Evaluation Of Spurious Trip Rate Of SIS Dependent On .
Mathematical Methods and Systems in Science and EngineeringEvaluation of Spurious Trip Rate of SIS dependent on demand rateN.T. DANG PHAMDepartment Computer Architecture and System ProgrammingUniversity of KasselWilhelmshöher Allee 71, 34121 KasselGERMANYMICHAEL SCHWARZDepartment Computer Architecture and System ProgrammingUniversity of KasselWilhelmshöher Allee 71, 34121 KasselGERMANYJOSEF BÖRCSÖKDepartment Computer Architecture and System ProgrammingUniversity of KasselWilhelmshöher Allee 71, 34121 KasselGERMANYAbstract: - Some of the spurious activations can lead to a hazardous state and therefore the plant cost can beextremely increased. For this reason the modelling of spurious activations in safety instruments systems (SIS)has been studied for over ten years and in different industry branches, for example: nuclear industry, offshoreonshore industry, process industry, . In line with the important standard IEC 61508, SISs are generallyclassified into two types: low-demand systems and high-demand systems. This article focuses on the estimationof “spurious trip rate” (STR) and “mean time to failure spurious” (MTTF Spurious) for these two different systemmodes. The research is based on block diagrams and the Markov model and is exemplified by a simple systemconfiguration: 1oo1.Key-Words: - demand rate, MTTFSpurious, spurious trip rate, 1oo11 IntroductionSafety instrumented systems (SISs) are widely usedin the process industry to respond to hazardousevents and unwanted events. If a hazardous situationoccurs within an EUC (Equipment Under Control)and is detected, a demand is sent to safety systemwith a rate DE. This demand serves to activate thesafety function to achieve the EUC in safe state(Fig. 1).The demand rate is not defined in standardIEC 61508 [1], but defined in the standard prENISO 13849-1 (2004) [17] as a frequency of demandsfor a safety-related action of a safety related part ofa control system (SRP/CS).ISBN: 978-1-61804-281-1SISSIL 1.SIL 4Demand rate entcontrolFig. 1. EUC and SIS [14], [15]According to the important standard IEC 61508[1], SISs are classified into two types: low-demandsystems and high-demand systems. A low-demandSIS has a frequency of demands not more than onceper year and not more than twice the proof testfrequency. Else, the SIS is considered as a highdemand system. However, there are no furtherdiscussions about the distinction between low- andhigh-demand systems. There is only a discussion17
Mathematical Methods and Systems in Science and Engineeringabout the difference of the reliability evaluationbetween systems: Probability of Failure on Demand(PFD) for low-demand systems and Probability ofFailure per Hour (PFH) for high-demand systems.The SIS can be regarded from one of twodifferent perspectives: safety or availability. Fromthe point of view of a safety perspective a SIS canbe evaluated by some important safety parameterssuch as PFD, PFH, MTTF (Mean Time To Failure).And other parameters like STR, MTTFSpurious, PFS(Probability of Failure Safe) are commonlycalculated for a SIS with availability perspective.While the safety integrity levels (SIL) are defined inthe standard IEC 61508 [1] to provide a measure ofhow often a function fails to operate when required(Table 1), spurious trip levels (STL) are defined in[5], [6] to measure how often a function is carriedout when not required (Table 2). The more financialdamage the spurious trip can cause, the higher theSTL of the safety function should be.Table 1.SILSafety Integrity Level [1]PFDavgPFH1 10 2 to 10 1 10 6 to 10 52 10 3 to 10 2 10 7 to 10 63 10 4 to 10 3 10 8 to 10 74 10 5 to 10 4 10 9 to 10 8Table 2.STLmodelling issues for this quantification for bothdemand modes. Issues like demand rate, demandduration make