Reliability and Risk Analysis in Naval Architecture and Ocean Engineering

Reliability and Risk Analysis in Naval Architecture and Ocean Engineering USP Escola Politécnica EPUSP Naval Architecture and Ocean Engineering Department Prof. Marcelo Ramos Martins (mrmartin@usp.br) Introduction Prof. Marcelo Ramos Martins (mrmartin@usp.br) Under graduated in Naval Architecture and Ocean Engineering (USP/1992) Naval Engineer at Brazilian Navy working on Nuclear Submarine design (1992-1994) MSc. and PhD. in Naval Architecture and Ocean Engineering (USP/1996 and 1999) Professor at Naval Architecture and Ocean Engineering Department since 2001 Visiting Professor at University of Maryland between 2011 and 2012 Associate Professor at USP since 2012 Associate Editor of Journal of Offshore, Mechanics and Arctic Engineering (JOMAE) Currently teaching: Hydrostatic and stability (under graduation) System Reliability (graduation) Risk Analysis (graduation) Special topics for system reliability and risk analysis (graduation) Interested topics: Analysis, evaluation and risk management Project system optimization 2 1

In 1893 Escola Politécnica was founded In 1934 POLI became part of the USP UNIVERSITY OF SÃO PAULO 1960 USP Capital Campus Hyde Park London, UK 2

USP - Capital Campus São Paulo, Brazil Escola Politécnica 141,500m 2 3

LABRISCO Analysis, Evaluation and Risk Management Laboratory Reliability of complex and/or critical systems. Evaluation and risk management. Human error contribution. www.labrisco.usp.br USP today In 2015 USP was ranked amongst the best 200 universities in the world #51-100 - QS World Univ. in Engineering and Technology #143 - QS World University (overall) #51-60 - Times Higher Education (#178 in 2011) #100-150 ARWU (Academic Ranking World Universities) 1 st between Latin American Universities #1 - QS Latin American University Ranking 2015 8 4

What is and Why study System Reliability? What is System Reliability? Definition: Reliability is the probability that an item, component or system execute its function during a specified mission time and under designated operating conditions, given that it was operating or able to operate at the initial time. Pr 1, 2... R t T t c c T: time of failure (random variable) t: mission time c 1, c 2,... Designed operating conditions 10 5

Why study System Reliability? 11 Why study System Reliability? 12 6

Mathematical definition System Reliability: t Pr T t f t dt F t to t 0 o Conditions c,c... implicity 1 2 F t cdf Unreliability 0 F t 1 1 0 T 13 System Reliability Summarizing: R t Pr T t c 1,c 2... Ft Pr T t c 1,c 2... R t f t dt F t f t dt t 0 R t 1 F t F t 1 R t t R t 1 f t dt F t 1 f t dt t 0 t t t 0 R t 1 0 F t 1 R 0 1 F 0 0 lim R t 0 lim F t 1 14 7

Failure rate / Hazard rate () Definition: It is the rate of occurrence of failure in a given time dr t 1 f t t dt R t R t R t dr t t dt R t 0 e t d 15 Exponential distribution f(t) 2.5 2 1.5 1 0.5 = 2.0/hr = 1.0/hr = 0.5/hr f(t) = e R(t) = e t t 1 MTTF = 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t 16 8

Exponencial distribution 1.2 f(t) = e t 1 R(t) = e t R(t) 0.8 0.6 = 0.5/hr = 1.0/hr MTTF = 1 0.4 0.2 = 2.0/hr 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t 17 Exponencial distribution 1.2 1 = 2.0/hr 0.8 F(t) 0.6 0.4 = 1.0/hr 0.2 = 0.5/hr 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t 18 9

Weibull distribution The most useful distribution in reliability studies Can be used to model DFR and IFR (region I and III); The failure rate is defined by: (t) a t Or, for mathematical convenience, by: t (t) scale factor []=time shape factor b 1 19 Weibull distribution Therefore: n 1 = n! for n integer d t 0 R t e e f t = 3.75 represents a normal distribution t 1 t dr t t e dt + 1 MTTF = 20 10

