Emergency Response Plan for Condensate Fraction Unit Phase 2 for two different scenarios with and without involvement of fire.pdf

Handling Uncertainty in Emergency Plan EvaluationUsing Generalized Petri Nets Case study: Loss of a Condensate Tank Containment Innal Fares, Hamzi Rachida, Djeddi Choay...

Handling Uncertainty in Emergency Plan EvaluationUsing Generalized Petri Nets Case study: Loss of a Condensate Tank Containment Innal Fares, Hamzi Rachida, Djeddi Choayb Institute of Health and Occupational Safety University Hadj Lakhdar Batna Batna, Algeria [email protected], [email protected], [email protected] Abstract—Emergency plans (EP) are complex systems which according to its magnitude are successively the Internal must be executed under time and efficiency constraints. They Emergency Plan (IEP), the External Emergency Plan (EEP) include elements of three different natures, technical, human and and Crisis Plan (CP).They include elements of three different organizational where complex relationships exist between them. natures, namely: technical, human and organizational where This inherent complexity may leads to a number of failures, such complex relationships exist between them. The failure of one as unavailability of critical personnel or technical assets and of these elements during the EP execution could result in vast inappropriate operators’ actions.In this paper we present a Petri dramatic consequences. Such failures may be inappropriate Net-based approach to model and evaluate the performance of an operator action, non response of equipments on demand, EP related to condensate storage tank fire scenario, where wrong decision regarding the EP achievement, etc. These uncertainties relating to task execution durations and reliability events impact the performance of the EP and make its success characteristics of technical equipments are considered. In fact, uncertain. This kind of uncertainty is called “aleatory Petri Nets are a powerful tool to describe complex systems and uncertainty”andbelongs to the irreducible physical variability their inherent interactions. Due to the EP complexity and uncertainty, results are obtained thanks to Monte Carlo (natural randomness) of a system response. simulation. A second source of uncertainty which could affect the emergency response is the lack of knowledge about a given Keywords—Emergency plans (EP); performance evaluation; system. It is termed “epistemicuncertainty” and may be uncertainty; Petri nets; Monte Carlo simulation. reduced when new information is provided. In general, three sources of epistemic uncertainty are distinguished : I. INTRODUCTION completeness uncertainty, model uncertainty, and parameter The upset of modern industrial installations may result in uncertainty. Completeness uncertainty is about factors that are major hazard accidents.In order to limit their consequences, not properly included in the analysis (e.g. neglecting some regulatory bodies require the establishment of Emergency human errors).Model uncertainty is linked to the Plans (EP) in accordance to the identified accident scenarios. simplification of the reality it is designed to represent (e.g. Within the framework of Algerian Oil and gas industries, allocation of a constant probability rather than using a time many factors played a major role in crisis management policy, dependent model).Parameter uncertainty is related to the lack including: of knowledgeaboutthe parameter values used in the - Increasing number of major accidents occurred during the quantification (e.g.: failure probability of an equipment, task last decade, particularly: Skikda refinery fire (2004, 2005) duration, etc.). and Skikda LPG Unit explosion (2004), - Lack of the experience feedback (often referred to as According to the IEP structure and the inherent “lessons learned”), uncertainties, it may be considered as a very complex system - Insufficiency of local regulatory related to the major hazard which requires powerful modelling and analysis tools in order accidents. to assess its effectiveness. In this context, Petri Nets, in particular due to their graphical representation and Regarding this fact, the Algerian authorities –according to mathematical tools, have been widely used in the modeling the article 2 of the executive decree 09-335/20 October 2009 – and the performance assessment of nowadays complex required the establishment of so-called “Internal Emergency systems. In