the difference between low-demandand high-demand systems. The borderline betweentheses system modes is discussed and shown by thequantification of SIS reliability with Markovmodelling [10], [13]. But this borderline has notbeen considered for the evaluation of a SIS from anavailability perspective. STR and MTTFSpurious havebeen commonly calculated for a low-demandsystem.The main purpose of this article is to verify thedifference between low-demand and high-demandsystems for de-energized to trip application by usingthe block diagram and the Markov method for theSTR and MTTFSpurious calculation. This paper isorganized as follows: section 2 discusses thedefinition and causes as well as the characteristics ofspurious activation. In section 3 the differencesbetween low-demand and high-demand systems aredescribed. In the next section, section 4, theevaluation of spurious trip rate and MTTFSpurious ofthese system modes is studied for 1oo1 systems.The analysis is based on block diagram and Markovmodel. And finally, a discussion on the overall studyis provided in Section 5.2 Spurious TripA spurious trip is one cause of an unexpected plantshutdown initiated by a safety-instrumented system.Namely, if a safety loop component fails tofunction, the safety instrumented system isprompted to shut down that part of the plant’soperation. This is done because the failure of aparticular safety loop can prevent the safetyinstrumented system from functioning properly. Itdoes not guarantee plant safety. Therefore, spuriousactivation normally leads to lost production or lowavailability of the EUC [9].Industry data report that when a process unitexperiences a high number of spurious alarms, theoperators become ambivalent and are likely torespond slowly or not at all to a critical “real alarm”[7]. This means that spurious trip is not onlyexpensive, but also in most cases can be consideredas dangerous too. The standard IEC 61508 has norequirement related to spurious activations, whileIEC 61511 requires that a maximum STR isspecified, but the standard does not provide how therate should be estimated [1], [4] and [9].Spurious-Trip Level [5], [6]Probability of Fail SafePer YearSpurious-Trip CostX 10 ( x 1) to 10 x. 5 10 6 to 10 510M - 20M 4 10 5 to 10 45M - 10M 3 10 4 to 10 31M - 5M 2 10 3 to 10 2500k - 1M 1 10 2 to 10 1100k – 500k The SIS reliability is analyzed by differentmethods, like reliability block diagrams [2], Markovmodels [3], approximation formulas [8], etc. Mostof the references focus on low-demand systems anddo not take high-demand systems into considerationas well as the borderline between two SIS types.Some authors suggest to incorporate the rate ofdemands into the analysis by using the Markovmodel [11], [8], [12]. However, H. Jin, M.ALundteigen and M. Rausand [10] listed somecriterion in the quantification of the SIS reliabilityperformance (PFD and PFH) and presentedISBN: 978-1-61804-281-118
Mathematical Methods and Systems in Science and Engineering2.1 Spurious Trip RatePFS avg (T ) The spurious trip rate or also known as “false triprate” is defined in [3]: “the term spurious trip rate(STR) refers to the rate at which a nuisance orspurious trip might occur in the SIS”. The unit ofSTR is 1/h and describes how available acomponent or a system is. The availability is higherif the STR is smaller.To estimate the STR, the oil and gas industryoften use the formulas presented in [3] and [8].When comparing these formulas, it becomes evidentthat there is no unique interpretation of the conceptof spurious trip. While the PDS method [8] defines aspurious trip as “a spurious activation of a singleSIS element or of a SIF”, ANSI/ISA-TR84.00.022002 [3] refers to a spurious trip as a “non-intendedprocess shutdown”. As a result, the concept ofspurious trip is rather confusing and