Formal Dependability Modeling and Analysis: A Survey Waqar Ahmed and Osman Hasan School of Electrical Engineering and Computer Science National University of Sciences and Technology (NUST) Islamabad, Pakistan CICM 2016 Bailystock, Poland July 27, 2016
Outline Introduction and Motivation 1 Dependability Modeling Techniques 2 Formal Techniques for Dependability Analysis 3 Conclusions 4 W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 2 / 48
Dependability W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 3 / 48
Safety-critical Systems More stringent dependability requirements Main motivation for Formal Dependabiltiy Modeling and Analysis W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 4 / 48
Dependability Dependabililty Reliability Availability Maintainability The ability of system to The ability of system to The ability of a system deliver services as deliver services when to restore to operational specified within a given required status after a failure time occurs W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 5 / 48
Dependability Dependabililty Reliability Availability Maintainability The ability of system to The ability of system to The ability of a system deliver services as deliver services when to restore to operational specified within a given required status after a failure time occurs W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 6 / 48
Dependability Dependabililty Reliability Availability Maintainability The ability of system to The ability of system to The ability of a system deliver services as deliver services when to restore to operational specified within a given required status after a failure time occurs W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 7 / 48
Formal Definitions Reliability = P (no failure occurs before certain time) R ( t ) = Pr ( X > t ) = 1 − Pr ( X ≤ t ) = 1 − F X ( t ) W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 8 / 48
Formal Definitions Reliability = P (no failure occurs before certain time) R ( t ) = Pr ( X > t ) = 1 − Pr ( X ≤ t ) = 1 − F X ( t ) Availability is typically derived from reliability and maintainability measures MTBF A(t) = MTBF + MTTR where MTBF = MTTF + MTTR MTBF = Mean time between failures (Reliability Metric) MTTF = Mean time to failure (Reliability Metric) MTTR = Mean time to repair (Maintainability Metric) W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 8 / 48
Traditional Dependability Analysis Steps Start Conceptual Behavioural Model of the System Mean Time To Failure (MTTF) Reliability and Availability Component Mean Time Between Failure Level (MTBF) Metric Calculation Mean Time To Repair (MTTR) Reliability Block Diagram (RBD) Selection of Reliability Fault Tree (FT) Modeling Technique Markov Chain (MC) System Level Analytical Selection of Reliability Simulation Analysis Technique Formal Methods W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 9 / 48
Traditional Dependability Analysis Steps Start Conceptual Behavioural Model of the System Mean Time To Failure (MTTF) Reliability and Availability Component Mean Time Between Failure Level (MTBF) Metric Calculation Mean Time To Repair (MTTR) Reliability Block Diagram (RBD) Selection of Reliability Fault Tree (FT) Modeling Technique Markov Chain (MC) System Level Analytical Selection of Reliability Simulation Analysis Technique Formal Methods W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 10 / 48
Traditional Dependability Analysis Steps Start Conceptual Behavioural Model of the System Mean Time To Failure (MTTF) Reliability and Availability Component Mean Time Between Failure Level (MTBF) Metric Calculation Mean Time To Repair (MTTR) Reliability Block Diagram (RBD) Selection of Reliability Fault Tree (FT) Modeling Technique Markov Chain (MC) System Level Analytical Selection of Reliability Simulation Analysis Technique Formal Methods W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 11 / 48
Traditional Dependability Analysis Steps Start Conceptual Behavioural Model of the System Mean Time To Failure (MTTF) Reliability and Availability Component Mean Time Between Failure Level (MTBF) Metric Calculation Mean Time To Repair (MTTR) Reliability Block Diagram (RBD) Selection of Reliability Fault Tree (FT) Modeling Technique Markov Chain (MC) System Level Analytical Selection of Reliability Simulation Analysis Technique Formal Methods W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 12 / 48
Outline Introduction and Motivation 1 Dependability Modeling Techniques 2 Formal Techniques for Dependability Analysis 3 Conclusions 4 W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 13 / 48
Dependability Modeling Techniques Some widely used modeling techniques are: Reliability Block Diagram Fault Tree Markov Chain W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 14 / 48
Reliability Block Diagrams Model the failure relationship of system components as a diagram of sub-blocks and connectors (RBD) Judge the failure characteristics of the overall system based on the failure rates of sub-blocks 1 N I O M W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 15 / 48
Reliability Block Diagrams Model the failure relationship of system components as a diagram of sub-blocks and connectors (RBD) Judge the failure characteristics of the overall system based on the failure rates of sub-blocks 1 N I O M The overall system failure happens if all the paths for successful execution fail Add more parallelism to meet the dependability goals W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 15 / 48
Types of RBD RBDs Mathematical Expressions N N � � R series ( t ) = Pr ( E i ( t )) = R i ( t ) I 1 N O O i =1 i =1 1 M M � � R parallel ( t ) = Pr ( E i ) = 1 − (1 − R i ( t )) I O i =1 i =1 M 1 N M N M N � � � � R parallel − series ( t )= Pr ( E ij ( t ))= 1 − (1 − ( R ij ( t ))) O I i =1 j =1 i =1 j =1 M 1 N N M N M � � � � R series − parallel ( t )= Pr ( E ij ( t ))= (1 − (1 − R ij ( t ))) I O i =1 j =1 i =1 j =1 M W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 16 / 48
Example: Power Supply System Waqar requires continuous supply of power for his Lab PC The UPS can support the load during a switch from the main supply to the generator Wants to determine the reliability of power supply system W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 17 / 48
Example: Power Supply System Step 1 Construct an RBD Model Power Supply RBD Transformer Main (T) (M) Generator (G) UPS (U) W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 18 / 48
Example: Power Supply System Step 1 Construct an RBD Model Power Supply RBD Transformer Main (T) (M) Generator (G) UPS (U) pow sys rbd = ( M ∩ T ) ∪ G ∪ U W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 18 / 48
Example: Power Supply System Step 2 Identify the RBD type Step 3 Use the corresponding mathematical expression to evaluate the overall reliability based on the sub-components reliability P (( M ∩ T ) ∪ G ∪ U ) = 1 − ( 1 − P ( M ) ∗ P ( T )) ∗ ( 1 − P ( G )) ∗ ( 1 − P ( U )) W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 19 / 48
Fault Tree A graphical method used to identify potential causes of system failure A fault tree is constructed having Events: describing the failure of system components Logic Gates: representing logical relationship between events AND, OR, NOR, NAND, NOR etc. TOP event First Level Contributor to TOP Event by Logic Gates First Level Events Second-level Contributors to TOP by Logic Gates Second-level Contributors Basic Failure Events W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 20 / 48
Types of FT Gates FT Gates Failure Probability Expressions N N � � F ( t ) = Pr ( A i ( t )) = F i ( t ) i =2 i =2 N N � � F ( t ) = Pr ( A i ( t )) = 1 − (1 − F i ( t )) i =2 i =2 N � F ( t ) = 1 − F OR ( t ) = (1 − F i ( t )) i =2 k N k N � � � � F ( t )= Pr ( A i ( t ) ∩ A i ( t ))= (1 − F i ( t )) ∗ ( F j ( t )) i =2 j = k i =2 j = k F ( t )= Pr ( ¯ A ( t ) B ( t ) ∪ A ( t ) ¯ B ( t )) = F A ( t )(1 − F B ( t )) + F B ( t )(1 − F A ( t )) F ( t ) = Pr ( ¯ A ( t )) = (1 − F A ( t )) W. Ahmed and O. Hasan (NUST) Formal Dependability Modeling and Analysis July 27, 2016 21 / 48
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