our case, Petri Nets provides a suitable tool to Plan (IEP)”, which describes the measures to be taken inside consider both aleatory and epistemic uncertainties through the establishment in case of a major industrial accident aiming Monte Carlo simulation. to protect people, property and the environment. The structure of the IEP is shown in Fig. 1. The different plans that can The rest of this paper is organized as follows. A brief be triggered when an emergency situation has occurred and presentation of PNs and Monte Carlo simulation are given in Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  Section 2. The object of Section 3 is twofold. First, we may be assigned to transitions (e.g. required time to carry describe the accident scenario and the related IEP used to out a given task). demonstrate our approach. Secondly, the modelling and the - oriented arcs connecting places to transitions (upstream or performance evaluation of this IEP are presented. Section 4 input arcs) and transitions to places (downstream or output summaries our concluding remarks. arcs). Arcs are weighted with a positive number. For example, the weight of an upstream arc may indicate the required resources to achieve a given action whereas that of a downstream arc may indicate the amount of the output resulted from this action. This weight equals to one if it is not explicitly mentioned on the graph. Dynamic part: - tokens pictured by small solid dots. Each place may potentially hold either none or a positive number of tokens which illustrate that the corresponding place is currently allocated. The distribution of tokens in places is referred as the marking. Tokens move through transitions when events occur. A token may, for example, represent the presence or absence of a resource. - predicatesor guards, any formula which may be true or false, enabling transitions. - assertions, any equation, updating some variables when a transition is fired. It is useful to make a distinction between “enabling” and “firing” of transitions: - A transition is enabled when all input places contain at least the number of tokens required by each input arc (indicated by its weight) and all predicates must be ‘true’. - A transition is fired when all preconditions are satisfied (i.e. it is enabled) and a required delay is elapsed (duration from the enabling until the firing). This delay may be deterministic or stochastic (random delay, e.g. negative exponential). If no delays exist (delay = 0) then enabling Fig.1 IEP structure coincides with firing. II. OVERVIEW OF PETRI NETS (PNS) AND MONTE CARLO On the firing of a transition: ANALYSIS - input places lose as many tokens as specified by the weights of input arcs. A. Petri Nets - output places gain as many tokens as specified by the Petri Nets were developed by Carl Adam Petri during his weights of output arcs. PhD thesis on communication with automata. Their - assertions are updated. purpose was initially the description of causal relationships between conditions and events in a computer system. Since In the case where deterministic and stochastic delayed then, many extensions related to PNs have been made in order transitions are involved, which is the case for real life systems, to enlarge their modelling capabilities. In this article, the PN the resulting PNs is termed “generalized PNs” and cannot be presentation is deliberately limited to the necessary concepts solved easily using analytical approaches. Hence, a simulation which are used in the following Sections. For the interested approach has to be considered to efficiently asses the expected readers, a detailed description of PNs theory is given in. performance measures. This been the case, Monte Carlo simulation is an effective tool to deal with stochastic A Petri net is a graphical notation with an underlying processes. The principle of Monte Carlo simulation is mathematical structure suited to model event-driven systems described hereafter. (discrete event systems). It may be identified as a particular kind of bipartite directed graph which contains two B. Monte Carlo Simulation parts : Its main idea is to use random numbers to animate a Static part which include three objects: behavioural model of the real system. It is worth notingthat - places, depicted as circles or ovals in the graphical PNs provide a very efficient support for performing Monte representation, are states of system components. Carlo simulation.TheMonte