it is difficult tocompare the STR in different applications [9]. STRformulas of some conventional methods arepresented in the following table:Table 3. STR( )dt0(2)2.3 Mean Time To Failure Spurious1oo2 STR 2( S DD )STR 2 STUSTR (2 sp ) 1spoo2Mean Time to Failure Spurious is abbreviated asMTTFSpurious and is the estimated time betweenspurious failures of a component or a system [3]. Toestimate the MTTFSpurious value, ISA [3] introducesthree methods: simplified equation, fault treeanalysis and the Markov model. MTTFSpurious is inproportional to the availability. This means that acomponent or a system is more available if theMTTFSpurious value is higher. The following equationpresents the calculation of MTTFSpurious bysimplified equation: MTTFSpurious RSpurious(t ) dt(3)0 1spoo2 sp1 sp 2 SF3 Low demand and high demandsystemSTR STU ( S DD ) SFSTR C2oo3 STU ( S DD ) SF3STR sp 2oosp 2spoo3 ( sp1 sp 2 sp1 sp 3 sp 2 sp 3 ) / 32oo4 STR 12( )3 MTTR 2SDD1(1 RSpurious(t )) dtT 0RSpurious(t ) e1oo1 STR SSDDF2oo3 STR 6 S ( S DD ) MTTR(1)tMachleidt & Litz[16]STR sp S2oo2 STR 2 S ( S DD ) MTTR0with RSpurious(t) is calculated by the followingequation:PDS-Methode[8]STR STU ( S DD ) PFS (t ) dtTSpurious Trip Rate formulas of conventionalmethodANSI/ISA TR84.00.02-2002[3]T1TSTR C3oo4 STU ( S DD ) SF2.2 Probability of Spurious TripProbability of Failure Spurious (PFS) is theprobability of failure due to the spurious trip. Thesmaller this value, the more available the system is.For the evaluation and comparison of systems, theaverage PFSavg is calculated as followed:ISBN: 978-1-61804-281-119A SIS has to achieve or maintain a safe state for thesystem. The SIS is protecting with respect to aspecific process demand. Safe state can be defineddifferently for each system. In some cases, the safestate is to maintain before the demand occurs, whilein other cases, it means to stop the EUC. Typicallow-demand systems are emergency shutdownsystems (ESD), process shutdown systems (PSD) orairbag systems in automobiles. And the typicalhigh-demand systems are railway signal systems,safety-related electrical control systems formachinery. One of the important aspects of SIS withlow-demand is that the EUC remains in the safestate after the SIS has responded to a demand. Andfor a SIS with high-demand the EUC will bereturned to the normal operating state after thedemand [10]. For example, a railway signalingsystem is always ready to respond to a new requestwhen the previous train has left the rail section [10].Another difference between low-demand andhigh-demand systems is the functional testing. For alow-demand SIS, it is important to perform
Mathematical Methods and Systems in Science and Engineeringfunctional testing to detect DU-failure (dangerousundetected) but it is not always required for highdemand. Due to the fact that the demand rate is highit may not be possible to use functional testing todetect and repair DU-failures before the nextdemand. However, it is important to perform regulartesting for high-demand systems to prevent theoperating of SIS with reduced fault tolerance [10].The diagnostic testing is an automatic self-testthat is implemented in SIS to reveal failure withoutan interruption of the EUC and it is frequent. It cantake place every few seconds, minutes or hours.This test should be carefully considered for the bothsystems. This means, for low-demand systems, thereis usually enough time to repair and restore thefunction until the next demand appears. But forhigh-demand systems, the demand rate and thediagnostic test frequency may be the same [10].The demand rate varies from low to high orcontinuous and the duration of each demand mayvary from short to long period. So, the sameequation can usually not be applied to all systems[13]. With the Markov method several authors