Life testing Objective: Obtain data to allow the estimation of the reliability Possible configurations: Not censored: The test ends only when all units fail. Censored: The test can end after a specified number of failures or time duration Can be accelerated 21 BAYESIAN METHODS FOR ESTIMATING PARAMETERS Visão geral: Model for Data Data Prior f () Π θ E Likelihood L( Data ) Bayesian Inference PE L E θ f θ MLE Posterior (Data) 22 11

APPLICATION TO RELIABILITY ESTIMATION Example: Consider the prior distribution for reliability R of a new device as: 3 f R = 4R 0 < R < 1 so; 0 1 3 4 5 1 ER = R 4R dr = R = 0.80 5 0 23 Método de Bayes para estimativa de parâmetros Example (cont.): If we have a evidence of a success (s) during a mission time: and, f R Pr s R 3 4 4R R 4R gr s = = = = 5R 1 1 4 4 f R Prs R dr 4R dr 5 0 0 4 1 1 6 1 4 5R E R s = R g R s dr = R 5R dr = = 0.83 6 0 0 0 24 12

Método de Bayes para estimativa de parâmetros Example (cont.): If we have a evidence of a failure (f) during a mission time: and, 3 f R Pr f R 4R 1R g R f = = = 5 4R R 1 1 3 f R Pr f R dr 4R 1R dr 0 0 3 4 1 1 3 4 2 ER f = R gr f dr = 5R 4R R dr = = 0.67 3 0 0 25 Método de Bayes para estimativa de parâmetros Example (cont.): Summarizing: Evidence: 1 success Evidence: 1 failure ER s = 0.83 ER = 0.80 E R f = 0.67 26 13

Evaluating System Reliability Methods: Reliability Block Diagrams Standby, Share load systems and complex configuration Consider also the functional configuration not only the physical configuration Logic-Based Diagrams Fault tree, Success tree e Event tree Event tree considers that the components act in a certain chronological order to fulfill its mission All methods treat the components of the systems as being statistically independent 27 Block Diagram Series components: The system will be available only when all its components are ready to operate The system is at fault condition when some of its components are defective. Hence: A B C Z R s Rs t t Pr A Pr A B Pr B C Pr C Z Pr Z R t R t R t R t R t s A B C Z n RS t Ri t i1 Considering all components as independent 28 14

Block Diagram Parallel components : S The system is available when at least one of its components are ready to operate The system is at fault condition when all components are in failed state F Pr A B Z n i F F t F t F t S A B Z 1R t F t S i1 n i1 RS t 1 1Ri t 29 Block Diagram k-out-of-n system If any of the k blocks out of N independent and identical blocks should work so that the system works, then: N N r Nr RS t R t 1 R t r k r k1 N 1 R t 1 R t r 0 r r Nr 30 15

Diagrama de blocos Series parallel system: 31 Diagrama de blocos Series parallel system: Reduction system into subsystems in series and in parallel R X / /Y 1 1R 1R R R R R RX R1 R3 R4 R3R4 R1RT R R R R R R R R S X Y X Y X Y Y 2 5 6 5 6 2 V If all the components have exponential distribution of failure: 1 t 3t 4 t 3 4 t 2 t 5t 6t 5 6 t RS t e e e e e e e e 1 2t t t 3 4t t - t 5 6t 3 4 5 6 e e e e e e e MTTFs RS t dt 0 32 16

Logic Tree Analysis It is a top down deductive decomposition of a failure into its basic causes using Boolean Logic Gates (Logic Representation) in Logic Trees Gate OR C AB C AB Gate NOT OR C A B C A B Gate AND C AB C AB Gate NOT AND C A B C A B 33 Fault Tree Analysis Example: Qualitative Analysis: Cut sets e path sets Quantitative Analysis: It must be done carefully Fonte: Modarres (2009) 34 17

Event Tree Analysis If successful operation of a system depends on the chronological operation of some of its units or subsystems, then an event tree is a useful logical model for the system. ac Source P Sink A fault tree can be used to determine the probability of each branch of the event tree 35 Bayesian Network BN is a Directed Acyclic Graph (DAG) which is defined as G = (V,E), where V are the nodes, that can represent discrete or continuous variables, and E is a set of ordered pairs of distinct elements of V and it is called arcs (or edges), that represent the dependencies between the nodes. The conditional probabilities associated with the variables are the quantitative component. 36 18