Carlo simulation is run - transitions, drawn as bars or boxes, corresponding to toproduce a large statistical sample from which statistical potential events that change the state of a Petri Net. Delays results are obtained. For a given simulated parameter X, the basic statistics allow the calculation of the average, variance Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  and confidence interval of the sample (Xi) which has been simulated: n X = ∑ xi / n i (1) n σ = ∑ ( xi − X ) / n 2 2 (2) i [ Confidenceinterval= X − E ⋅ (σ / n), X + E ⋅ (σ / n) ] (3) e.g.:E = 1.6449for confidence= 90 %. Some of the above elements and rules are illustrated on the basis of the following Petri Net (Fig. 2) which represents the behaviour of a repaired component C. It has four places {P1, P2, P3, P4} and three transitions {T1, T2, T3}. Initially (i.e., at Fig. 2. Petri Net related to a repaired component time t = 0), the marking of the PN may be represented by the following vector [1, 0, 0, 5], meaning that initially there is one The component C is therefore coming back in its good token in place P1, no tokens in places P2 and P3 and five working state: the token disappears from P3 and put in P1 and tokens in P4. Places P1, P2 and P3 correspond to states may be the variable “C_KO” becomes false. The two repairmen are reached by the component C and respectively represent: again available: two tokens are added to the place P4 and NR operational state (C_working), waiting for repair state is updated through the assertion “NR = NR + 2”. And so on as (C_waiting repair) and restoration state (C_ repair). P4 is an long as the firing of next valid transition belongs to the period auxiliary place that models the repair team availability (five underinterest [0, T]. repairmen are available). Transitions T1, T2 and T3 model the When the next firing is no longer inside [0, T], the events occurring on component C, respectively: failure simulation is stopped and one history of the component is (C_fails), start of repair (C_starts repair) and end of repair achieved. All along the progress of the history, relevant (C_ends repair). Also, transitions T1 and T3 have a stochastic parameters may be recorded as the mean marking of the places delays defined by δ1 = f (λC ) and δ 3 = g(μC ) , respectively. (i.e., the ratio of the time with one token in the place over the We consider for example that f and g are negative exponential duration T), the transition firing frequencies, the time to the functions: λC and μC refer to the failure and repair rates of C. first occurrence of a given event, etc. The principle of Monte Carlo simulation is to realize a great number of such histories Transition T2is deterministic ( δ 2 = 0 : instantaneous). and to perform classical statistics on the results in order to assess the relevant parameters. As indicated by the initial marking of the considered PN, component C is in good working order. Therefore, only the transition T1 is enabled, because the weight of its input arc C. Handling uncertainty via Monte Carlo sampling (connecting P1 to T1) is equal to the marking of P1(=1). T1 is Uncertainty assessment allows a model-user to be more fired as soon as its delay is elapsed (i.e. δ1 = − (1/ λC ) ⋅ ln(R1 ) , informed about the confidence that can be placed in model results.It may be achieved by means of different where Ri is a random variable uniformly distributed over [0, 1] approaches depending on the level of uncertainty associated to and obtained by Monte Carlo sampling. As a result, the token the considered parameters. Monte Carlo sampling, fuzzy sets is removed from P1 and a token appears in P2 and then the based-approach, intervals analysis are among these variable C_KO becomes “true” (initially C_KO=false). Thus, approaches. Monte Carlo sampling method has the component C reaches a failed state and waits for repair. become the industry standard for propagating uncertainties Consequently, the transition T2 becomes enabled if the guard.In the following its main steps are briefly described. “SP = true”is true, which is assumed to be the case (SP stands for Spare Parts). SP may be updated according to the Construct a probability density function (pdf), on the basis evolution of another PN related, for example, to a given of available knowledge, for each input parameter. In the supply chain. The restoration of C involves two repairmen (the context of emergency response, input parametersmay