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## State-Based Dependability Modeling

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Lecture Structure

- Boolean Reduction Example (00:00:03)
- Quantitative Analysis of Fault Trees (00:01:51)
- basic events to compute probability (00:01:51)
- - Utilize probability of independent (00:01:51)
- - Assuming independence of basic events (00:01:51)
- - Determine probability of TOP event by (00:01:51)
- Pr ) TOP P 7 Pr ( X 1 L ) + PI‘l 4 SL‘ , 3 lAP 7 ‘l 4 r 4 * . Pr 5 l — Pr ( X 1 Pr ) —Pr [ . 14 (00:01:51)
- Method for Obtaining Cut Sets ( MOCUS ) [ Rausand ] (00:02:24)
- Quantitative Analysis of Cut Sets (00:04:39)
- - Sum up all Qa ( t ) for out sets that contain K — > ek t ) : Qsg? 1 ( t ) + Qu 2 ( t ) + / 03 ( 1 ) (00:04:39)
- - Determine system unavaxlabxtity Qg t ) — E ; t ) : Qa ( t ] / Qs ( t ) (00:04:39)
- - Finding the dominant minimal out set : Calculate the probability of each minimal (00:04:39)
- Fixing Cut Sets (00:07:45)
- - providing fault tolerance for G 4 (00:07:45)
- - preventing failure of both A 1 and A 2 (00:07:45)
- - preventing failure of A 3 (00:07:45)
- - Protect G 3 by preventing failure of A 4 (00:07:45)
- ‘ OR gates can be protected by disallowing all inputs or by providing error recovery (00:07:45)
- - Test for failure condition and recovery routine (00:07:45)
- Exhaustive testing or formal proof to show that the component cannot fail (00:07:45)
- ‘ AND gates can be protected by disallowing one of the inputs (00:07:45)
- Dynamic Fault Trees ( Dl - T ) (00:08:06)
- - What is the probability of (00:08:06)
- Lass and ry and 9 (00:08:06)
- and dynamic probability changes (00:08:06)
- Dynamic Fault Trees (00:10:42)
- FDEP for lnlerdependency Modeling (00:12:42)
- Dynamic Fault Trees (00:13:36)
- 1 % ‘ * (00:15:51)
- HECS Example aux nmunnam mu ans Manny Bx um ! um So my mulaae Sonware ugg arI (00:17:51)
- HECS Example (00:19:00)
- HECS Example (00:19:36)
- ®I @ n (00:19:36)
- ‘Q _ § : $ IE» (00:19:36)
- - Importance analysis with (00:20:48)
- HECSFNLURE FAILURE lvrmuhigiw RE f Ul am IUEéIa 0 DIlIW ‘f - am for (00:20:48)
- Fault Tree Construction [ NASA ] (00:21:36)
- Fault Tree Construction [ Misrall (00:23:09)
- - Step 4 : Complete the gates (00:23:09)
- ‘ Level of resolution — How detailed should be the analysis for potential reasons ’ (00:23:09)
- ‘ Step 1 : Define the undesired event to be analyzed — what . where . when (00:23:09)
- Fault Tree Construction (00:23:15)
- - Logic can be tested in success domain by inverting all statements and gates (00:23:15)
- ~ Statistically independent . immediate contributors to an event (00:23:15)
- - Proper and consistent naming is very important ( what failed and how ) (00:23:15)
- I - ‘FA Report ( Clemens & Sverdrup ) (00:26:00)
- TOP Probability ( Give Con?dence Limits (00:26:00)
- Trade Studies ( I ! done ) (00:26:00)
- Path Sets ( I 1 analyze (00:26:00)
- EXECUTIVE SUMMARY ( A : : s 1 raw 0 ’ wmptehs (00:26:00)
- l - TTA—based Decision Making (00:26:15)
- ‘ and optimize resources — identify what is unimportant (00:26:15)
- ‘ monitor the performance of the system by F re—eva A re - evalutation , (00:26:15)
- proactively prevent the TOP event by applying targeted upgrades (00:26:15)
- the contributors leading to the top event ( typically 10 % — 20 % ) (00:26:15)
- REED vs . F (00:26:21)
- REED vs . l - TA (00:27:51)
- Representing Structures By Paths / Cut Sets [ Rausarid ] (00:29:42)
- its minimal cut (00:29:54)
- very Compute‘ intense ( alternatives : ERAC‘ ea?y early term cancellation , . . . ) (00:29:54)
- - Allows exact system calculation . but principle is (00:29:54)
- —A - System can be computed by determining the probability (00:29:54)
- - The Q of the system is : Q In pr U [ EJ 1 (00:29:54)
- - Let E , denote the event that the minimal cut set structure K failed (00:29:54)
- - System fails as soon as one of (00:29:54)
- Event Tree Analysis (00:31:21)
- Event Tree Analysis - Accident scenario : Series of events that result in an accident (00:32:18)
- Event Tree Analysis (00:33:33)
- damage (00:33:33)
- - Death / Imuryexlenswe n ) ury , ex ensive o (00:33:33)
- damage (00:33:33)
- - beam onoooe Injury n extensive ury , exxenaive (00:33:33)