Bayesian Network: A simple example 37 Converting a FT into BN AND Gate Conversion OR Gate Conversion E A B E A B A B E A B E P(E=1 A=0,B=0)=0 P(E=1 A=0,B=1)=0 P(E=1 A=1,B=0)=0 P(E=1 A=1,B=1)=1 P(E=1 A=0,B=0)=0 P(E=1 A=0,B=1)=1 P(E=1 A=1,B=0)=1 P(E=1 A=1,B=1)=1 38 19

Fault tree Heat of ignition source present LNG Explosion or Fire LNG Concentration within the flamability range Oxygen present LNG leak No dispersion of LNG LNG Supply System Leak Conversion System Leak Heat Exchange System Leak Compression System Leak Deliver y Pipe P1 V6 V1 V2 Pipe 2 Pipe 12 Insulator 1 T1 Pipe 1 Ac2 V7 Pipe 4 C1 Pipe 5 LNG/Propane System Leak LNG/Water System Leak Insulator 2 V3 Pipe 3 HE1 V4 V5 HE2 Insulator 3 Equivalent Bayesian Network Insulator1 Pipe3 Insulator3 C1 ok 99.5 Insulator2 ok 99.4 ok 99.5 ok 100 Fault 0.51 ok 99.5 fault 0.56 Fault 0.51 fault wiyhout leakage 0 + Fault 0.51 fault with leakage 0 + T1 Pipe12 Pipe5 ok 100 ok 99.4 V4 ok 99.4 fault 0 + fault 0.56 ok 99.6 fault 0.56 HE1 fault 0.40 V7 Ac2 ok 98.7 ok 99.6 Pipe1 fault 1.28 ok 99.8 fault 0.40 fault 0.24 ok 99.4 fault 0.56 V3 ok 99.9 LNGPropaneLeak V5 Pipe4 fault 0.12 true 2.84 P1 HE2 ok 99.4 false 97.2 ok 99.6 ok 98.2 V1 ok 99.9 fault 0.40 fault 0.56 fault 1.82 ok 99.9 fault.094 fault 0.12 LNGWaterLeak V2 HeatExchangeSystemLeak true 1.0 V6 CompressionSystemLeak false 99.0 ok 99.9 ok 99.9 true 3.81 true 1.76 fault 0.12 fault 0.12 false 96.2 false 98.2 Pipe2 ok 99.4 fault 0.56 ConversionSystemLeak true 6.00 false 94.0 DeliveryPipe ok 99.5 fault 0.53 SupplySystemLeak true 4.30 false 95.7 LNG_Leak true 10.0 false 90.0 IgnitionSourcePresent true 5.00 false 95.0 LNGConcFlamabilityRange true 0 + false 100 LNG_Explosion_or_Fire true 0 + false 100 NoDispersionOfLNG true.005 false 100 OxygenPresent true 90.0 false 10.0 40 20

