/IL2202/Slides/lec-01-intro.pdf"[16] Periodic Tabe Of Visualization, "http://www.visual-literacy.org/periodic_table/periodic_table.html"[17] Frank Bushmann , Regine Meunier , Hans Rohnert , Peter Sommerland ,Michael Stal:"Asystem of Patterns" ,John Wiley &Sons , 1996[18] Erich Gamma,Richard Helm , Ralph Johnson , John Vlissides, "Design Patterns" ,Addison- Wisely , 1995[19] Patterns, http://hillside.net/patterns/patterns.html[20] www.tml.tkk.fi/Opinnot/Tik-109.450/1998/niska/[21] http://www.cmcrossroads.com/bradapp/docs/patterns-intro.html[22] Wasson, "System Analysis, Design, and Development - Concepts, Principles, andPractices" - 0471393339
93. 93. [23] Methodology, http://www.merriam-webster.com/dictionary/methodology[24] Principal Component Analysis,"http://en.wikipedia.org/wiki/Principal_component_analysis"[25] Lindsay I Smith, “A tutorial on Principal Components Analysis”, 2002[26] Jonathon Shlens, “A tutorial on Principal Component Analysis”, April, 2009.[27] Signals and Systems group, Uppsala Univ., “Instruction for Image Compression usingPCA”, 2005.[28] M. Mudrova et al., “Principal Component Analysis In Image Processing”.[29] I.T. Jolliffe, “Principal Component Analysis”, Springer, 2002.[30] Mendenhall, Beaver , Introduction To Probability & statistics ,2009[31] Laprie, Randell, & Landwehr, "Basic Concepts and Taxonomy of Dependable and SecureComputing," IEEE Transactions on Dependable and Secure Computing(2004)[32] Randell,"Software Dependability: A Personal View", in the Proc of the 25th InternationalSymposium on Fault-Tolerant Computing(1995)[33] Laprie. "Dependable Computing and Fault Tolerance: Concepts and terminology”(1985)[34+ Randell, Laprie “Fundamental Concepts of Dependability”(2001)[35] Xing, "Dependability Analysis of Hierarchical Systems with Modular Imperfect Coverage"[36] Baquero, "PETRI NET WORKFLOW MODELING FOR DIGITAL PUBLISHING MEASURINGQUANTITATIVE DEPENDABILITY ATTRIBUTES", 2006[37] Mikael Asplund, "Lecture Notes: Dependability and fault tolerance"[38] Robert Brill, "MEADEP and Its Application in Dependability Analysis for A Nuclear PowerPlant Safety System", 1997[39] Lorenzo Strigini, "Resilience assessment and dependability benchmarking: challenges ofprediction", 2008[40] Mili, ": Measuring Dependability as a Mean Failure Cost", 2007[41] Tang, "MEADEP and Its Applications in Evaluating Dependability for Air Traffic ControlSystems" ,1998[42] Laprie, Avizˇienis, "Fundamental Concepts of Computer System Dependability", 2001[43] IPLU team, "The dependability of an IP network – what is it?", 2006
94. 94. [44] Hecht , "An Approach to Measuring and Assessing Dependability for Critical SoftwareSystems", 1997[45] Hossam A. Ramadan, "Towards More Comprehensive Measurable Dependability",2008[46] Laprie, "Basic Concepts and Taxonomy of Dependable and Secure Computing", 2004[47] Eusgeld, "Introduction to Dependability Metrics",2008[48] Oliver Tschache , "Dependability Benchmarking of Linux based Systems"[49] Dependability Management "CONCEPT OF DEPENDABILITY",2009[50] Sommerville, " Software Engineering: Ch16.Dependability",2000[51] Performance and Dependability Benchmarking Slides.[52] IGI Global, "Chapter I: Dependability and Fault-Tolerance: Basic Concepts andTerminology" , 2009[53] Knapskog, Sallhammar, "A Framework for Predicting Security and DependabilityMeasures in Real-time", 2007[54] Chaparro, "Measuring quantitative dependability attributes in Digital Publishing usingPetri Net Workflow Modeling",[55] Miller, " MEADEP — A Dependability Evaluation Tool for Engineers"[56] Siewiorek, "Measuring Software Dependability by Robustness Benchmarking",1994[57] Knight," Dependability Analysis Techniques – 1 Including Probabilistic Risk Analysis(PRA)", 2009
95. 95. Figures Part(1) Figure RepresentFigure .121 System Definition RepresentationFigure .122 System Pattern ClassificationsFigure .123 System Characteristics typesFigure .124 System Life cycleFigure .125 System Development Life cycleFigure .131 Modeling MethodsFigure .132 Periodic Table Of VisualizationFigure .133 Category Of VisualizationFigure .134 Example : Physical Modeling Part(2) Figure Represent Figure .221 Measure by Central tendency Figure .222 The Mean Types Figure .223 When We Use Each Of The Central Tendency Measures Figure .224 Causes of not knowing things precisely Figure .225 Sample space Figure .226 An Event Figure .227 Union Figure .228 Intersection Figure .229 Disjoint sets Figure .2210 Disjoint Union Figure .2211 Set Differences Figure .2212 Symmetric Differences Figure .2213 Complement Figure .2214 Example: Probability density function Figure .2215 Example: Cumulative Distribution function Figure .2216 Distribution Types as examples Figure .2217 Standard Deviation Showing The Mean Figure .2218 Standard Deviation Showing The sigma Figure .231 Coin Toss Process Figure .232 State Transition on markov chain Figure .233 Example: State transition with weight Figure .234 Example: Matrix representation Figure .235 Example2: state transition with weight Figure .236 Example2: Matrix Representation Figure .241 PCA: Graphical Model Figure .242 Example : Data Figure .243 Example: Choosing Component Figure .244 Example: New Data Figure .245 Example: Matlab function Part(3) Figure .311 Performance Concept Figure .321 Dependability Elements
96. 96. Figure .322 Dependability TreeFigure .323 Dependability AttributesFigure .324 Dependability threatsFigure .325 Fault – Error RelationFigure .326 Error StateFigure .327 Error-Failure RelationFigure .328 Fault-Error-Failure ChainFigure .329 Dependability MeansFigure .331 Elementary Fault ClassesFigure .332 Combined Fault Matrix RepresentationFigure .333 The Failure ClassesFigure .334 Failure With respect to domain modeFigure .341 Basic Structure of The fault TreeFigure .342 Fault Tree StructureFigure .343 Fault Tree CalculationsFigure .344 Example: Analysis Of Dual-Core ComputerFigure .345 Example: Heart Pulse MechanismFigure .346 Example: Heart Pulse Mechanism – Trigger PulseFigure .347 Software Tools For Measuring DependabilityFigure .351 Dependability Benchmark Elements ExtractionFigure .352 Dependability Benchmark ElementsFigure .353 Workload Essential Elements