haveshown the best suited for analyzing safety systems.By using this method, it is possible to modeldifferent states with different failure modes of thecomponents, different points in time, periods andtest strategies. Therefore the authors in [10], [13]have used the Markov model to illustrate theborderline between low-demand and high-demandsystems in a better way. The whole calculations ofPFD and PFH are dependent on the demand rate andthe demand duration. Based on this result andavailability theory, a STR-, PFS- and MTTFSpuriouscalculation of the 1oo1 system will be presented inlow- and high-demand in this article.1oo1, SEventDemandwithout demandEUC demandSafe failureNormal stateSISStop & safe stateNormal stateSpurious TripT1tFig. 2. EUC and SIS of 1oo1 architecture [14]4.1 Block diagramA block diagram of a SIS with 1oo1-architecture isillustrated in Fig. 3 with three elements: input, logicand output: InputLogicOutput-Fig. 3. Block diagram of 1oo1-architectureA SIS with 1oo1-architecture fails spurious,when a safe failure in SIS or a false demand arises.Therefore, the spurious trip rate consists of not onlythe rate of safe failures S but also of the demandrate DE. Let the factor 0 1 be the ratio of falsedemand to total demand of SIS in a considered timeinterval, the calculation of spurious trip rate for1oo1 architecture is described in the following way:STR1oo1 S DE(4)PFDavg 1oo1 can be calculated by using simplifiedequation:4 Modeling of 1oo1 systemTIf the system fails because of a spurious trip failure,the system will be in de-energized state. This meansthat the system is not available anymore. Thecharacteristics of 1oo1-architecture will bepresented in Fig. 2. The EUC enters a safe statewithout demand, when a safe failure respectivelyspurious trip failure occurs in the SIS.PFS avg 1oo1 1PFS1oo1 (t ) dtT 0T 1(1 RSpurious 1oo1 (t )) dtT 0(5)for 1oo1-architecture the reliability is estimatedas follows:RSpurious 1oo1 (t ) 1 e STR1oo1t(6)ISBN: 978-1-61804-281-120
Mathematical Methods and Systems in Science and Engineeringdangerous state Z6 with the transition rate DE. Andwith the transition rate 0 1/ Test the system canreach the safe state.--State Z5 represents the dangerousundetected state. This state can change into state Z0at the end of its lifetime and subsequently replacedor repaired with a transition rate LT 1/ LT. If thesystem is at this state and a demand occurs, thesystem can reach the dangerous state Z6 with thetransition rate DE.--State Z6 is the hazardous state, where thesafety function fails and the system cannot reach thesafe state.--State Z7 presents the demand state, wherethe activation of the safety function is requested.Derived from equations (4), (5) and (6) theformula of PFDavg for 1oo1-architecture is describedas:T PFS avg 1oo1 (T ) 1(1 e STR1oo1 t ) dt T0STR1oo1 T2( S DE ) T 2 (7)MTTFSpurious 1oo1 can be calculated by: MTTFSpurious 1oo1 RSpurious 1oo1 (t ) dt0 e STR1oo1 tSys. SDZ2 SD DE 00 1 S DE SUSys. OKZ0(8)SafeZ1 R RN LTSys. SUZ3 DE DD4.2 Markov-ModellBy the use of simplified equations the effect ofdemand rate and demand duration cannot beshown precisely. For this reason Markov modelwill be used. It is better to model different stateswith different failure mode of the components.Fig. 4 presents 8 states of the Markov model ofa 1oo1-architecture. State Z0 represents thefailure free state and the system is operatingcorrectly. From this state, seven other states canbe reached: LTSys. DUZ5U D DD DEDemandZ7Sys.HazardousZ6 DEMarkov model of 1oo1-systemThe transition matrix is described in thefollowing way:--State Z1 presents the safe state (deenergized state) or spurious trip state. This state canbe left with a transition rate R 1/ Repair, with Repairwhich is the time the system requires for repair andstartup.