Most Probable Explanation (MPE) Insulator1 Pipe3 Insulator3 C1 ok 99.5 Insulator2 ok 99.4 ok 99.5 ok 100 Fault 0.51 ok 99.5 fault 0.56 Fault 0.51 fault wiyhout leakage 0 + Fault 0.51 fault with leakage 0 + T1 Pipe12 Pipe5 ok 100 ok 99.4 V4 ok 99.4 fault 0 + fault 0.56 ok 99.6 fault 0.56 HE1 fault 0.40 V7 Ac2 ok 98.7 ok 99.6 Pipe1 fault 1.28 ok 99.8 fault 0.40 fault 0.24 ok 99.4 fault 0.56 V3 ok 99.9 LNGPropaneLeak V5 Pipe4 fault 0.12 true 2.84 P1 HE2 ok 99.4 false 97.2 ok 99.6 ok 98.2 V1 ok 99.9 fault 0.40 fault 0.56 fault 1.82 ok 99.9 fault.094 fault 0.12 LNGWaterLeak V2 HeatExchangeSystemLeak true 1.0 V6 CompressionSystemLeak false 99.0 ok 99.9 ok 99.9 true 3.81 true 1.76 fault 0.12 fault 0.12 false 96.2 false 98.2 Pipe2 ok 99.4 fault 0.56 ConversionSystemLeak true 6.00 false 94.0 DeliveryPipe ok 99.5 fault 0.53 SupplySystemLeak true 4.30 false 95.7 LNG_Leak true 10.0 false 90.0 IgnitionSourcePresent true 5.00 false 95.0 LNGConcFlamabilityRange true 0 + false 100 LNG_Explosion_or_Fire true 0 + false 100 NoDispersionOfLNG true.005 false 100 OxygenPresent true 90.0 false 10.0 41 Some publications using BN Martins, MR; Schleder, AM; Droguett, EL. A Methodology for Risk Analysis Based on Hybrid Bayesian Networks: Application to the Regasification System of Liquefied Natural Gas Onboard a Floating Storage and Regasification Unit. Risk Analysis, v. 34, 2014. Martins, MR; Maturana, MC. Application of Bayesian Belief networks to the human reliability analysis. Reliability Engineering & Systems Safety, v. 110, 2013. Schleder, AM; Martins, MR; Modarres, M. The use of Bayesian Networks in reliability analysis of the LNG regasification system on a FSRU under different scenarios. International Offshore and Polar Engineering Conference - ISOPE2012. Martins, MR; Silva, DF; Maruyama, FM; Loriggio, FF. The Bayesian Networks applied to a steering gear system fault diagnostics. International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, OMAE2010. 42 21

Human Reliability Human reliability is the probability that a person will correctly perform some system-required activity during a given time period (assuming time is a limiting factor) without performing any extraneous activity that can degrade the system. FSA Step 1 Hazard Identification Step 2 Risk Analysis Step 3 Risk Control Options Step 4 Cost Benefit Assessment Tasks Required to Incorporate the HRA Human related hazards High level task analysis Preliminary description of outcome Detailed task analysis for critical tasks Human error analysis Human error quantification Risk control option for the human element Step 5 Recommendatio n for Decisionmaking 43 Fault tree 2 Ineffective Evasive Action 5.25E-2 1 Collision 1.48E-4 3 Hazardous Situation 2.82E-3 4 Error in the Performed Action 5.25E-2 5 Another Ship is not Detected 1.00E-11 6 Evasive 8 Patthern Another Ship is Failure Detected (COLREG) 1.00E-0 5.00E-1 15 Ship Leaves the Planned Route 2.81E-3 17 Route Diversion 18 2.81E-3 Safe Planned Route 1.00E0 16 Unsafe Planned Route 1.01E-5 38 39 Planning Failure Captain 1.01E-3 Verification Failure 1.00E-2 7 Emergency Procedure Failure 1.05E-1 40 Exact Information and Wrong Use 1.01E-3 41 Inaccurate Information 0.00E0 9 Wrong Action 2.51E-3 10 Communication Failure 1.03E-1 19 Ineffective Corrective Action 2.51E-3 20 Monitoring Failure 3.01E-4 42 Exact Information 1.00E0 43 Failure in Drawing the Route 1.01E-3 11 Command Failure 2.01E-3 12 Wrong Answer 4.99E-4 22 No detected Error 1.00E0 27 Detection by Measuring 4.00E-4 28 Visual Monitoring 7.53E-1 13 Nautic Officer gives Wrong Order 9.98E-1 21 Ineffective Action 2.51E-3 14 Helmsman Failure 5.00E-4 29 Marking Error 3.00E-4 30 Error Detection Failure 1.00E-4 34 No Visual Indication 7.50E-1 35 No Visual Detection 2.50E-3 23 24 Command Wrong Answer Failure 4.99E-4 33 2.01E-3 Nautic Officer 31 Failure Exact Marking 1.00E-2 1.00E0 25 Helmsman 26 32 Wrong Nautical Officer Gives Captain Answer Exact Order Failure 5.00E-4 9.98E-1 1.00E-2 36 Attention Failure 1.00E-2 37 Visual Indication 2.50E-1 22