weight of the input arc connecting P4 to T2 equals to 2). As T2 include: failure probability under solicitation (γ), is instantaneous, it is fired immediately after the marking of P2 intervention team availability, task durations, etc. Different indicating the start of the component C restoration. This firing probability distributions can be chosen according to the state result in the removing of the token of place P2 and two tokens of knowledge about the value of parameters, e.g.: uniform, from the place P4 and a token appears in place P3. In addition, triangular, normal, lognormal, Chi-square, beta, gamma, etc. the assertion “NR = NR – 2”is used to update the number of Generate one set of input parameters by using random the available repairmen (initially NR = 5). This assertion may numbers (uniformly distributed between 0 and 1) according be used by another PN without incorporating the place P4. The to pdfs assigned to those parameters. marking of the PN at this stage is [0, 0, 1, 3]. Accordingly, the Quantify the output function (in our case, PNs models) using transition T3 is enabled and fired when its associated the above set of random values. The obtained value is a stochastic delay, δ3 = −(1/ μC ) ⋅ ln(R2 ) , is elapsed (when the realization of a random variable (X). It is worth noticing that repair is completed). this quantification (based on PNs) requires in its turn a Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  Monte Carlo simulation of the constructed PNs (m histories) - 3 gas detectors (GD): at least the working of one GD is for each generated set of input parameters. required. Also, each GD may fail under solicitation with a Repeat steps 2 to 3 n times (until a sufficient number, e.g., probability equals to 0.05. 1000) producing n independent output values. These n - Programmable Logic Controller (PLC), which has a output values represent a random sample from the probability of failure equals to 0.022. probability distribution (empirical distribution) of the output - Gas indicator (GI: situated in the control room), which has a function. Note that the total number of Monte Carlo histories probability of failure equals to 0.01. is equal to m*n, since the resulting process (quantification + uncertainty propagation) represents a double-loop Monte In addition, the LOC could be detected by on-site operator Carlo simulation. (witness). According to portion of time the operator should be Generate statistics from the obtained sample for the output near the storage tank, he can fail to detect the incident with a result (e.g., probability of extinguishing fire under a given probability equals to 0.2.Once the LOC is detected, the alert is required time): mean, standard deviationσ, confidence triggered instantaneously in case of automatic detection, interval (percentiles), etc. whereas it takes 4 min with operator detection. Then the IEP (level 1) is deployed. It aims to limit and therefore control the condensate LOC. For this level, the necessary emergency III. SCENARIO DESCRIPTION AND ITS IEP ANALYSIS actions should be carried out with respect to the following chronological order. A. Scenario description The chosen accident scenario relies on the Loss Of Operational team intervention. It consists in closing valves Containment (LOC) in a condensate storage tank and pumps, allowing the filling of the condensate tank, in (appertaining to SONATRACH/DP Hassi R’mel: Algerian Oil order to limit the condensate leakage amount. Note that this company). Note that the description and the data given operation must be achieved under a specified time (Critical hereafter are provided by operational and intervention teams Time = 15 min). Beyond this time, the LOC may lead to a in charge of the installation. The situation of the considered band fire which is difficult to control. One has to consider the tank regarding the whole installation is depicted in Fig. 3. following element: - The closing of pumps may be achieved according to three The studied scenario is described in Fig.4. A complete ways: (1) instantaneously if the Emergency Shutdown scenarios description resulting from a LOC is given in. Push Button works (probability of failure = 0.044), else (2) We assume that the initiating event, the condensate Loss Of after 5 min if the whole operational team (team 1) is Containment (LOC), is produced on the piping enabling the available or after 10 min if the team number is not storage tank