--State Z2 has got a safe detected failure andwill reach the safe state with the transition rate DEwhen a demand occurs or with the transition rate 0 1/ Test, with Test which is the test time interval.--State Z3 has got a safe undetected failure.With the transition rate LT 1/ LT (with LT whichis the lifetime) the system is able to reach the failurefree state. And with the transition rate DE thesystem can reach the safe state.--State Z4 has got a dangerous detectedfailure. If a demand occurs, the system can reach theISBN: 978-1-61804-281-1 0 DE DUFig. 4. DESys. DDZ4 1 A0 R 0 P LT 0 LT RN DE0 SD SU DD DU01 R0000000 DE 0 1 A200 DE01 A30 0001 A4000 DE DE1 RN DD DU1 A500000000000000 DE 0 0 0 0 0 0 1 A7 with:A0 SD SU DD DU DE(9)A2 A4 DE 021(10)
Mathematical Methods and Systems in Science and EngineeringA3 A5 DE LTPFS1oo1 P1 P7(11)The steady-state equation corresponding to theMarkov model in Fig. 4 can be obtained:The spurious trip rate of 1oo1-system will begiven by the following equation: R P1 ( DE 0 ) P2 DE P3 0 P4PFS1oo1 1 RSpurious 1oo1 (t )( DE 0 ) P2 SD P0( DE LT ) P3 SU P0 1 e STR1oo1 tln(1 PFS1oo1 ) STR1oo1 t(12)( DE 0 ) P4 DD P0(22)(23)( DE LT ) P5 DU P0And the Mean Time To Failure Spurious iscalculated as follows: RN P6 DE ( P4 P5 ) ( DD DU ) P7( DD DU DE ) P7 DE P0P0 P1 P2 P3 P4 P5 P6 P7 1 MTTFSpurious 1oo1 RSpurious 1oo1 (t ) dtSolving this equation system we have:0 e STR1o o1 t SU SD A SD DE 1 DE 0 R R DE LT 0 1 DE RN R DU DE 1 LT DE RNP0 P1 P2 P3 (13) DD DE 0 DE 1 D RN DE D1A 8 tln(1 PFS1oo1 )11 MTTR 8S 0,5 SD P0 P SD 0 21 DE 0(16) SU P0 SU P0 31 DE LT(17)(18)P5 DU P0 DE LT(19) DD P0 DU P0 DE P0 D DE D DE 0 LT DE DE RN DE P0 DE P0 DD DU DE DE DDC 0,9 Test 24h 0 124 D 0,01 0,02T 8760h DE 10 8 10 6 10 4 10 2 DE 10 4 10 3 10 2 10 1 RN 10 6 0,01The following Figures (Fig. 5, Fig. 6 and Fig. 7)show the functions of PFS1oo1, STR1oo1 andMTTFSpurious 1oo1 in dependence on demand rate,which are deviated from Markov model in thiswork. At first, we study the effect of varyingdemand rate on the PFS1oo1 (Fig. 5). The PFS1oo1function will increase, when the demand rate ordemand duration increases. The PFS1oo1-value will(20)(21)The PFS1oo1 value is the sum of the probabilitiesP1 and P7:ISBN: 978-1-61804-281-11 Test B 5 10 6 DD P0 P DD 0 DE 41 DE 0P7 1STR1oo1MTTR 8h R (15)P4 P6 The following parameters will be used as anexample for an estimation of the parameters ofspurious trip failure:(14) DE 0 P2 DE P3 0 P4(24)022
Mathematical Methods and Systems in Science and Engineeringreach STL 4 when the demand rate is low and reachSTL 2 when demand rate is high.Fig. 7.Fig. 5.PFS with different demand rate of 1oo1-systemFig. 8 shows the function of STR1oo1 independence on diagnostic coverage factor DC withdifferent methods. The function of STR1oo1 bymethod of Machleidt & Litz [16] is like the functionof STR1oo1 by the reliability block diagram method,which is deviated from this work. STR1oo1 functionby ANSI/ISA TR84.00.02-2002 [3] is over anotherfunctions.Fig. 6 describes the function of STR1oo1 whichdepends on the demand rate. Like the PFS1oo1function, the STR1oo1 function will decrease whenthe demand rate or demand duration decrease. Witha low demand rate the function of STR1oo1 decreasesslightly, But with a high demand rate the differenceof STR1oo1 is shown explicitly.Fig. 8.Fig. 6.MTTFSpurious with different demand rate of 1oo1systemSTR with different demand rate of 1oo1-systemSTR with different demand rate of 1oo1-system5 ConclusionThe MTTFSpurious 1oo1 function is shown in theFig. 8. MTTFSpurious 1oo1 value increases when thedemand rate or demand duration decreases.ISBN: 978-1-61804-281-1This article has analyzed the relationship betweenSIS reliability and demand rate, as well as thedemand duration for 1oo1 system. Finally, theMarkov model provides better ways to analyze thisrelationship than the block diagram. Therefore, wecan say that it is not always possible to use acommon formula of reliability calculation for allsystems. PFS values are not equal to all systems:low demand and high demand. The same is true for23