Network for PSFs 45 Integration of FT and BN 46 23

Task Dynamic Network 47 Putting all pieces together 48 24

Possible results 49 Some publications about HRA Martins, MR; Maturana, MC. Application of Bayesian Belief networks to the human reliability analysis. Reliability Engineering & Systems Safety, v. 110, p. 89-109, 2013. Martins, MR; Maturana, MC. Human error contribution to risk in collision and grounding of oil tankers. Risk Analysis, v. 30, p. 674-698, 2010. Martins, MR; Maturana, MC; FRUTUOSO, PFF. Methodology for system reliability analysis during the conceptual phase of complex system design considering human factors. PSA 2015 International Topical Meeting on Probabilistic Safety Assessment and Analysis, Sun Valley, 2015. Martins, MR; Maturana, MC. The application of the bayesian networks in the human reliability analysis. International Mechanical Engineering Congress and Exposition, 2009, Orlando. 2009. 50 25

Hazards, Accident and Risk Hazard: Potential of an event, if it occurs, to cause a negative consequences to people, to property and/or to the environment ACCIDENT An unforeseen and unwelcome event that causes a negative consequence to people, to property and/or to the environment. RISK: Concept attributed to the uncertainty used for assessing the potential effect of an accident in terms of its likelihood of occurrence and the magnitude of their consequences. 51 Risk Analysis x Risk Assessment 52 26

Risk Analysis Qualitative x Quantitative Qualitative analysis: qualitatively evaluates the risk related to all possible hazardous events in the installation, considering the likelihood of such events occur, and the effects from these events In general, it is previously performed a quantitative risk analysis Quantitative analysis: quantitatively analyzes the risks identified during the qualitative analysis with high probability of occurring and / or causing major damage to the structure, to people or the environment numerically quantifies the probability of occurrence of the event and its consequence. 53 Qualitative Risk Analysis 54 27

Quantitative Risk Analysis The total risk is commonly defined mathematically by: R i P C i i P i : probability of occurrence of event i C i : expected severity of the event i i : possible hazardous events Some authors propose the inclusion of the probability of detection means provided in the system for calculating risk 55 Formal Safety Assessment 56 28

Techniques for Hazards identification Support techniques: Unifilar diagram Functional tree Techniques for hazards identification What if analysis HAZID Hazard identification HAZOP Hazard and Operability Studies PHA Preliminary Hazard Analysis FMEA Failure Mode and Effect Analysis FEMECA Failure Mode, Effect and Criticality Analysis 57 Consequence Analysis Use available model and tools to analyze: Vapor cloud dispersion Pool formation, dispersion and evaporation Flash fire and cloud explosion Jet fire Fire ball and BLEVE (Boling Liquid Expansion Vapor Explosion) 58 29

Case Study Brazilian Offshore LNG Terminal Pecém Terminal: Total length of access bridge: 2.142m Deep: ranging from 15 to 18 m Terminal: 1.950m away from the coast 59 Consequence Analysis of possible scenarios 60 30

Pecém Terminal Cases to be presented: Case I: catastrophic rupture of the connection pipe to the terminal at the end of the carrier ship's cargo transfer to the FSRU and possible cascade events Case II: Comparative analysis of onshore and offshore LNG terminals 61 Pecém Terminal Case to be presented: Catastrophic rupture of the connection pipe to the terminal at the end of the carrier ship's cargo transfer to the FSRU and possible cascade events 62 31

Catastrophic rupture of the connection pipe Hypothesis: Catastrophic rupture of the cryogenic hose All control and protection systems are available and in operation LNG composition: 100% methane Maximum flow transfer: 10,000m 3 / h of LNG Characteristic time of the ESD system (emergency shut down system): 30s for failure identification and 30s to its isolation Release 167m 3 LNG Instantaneous release without ignition source during the leakage Circular pool and cloud formation Cloud ignition when it gets LFL 63 Catastrophic rupture of the connection pipe Primary event: 64 32

Catastrophic rupture of the connection pipe Flash fire envelope 65 Catastrophic rupture of the connection pipe Pool thermal radiation 66 33