filling. sufficient. - The closing of valves may be achieved according to three ways: (1) instantaneously if they work automatically (probability of failure = 3.28E-3), else (2) after 10 min if the whole operational team (team 2) is available or after 16 min if the team number is not sufficient. Emergency team intervention. Its actions are delayed 3 min regarding the first intervention and are the following: - Safety bounder establishment: this operation has an efficiency of 90% (the 10% of inefficiency is due to the Fig. 3.Condensate tank situation large area to be prevented). - Ignition sources prevention: its efficiency = 91 % (due to mobiles, synthetic clothes, cars). - Foam film establishment: it depends on the water pumps and emulsifier. There are 5 water pumps (3 on-site and 2 off-site). The starting of Water pumps may be performed according to three ways: (1) instantaneously if the ESD Push button works (probability of failure = 0.044) and the pumps work (with probability of failure for each pump = 0.019) or the off-site pumps work (probability of failure= 0.019), else (2) after 3.50 min if the whole operational team (team 3) is available or (3) after 7 min if the team Fig. 4. Scenario description number is not sufficient. The emulsifier tank may fail according to a probability = 0.09 (provided after 5 min). In The LOC should be detected thanks to a gas detection case of its failure, a rescue emulsifier is provided within 2 system, made up of the following: min. If the first level emergency deployment fails in limiting the condensate LOC under the Critical Time constraint (15 min), a Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  band fire may occur if both ignition sources exists and the Condensate LOC and Gas detection. At time = 0, we made failure of foam film establishment in due time (10 min). In the assumption that the LOC is occurred. This fact is modeled that case, a second level emergency has to be implemented: by the PN of Fig. 5(a). Fig. 5(b) model the behavior of Gas Cooling actions, carried out by fixed means, to answer the detector 1 (GD1) under solicitation (?? LOC==true). Note protection of LPG spheres and Condensate tanks in the that all component behaviours under solicitation are modelled vicinity of the damaged condensate tank. The cooling according to the general scheme of Fig. 5(b). Once the system success depends on the functioning of water system detection is performed, the Alert must be given (!! Alert = (described above) and two nozzles (sphere and tank). Each true) to deploy the IEP of level 1, see Fig. 5(c). nozzle may fail according to a fixed probability equals to Operational team intervention. We recall that its function is 0.023. to control the LOC through the closing of pumps and valves, Fire extinguishing actions using four trucks (two trucks see Fig. 6. among them are needed to control the fire). Each truck has a probability of failure = 0.01, due to emulsifier storage failure Emergency team intervention. We only present the foam or truck mechanical failure. film PNs models, which depends on water pumps (not depicted hereafter) and emulsifier availability: ??(#81==1 or B. IEP performance indicators #86==1) and #89==1 (Fig. 7). The aim of this paragraph is to describe the performance Fire starting and extinguishing. Fig. 8(a) presents the three indicators of the IEP described above. These indicators are conditions that the junction is required to trigger the fire: based on the duration taken to perform the two emergency (ignition, foam insufficiency and uncontrolled LOC (within 15 levels. In particular, we are interested in the following min), whilst Figure 8(b) shows the fire extinguishing process. indicators: Note that trucks behavioursare note depicted below. Condensate LOC emergency. As we have mentioned, we assume that operation should at most take 15 min. Beyond this critical time, the LOC could result in a fire band. The performance of this action is evaluated through the probability (P1) that LOC control duration be lower than 15 min. (a) Fireextinguishing. This operation is assessed according to the fire extinction duration. In other word, the time elapsed between the starting and the extinguishing of the band fire. That performance is measured with respect to the probability (P2) that this duration be lower than 60 min. Avoiding domino effects. Its performance is characterized by the probability (P3) of either the fire extinction