Mathematical Methods and Systems in Science and EngineeringSTR and MTTFSpurious. This is based on the recentrevision of IEC 61508.References:[1] rogrammable electronic(E/E/PE) safety related systems, Part 1-7,Deutsche Fassung EN 61508: 2010.[2] H. Guo, X. Yang, A simple reliability blockdiagram method for safety integrityverification, Reliability Engineering andSystem Safety, Volume 92, Issue 9,Page(s):1267-1273, 2007.[3] ISA-TR84.00.02-2002, Part 1-5, 2002[4] IEC 61511, Functional safety: safetyinstrumented systems for the process industrysector, Part 1-3, CDV versions.[5] M. Houtermans, Safety Availability versusProzess Availability, Introduction SpuriousTrip Levels , White paper, RisknowlogyExpert in Risk, Reliability and Safety, May2006.[6] C.d. Sails, SIL certs can seriously impair plantsafety, Process Engineering, January /February, 2008[7] G. Gabor and D. Zmaranda, Techniques used todesign safe and reliable critical control orshutdown systems, Journal of ComputerScience and Control Systems, 01/2008.[8] SINTEF, Reliability prediction method forsafety instrumented systems, PDS MethodHandbook, 2010 Edition”, SINTEF 2010.[9] M. A. Lundteigen, M. Rausand, Spuriousactivation of safety instrumented systems in theoil and gas industry: Basic concepts andformulas, Reliability Engineering and SystemSafety 93 (2008), 1208-1217.[10] Hui Jin, Mary Ann Lundteigen, MarvinRausand, Reliability performance of safetyinstrumented systems: A common approach forboth low- and high-demand mode of operation,Reliability Engineering and Safety , Volume96, Issue 3, Page(s): 365-373, 2011.[11] J. Bukowski, Incorporating process demandinto models for assessment of safety systemperformance, Proceedings of RAMS’06symposium, USA, 2006.[12] F. Innal, Y. Dutuit, A. Rauzy, J. Signoret, Newinsight into the average probability of failureon demand and the probability of dangerousfailure per hour of safety instrumented systems,Journal of Risk and Reliability, Volume 224,Page(s): 75-86, July 2010.[13] Yiliu Liu, Marvin Rausand, Reliabilityassessment of safety instrumented systemssubject to different demand modes, Journal ofISBN: 978-1-61804-281-1Loss Prevention in the Process Industries 24,Page(s): 49-56, 2011.[14] P. Holub, J.Börcsök, Advanced PFHCalculation for Safety Integrity Systems withHighDiagnostic,ICAT2009XXIIInternational Symposium on Information,Communication and Automation Technologies,2009.[15] Dave Macdonald, Practical Hazops, Trips andAlarms, IDC Technologies, Netherlands, 2004.[16] Konstantin Machleidt, Lothar Litz, Anoptimization approach for safety instrumentedsystem design, Reliability and MaintainabilitySymposium (RAMS), Page(s) 1-6, 2011Proceeding – Annual.[17] prEN ISO 13849-1, DRAFT, Safety ofmachinery – Safety-related parts of controlsystems – Part 1. General principles for design(ISO/DIS 13849-1:2004), 200424
The analysis is based on block diagram and Markov model. And finally, a discussion on the overall study is provided in Section 5. 2 Spurious Trip . A spurious trip is one cause of an unexpected plant shutdown initiated by a safety-instrumented system. Namely, if a safety loop compo
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API RBI divides storage tank into two sections for risk assessment: (i) Bottom - consisting of the annular plates and floor island plates (ii) Shell Course/s - the tank shell strakes Basic design, operating and historical inspection data especially thickness and corrosion rate measurements are populated into import spread sheets, details of import spreadsheets are given below in section 2.4 .