- - Limited damage . we u . (00:33:33)
- — Limited damage 0 00504 (00:33:33)
- Fire Sprinkler (00:33:33)
- tn (00:34:21)
- ‘ tame (00:34:21)
- ‘ damage . mission mum (00:34:21)
- car ml started gamma 0 084 (00:34:21)
- NO 19 : 0 2 (00:34:21)
- Indtaxinsl (00:34:21)
- E Dggram cum Ljuaaunx D iv mlIaa Ema - all mum an - s E Diagram ‘ * B nag have - v . n raw L Templates D I - Resmwws 2 mm : (00:36:00)
- E IE ! ! ‘ (00:36:00)
- Dxaqram On am Duvatmn Durahun cm cw Items P 21 (00:36:00)
- 3 : ta ~ ~ ~ . = - w _ , A . 1 u 1 ‘A < . ? ? y T T T“ sstrmnruaur . . . . . . . . mam . mm . mm Engine 4 Wm cummumanms mac — nzzj 6 0 ’ mm Era‘ aitn u . : rrrrlrK 1 in ‘” um aux $ 3 as a . mum ni my m us ( 131 mu (00:36:00)
- Tool Support (00:36:33)
- - Throughput analysis (00:36:33)
- - Based on modeling fundamentals . existing tools support : (00:36:33)
- Ian . - 1 vi» pc . e _ m n? ppcr— Pa . welPumt — r mm : mm zmsuczu smwunr unnzcancs usesesmse 0 BiLDSCHiRMPRASENTATiON usexpnuegu ANSiCHiT SFORVEIDARDVNG . SENTATiON ussxmzurm ANSiCH (00:37:42)
- Menasmz , D : me mm A . vngum A dI ma da , l 1 mu A . nm Ca aci Models wm ma sum as Prentice mu ma Mmmd s Pr and nix . nu . ce HaH , 2 (00:37:51)
- State—Based Dependability Modeling (00:37:51)
- Dependability Modeling (00:38:18)
- - System understanding evolved from hardware to software to IT (00:38:18)
- Component - based models block 3 gi fault trees (00:38:18)
- Use a formalism to model system dependability (00:38:18)
- Structural vs State—Based Dependability Models (00:38:48)
- 9 State based Markov models : (00:38:48)
- Gsrnzcrmc > N . — _ CTMC c rMc snnz (00:38:48)
- Structural / combinatorial models : (00:38:48)
- State models (00:39:54)
- ° Solution through simulation (00:39:54)
- Analytical solution (00:39:54)
- - Component models based models work well if failure events are stochastically (00:39:54)
- State Transition Diagrams : Application (00:43:27)
- State Transition Diagrams : Analysis (00:44:51)
- Markov Chains (00:46:00)
- Markov Chains : Time Model (00:48:57)
- Markov Chains : DTMC (00:50:39)
- as 1 .23 M 5 ‘ Probability Malrixafterzsteps 37 JD bi (00:50:39)
- Initialstmprobabilities [ . 5 .3 . § .2 l . 4 .4 .2 = [ dinrihu?onvunorl E . 26 ] .3 ) .5 .3 (00:50:39)
- Dependability Modelling with CTMCs (00:52:33)
- Stationary : the probability to which the (00:52:33)
- ° Transition : assigned with component failure rate (00:52:33)
- State : represents a particular error state ( ) — - _ (00:52:33)
- Example : Analysis (00:55:27)
- 3 ? » 2 » i . ® u C 2 n © ”»u G (00:55:27)
- ° ”Static” Static computable if computable if are in (00:55:27)
- - Derived from probability vector : steady for state for the system (00:55:27)
- ° Interested in steady - state of the system (00:55:27)
- Example : 2 —out—of— 3 System M 1 / » . 0 Al 0 Eu O «i (00:57:42)
- Markov Chains : Complexity (00:58:18)
- - Structural decomposition : consider a system as set of independent (00:58:18)
- um um Inl u , L ’ / . l U : , . M ‘ (01:00:06)
- _ ‘ . . = 3 ® ‘ ‘ . L . ‘ F‘ ’ ‘ 1 J u . A ’ Ll (01:00:06)
- Petri Nets (01:02:15)
- - Conflict : When two transitions need the same token , only one can fire (01:02:15)
- - Bipartite graph (01:02:15)
- Petri Nets — Conceptual Mapping (01:04:03)
- Stochastic Petri Nets : Transitions (01:06:15)
- Stochastic Petri Nets — Properties (01:07:54)
- Example : 2 —of— 3 System (01:09:36)
- Stochastic Petri Nets vs Markov Chains (01:11:09)
- Example : K—of - N with Standby and Repairmen (01:12:03)
- Example : Priority AND 9 Stochastic Petri Net (01:13:24)
- Example : System with Input Buffer (01:14:39)
- Petri Net Simulation vs Analysis (01:15:45)
- Petri Net Simulation : Token Game bool Pstrinatshmlatlanzts 1 Mu 1 at 1 unStep ationStep Petr‘iNe‘t PetriNet‘ int tick int mt tick (01:17:42)
- tnRemove . amp 1 ace _ ba : k ( tt ) ; (01:17:42)
- / 1 tr has become enabled Enabled — start its timer (01:17:42)
- tr‘yImmediateTransitions = rnmsirLons ( tic , tick xnnedxatecanme 1 mned (01:17:42)
- my ila ( 1 mmedia‘teCanF (01:17:42)
- Rare Event Simulation : Importance Sampling (01:18:45)
- Tools (01:20:18)
- linuut I Pa ra miete (01:21:27)
- Runtime Dependability Evaluation (01:24:58)

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