in due time (60 min) or that of cooling system working. IV. PNS MODELS AND PERFORMANCE ASSESSMENT (b) A. PNs Models Construction In order to compute all the specified probabilistic quantities, PNs models relating to the described scenario have been established.Some explanations related to their related syntax are given: # i (i is an integer > 0) is the marking of the place number i on the network. jets indicates the number of tokens. !! introduces a list of variables assignments (these assignments take place when the transition is launched). ?? specifies a list of conditions that must be verified for the transition to be valid. drc d is Dirac’s law of duration d. @ (k) (e1, e2, …, en) is a the k out-of n Logic (ei are Boolean expressions). (c) We present in the following some of these PNs.Note that the interaction between these PNs is achieved through Fig. 5. (a) Condensate LOC, (b) Gas Detector 1 (GD1) behaviour and (c) Gas variables (guards and assertions). detection system Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  (a) (a) (b) (b) Fig. 6. (a) Closing of pumps and (b) Closing of valves PNs models Fig. 8. (a) Fire starting and (b) Fire extinguishing B. Obtained Results Two sets of results, with respect to the aforementioned performance indicators, are presented in the following. The first one is related to the simulation of the developed PNs without taking into account parameters uncertainties, i.e., uncertainties related to the emergency plan task execution (a) durations and failure probabilities. Thus, only aleatory uncertainties are taken. For this end, 105 histories have been performedwhich results in the numerical values provided in Table 1.The second set considers parameters uncertainties as gathered in Table 2. 103 sets of input parameters have been generated tanks to Monte Carlo sampling. The used probability density functions are Uniform (lower bound, upper bound) and Lognormal (Mean (M), Error Factor (EF)). Lower and upper bounds for the Lognormal law are: (M/EF, M*EF). For the PNs quantification and for each generated set, the previous number of histories is maintained. So, the total (b) number of histories is 108. The derived numeric values are Fig. 7. (a) Foam film and (b) Emulsifier availability gathered in Table 3. Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.  TABLE I. OBTAINED RESULTS(ALEATORY UNCERTAINTY) V. CONCLUSION Performance Averages Standard Lower bounds Upper bounds Emergency plans play a major role in limiting the indicators deviations (σ) (90%) (90%) consequences of hazardous accidents. Therefore, a particular P1 9.932E-1 8.242E-2 9.927E-1 9.936E-1 attention should be paid during their development. This paper P2 9.707E-1 1.686E-1 9.698E-1 9.716E-1 presents a novel approach aiming to assess the efficacy of an P3 9.988E-1 3.389E-2 9.987E-1 9.990E-1 emergency response; based on a high level model: Petri Nets. A particular accident scenario was studied and which concerns TABLE II. PARAMETER UNCERTAINTIES the loss of containment (LOC) of a condensate storage tank. Parameters Initial Uncertainties Its related emergency plan performance indicators were values defined in terms of three probabilistic measures: (i) probability Gas detector failure probability 0.05 Uniform (0.02, 0.08) that the LOC control duration be lower than a given critical PLC failure probability 0.022 Uniform (0.01, 0.035) time (15 min in our case), (ii) the probability that the fire Gas indicator failure probability 0.01 Uniform (0.009, 0.015) extinction duration be lower than 60 min and (iii) the On-site operator non-detection 0.2 Uniform (0.1, 0.3) probability of avoiding domino effects. Moreover, two probability quantifications have been performed relying on Monte Carlo Alert triggering time 4 min Lognormal (4, 1.5) Critical Time 15 min Constant (15) simulation. The first one considers onlyaleatory uncertainty, Shutdown Push Button failure 0.044 Uniform (0.03, 0.06) whereas the second one takes parameters uncertainties into probability account. This second quantification is more realistic and thus Closing of pumps duration if the whole 5 min Lognormal (5, 1.5) gives credit to the obtained results. In our case, the second operational team is available indicator is low such that the emergency plan cannot be Closing of pumps duration if the team 10 min Lognormal (10, 1.5) validated. number is not sufficient. Valves failure probability 3.28E-3 Uniform (2.9E-3, 3.5E-3) REFERENCE