Catastrophic rupture of the connection pipe Cascade event (26.000m 3 ): 67 Catastrophic rupture of the connection pipe Cascade event (26.000m 3 ): 68 34

Catastrophic rupture of the connection pipe Cascade event (26.000m 3 ): 69 Catastrophic rupture of the connection pipe Flash fire hazardous distance for each scenario: Scenario Maximum distance (m) of the Flash Fire effects Day (LFL) Day (½LFL) Night (LFL) Night (½LFL) 1 min 280 350 360 510 1tank 1,600 2,100 2,000 3,100 2 tanks 1,950 2,550 2,600 3,650 3 tanks 2,250 3,200 2,950 4,050 4 tanks 2,600 3,650 3,400 5,400 5 tanks 2,650 3,950 3,600 5,600 70 35

Catastrophic rupture of the connection pipe Late pool fire effect distance for all scenarios : Maximum distance (m) of the Pool Fire effects Scenario (5 kw/m 2 ) 1 min 450 1tank 2,650 2 tanks 3,400 3 tanks 3,800 4 tanks 4,000 5 tanks 4,200 71 Quantitative Risk Analysis Individual Risk 72 36

Quantitative Risk Analysis of a LNG Terminal 73 Quantitative Risk Analysis of a LNG Terminal 74 37

Quantitative Risk Analysis of a LNG Terminal 75 Case II: Onshore and offshore LNG terminals Three analyzed scenarios operational accidents (OA) include overpressure, sparks and ignition, collision and strike no operational accidents (NOA) consist of earthquakes, hurricanes, aircraft accidents, adjacent fires, sabotage and terrorist actions Worst case (PC) event used by many studies as the default for a worst catastrophe that could occur 76 38

Case II: Onshore and offshore LNG terminals Consequence analysis results obtained for the night Consequência OA_noite NOA_noite WC_noite Onshore Offshore Onshore Offshore Onshore Offshore Flash fire LFL 755m 1160m 1000m 2000m 2000m 4500m Early pool fire 12,5kW/m 2 315m 335m 320m 565m 325m 1355m 37,5kW/m 2 205m 185m 210m 310m 215m 735m Late pool fire 12,5kW/m 2 315m 580m 320m 980m 325m 1585m 37,5kW/m 2 205m 315m 210m 535m 215m 865m 77 Case II: Onshore and offshore LNG terminals Consequence analysis results obtained for the day OA_dia NOA_dia WC_dia Consequência Onshore Offshore Onshore Offshore Onshore Offshore Flash fire LFL 620m 1140m 825m 1800m 1900m 4500m Early pool fire Late pool fire 12,5kW/m 2 315m 340m 320m 570m 325m 1360m 37,5kW/m 2 205m 185m 210m 315m 215m 745m 12,5kW/m 2 315m 580m 320m 985m 325m 1595m 37,5kW/m 2 205m 320m 210m 540m 215m 875m 78 39

Some publications about Risk Analysis Schleder, AM; Pastor, E; Planas, E; Martins, MR. Experimental data and CFD performance for cloud dispersion analysis: The USP-UPC project. Journal of Loss Prevention in the Process Industries, v. 38, p. 125-138, 2015. Schleder, AM; Droguett, EL; Martins, MR. A Methodology for Risk Analysis Based on Hybrid Bayesian Networks: Application to the Regasification System of Liquefied Natural Gas Onboard a Floating Storage and Regasification Unit. Risk Analysis, v. 34, p. n/a-n/a, 2014. Ramos, MA; Droguett, EAL. ; Martins, MR. Comparison of possible consequences of LNG leakages in offshore and onshore terminals: the case of the port of Suape in the northeastern Brazil. International Journal of Modeling and Simulation for the Petroleum Industry, v. 8, p. 40-49, 2014. Salazar, MP; Martins, MR. Atmospheric dense gas dispersion models and their influence in the risk analysis studies assessment in the scope of the standard CETESB P4.261. European Safety and Reliability Conference - ESREL2015, 2015, Zurich. 79 Looking forward to seeing you at USP Prof. Marcelo Ramos Martins mrmartin@usp.br 40