Closing of valves durationif the whole 10 min Lognormal (10, 1.5) operational team is available DET NORSKE VERITAS (DNV), Plan d’Intervention Interne (PII), Rapport N° EP002720 N° 6 – HRM Centre, SONATRACH, 2010. Closing of valves durationif the team 16 min Lognormal (16, 1.5) number is not sufficient. R. Ferdous, F. Khan, R. Sadiq, P. Amyotte, and B.Veitch,“Analyzing Teams unavailability 0.1 Uniform (0.09, 0.15) system safety and risks under uncertainty using a bow-tie diagram: an Emergency team intervention delay 3 min Lognormal (3, 1.5) innovative approach,”Process Saf. Environ. Protect, vol. 91, pp. 1–18, 2013. Safety bounder efficiency 0.9 Uniform (0.85, 0.95) Ignition sources prevention efficiency 0.91 Uniform (0.85, 0.97) M. Abrahamsson,Uncertainty in Quantitative RiskAnalysis - Water pumps failure probability 0.019 Uniform (0.015, 0.025) Characterisation and Methods of Treatment.Ph. D. thesis, Department of Fire Safety Engineering, Lund University, Sweden, 2002. Water pumps starting delay if the 3.5 min Lognormal (3.5, 1.5) whole operational team is available NUREG1885, Guidance on the treatment of uncertainties associated Water pumps starting delay if the team 7 min Lognormal (7, 1.5) with pras in risk-informed decision. Technical report, United States number is not sufficient. Nuclear Regulatory Commission, 2009. Emulsifier tank failure probability 0.09 Uniform (0.08, 0.1) T.Gu and P.A Bahri, “A survey of Petri net applications in batch Emulsifier duration 5 min Lognormal (5, 1.5) processes,” Computers in Industry, vol. 47, pp. 99-111, 2002. Rescue Emulsifier duration 2 min Lognormal (2, 1.5) R.David and H.Alla, Discrete, continuous and hybrid Petri nets. 2nd ed. foam film establishment due time 10 min Uniform (8, 12) Berlin, Germany: Springer Publishing Company, 2010. Nozzle failure probability 0.023 Uniform (0.02, 0.03) C.-C.Huang and W.Y. Liang, “Object-oriented development of the Truck failure probability 0.01 Uniform (0.0095, 0.02) embedded system based on Petri-nets,” Computer Standards & Interfaces, vol. 26, pp. 187-203, 2004. TABLE III. OBTAINED RESULTS(ALEATORY UNCERTAINTY AND IEC 61508 standard, Functional safety of PARAMETER UNCERTAINTY) electrical/electronic/programmable electronic safety-related systems. Performance Averages Standard Lower bounds Upper bounds 2nd ed. Geneva, Switzerland: International Electrotechnical Commission, 2010. indicators deviations (σ) (90%) (90%) H. Blume, T. Von Sydow, D. Becker and T.G. Noll, “Application of P1 9.843E-1 9.459E-3 9.838E-1 9.848E-1 deterministic and stochastic Petri-Nets for performance modeling of P2 6.510E-1 3.416E-1 6.333E-1 6.687E-1 NoC architectures,” Journal of Systems Architecture, vol. 53, pp. 466- P3 9.828E-1 1.692E-2 9.819E-1 9.837E-1 476, 2007. EPA, Guidance on the development, Evaluation, and application of Environmental models. U.S. Environmental Protection Agency, 2009. Table 1 shows that the performance indicators that we are looking for are very high. Therefore, the robustness of the N.Buratti, B.Ferracuti, M.Savoia, G.Antonioni and V.Cozzani, “A fuzzy-sets based approach for modelling uncertainties in quantitative established emergency plan can be validated. However, when risk assessment of industrial plants under seismic actions,” Chemical parameter uncertainties are considered, the previous indicators Engineering Transactions, vol. 26, pp. 105-110, 2012. are reduced (see Table 3). If that reduction is minor for P1 and T. Aven and E.Zio, “Some considerations on the treatment of P3, it is significant in the case of P2(probability of fire uncertainties in risk assessment for practical decision-making,” extinction within 60 min = 0.651). Hence, about 1/3 of fire Reliability Engineering and System Safety, vol. 96, pp. 64-74, 2011. extinctions last more than 60 min, which is very dangerous. NASA, Probabilistic Risk Assessment Procedures Guide for NASA Given this fact, the existing emergency plan has to be Managers and Practitioners. NASA Office of Safety and Mission Assurance,Washington, 2002. improved, for example, by increasing the reliability of water J.Casal, M.Gomez-Mares, M.Munoz and A.Palacios, “Jet Fires: a pumps or that of the emulsifier storage tank. “Minor” Fire Hazard?,”Chemical Engineering Transactions, vol. 26, pp. 13-20, 2012. Authorized licensed use limited to: BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE. Downloaded on June 29,2024 at 17:02:23 UTC from IEEE Xplore. Restrictions apply.