Design and Analysis of Improved Alarm Delay-Timers

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1 Preprits of the 9th Iteratioal Symposium o Advaced Cotrol of Chemical Processes The Iteratioal Federatio of Automatic Cotrol Jue 7-0, 05, Whistler, British Columbia, Caada TuM4.6 Desig ad Aalysis of Improved Alarm Delay-Timers Hao Zag*. Fa Yag*. Deia Huag* * Tsighua Natioal Laboratory for Iformatio Sciece ad Techology (TNList) Departmet of Automatio, Tsighua Uiversity, Beijig 00084, Chia ( s:{zaghao, yagfa, huag}@tsighua.edu.c) Abstract: Alarm systems play a importat role i idustry to otify operators of abormal or fault situatios. I real idustrial plats, however, a majority of uisace alarm sigals, icludig false alarms ad missed alarms, iterfere with operators' judgmet. The techique of delay-timers, a commo meas to reduce both false alarm rate (FAR) ad missed alarm rate (MAR), is widely performed, yet it suffers from a delayed respose. I this paper we propose a improved delay-timer auciatio ad clearace method to ehace the performace of covetioal delay-timers via bypassig some states i state switch uder some coditios. Also the improved delay-timer performace idices are calculated by usig Markov chais. Keywords: Alarm systems, Markov processes, Delay-timers, False alarm rate, Missed alarm rate, Average alarm delay.. INTRODUCTION I large moder idustrial plats, abormal situatios ot oly affect their efficiecy, but also brig a lot of safety issues, eve major accidets or disasters, leadig to casualties ad ecoomic losses. Accordig to the Abormal Situatio Maagemet (ASM) Cosortium statistics, for the petrochemical idustry, the amout of ecoomic losses i the US is about 0 to 0 billio $ due to abormal situatios, ad a major accidet occurs every three years i average. Alarm systems are a importat meas to detect ad auciate abormal productio situatios so that operators ca take actios immediately, ad play a irreplaceable role i esurig both safety ad efficiecy i idustrial plats. A large umber of safety icidets have fully demostrated the importace of alarm systems i safe operatio, such as the uclear power accidet occurred at Three Mile Islad i 979, which is the worst uclear accidet i the US history. Desig of alarm systems has attracted great attetio of academia ad idustry i recet years, ad becomes oe of the emergig research field i the process cotrol ad automatio commuity (Izadi et al., 009). A major problem of the curret embodimet of alarm systems is the lack of efficiet ad specific idustrial techiques to meet the stadard requiremets, icludig ISA 8. (Iteratioal Society of Automatio, 009) ad EEMUA 9 (Egieerig Equipmet ad Materials Users' Associatio 03). A lot of research has bee doe, such as alarm system moitorig (Ahmed et al., 03, Kodaveeti et al., 03, Wag et al., 04), alarm system performace evaluatio ad alarm systems desig ad optimizatio (Zag ad Li, 04). Alarm auciatio ad clearace is a importat task of alarm system optimal desig. At the preset stage, we focus o two aspects: uivariate methods ad multivariate methods (Yag et al., 0a, Kodaveeti et al., 0, Yag et al., 0b, Yag et al., 03, Zhu et al., 005), as show i Fig.. Alarm Auciatio ad Clearace Methods Uivariate Multivariable Setpoit Multiple Setpoits Multiple Order Statistics Kowledg e Model Itelliget Algorithm Dyamic Threshold Deadbad Delaytimers Filterig Correlatio aalysis Paret-child aalysis Multivariable Combiatio Multivariate Statistics Fig.. Auciatio ad clearace methods of alarm system desig. Uivariate methods have reported wide rage of applicatios, because they are easy to desig ad implemet, ad the alarm iformatio is clear for operator s decisio-makig. The multivariate methods ca cotrol the umber of alarms ad alarm delay, especially alarm floods (Schleburg et al., 03). Uivariate methods are based o the sigal of the process variable; it geerates a alarm status iformatio by process data of a sigle variable through discrete or cotiuous fuctio calculatio. Alarm setpoit compariso is the most Copyright 05 IFAC 670

2 Probability desity MAR IFAC ADCHEM 05 Jue 7-0, 05, Whistler, British Columbia, Caada commo desig approach it is the method with a sigle order (oly the curret state is cosidered) ad sigle alarm setpoit i essece, ad it idetifies alarm status by compariso of real-time data ad setpoits. Reasoable setpoit is the key factor for alarm system efficiecy ad ca be obtaied by statistics, models, kowledge, or some itelliget algorithms. I some special coditios, the setpoit correspodig alarm state is chaged, the dyamic threshold desig ca solve such problems effectively (Zhu et al., 04). The traditioal setpoit method is uable to meet operators requiremets for alarm systems with icreasig compleity of idustrial systems i recet years, some uivariate methods with multiple orders or multiple setpoit methods have obtaied more etesive research ad applicatios. Multiple order methods deote that a alarm setpoit is obtaied by a fuctio trasformatio of several measured values i the past; whilst multiple setpoit methods deote that the auciatio ad clearace of a alarm state correspods to multiple setpoits. Alarm deadbad is a twosetpoit method, where differet values are used as alarm auciatio ad alarm clearace setpoits (Ada et al., 03). Alarm delay-timers (Ada et al., 0, Kodaveeti et al., 0, Xu et al., 0) ad alarm filters have bee applied i idustrial processes; they are multiple order methods (Yue et al., 03). Alarm delay-timers are trasformatio of discrete fuctios, whilst filters use a cotiuous fuctio trasformatio. Multiple setpoits ad multiple order methods icrease the umber of desig parameters, ad thus ca better cotrol the performace idicators such as FAR, MAR ad AAD. Amog all these methods, delay-timers are commoly used for its simplicity ad efficiecy; however, their disadvatage is the evidet time delays.. DELAY-TIMERS Ay method to detect alarms must be fast ad accurate. A widely used method is compariso betwee the real-time process data ad alarm setpoit to determie alarm status. Fig. shows the auciatio mechaism of the false alarms ad missed alarms, where X T is the alarm setpoit. Whe the system is i ormal state, the value of the process variable may eceed X T, resultig i a false alarm; ad whe the system is i abormal state, the value of the process variable may retur to the regio withi X T, the a missed alarm is geerated. False alarms ad missed alarms are a pair of cotradictios. The receiver operatig characteristic (ROC) curve i Fig. 3 shows that it is difficult to cotrol the false alarm rate (FAR) ad missed alarm rate (MAR) withi acceptable levels (Kodaveeti et al., 0). 00% 0 0 FAR 00% Fig. 3. The ROC curve of the alarm detectio. A delay-timer auciatio ad clearace method was proposed for this situatio (Xu et al., 0).It classifies the alarm status ad o-alarm status ito ad m sub-states, respectively. Whe the process variable value eceeds X T times cosecutively after a period of time i the ormal state, the system state switches from o-alarm state NA to alarm state A evetually (via NA,, NA ); if the value goes withi the alarm limit at ay sample i this accumulatio procedure, the state of the alarm tag immediately returs to state NA. O the other had, whe the value is withi X T times cosecutively after a period of time i the abormal state, the state switches from alarm state A to o-alarm state NA evetually (via A,, A ), otherwise jumps back to the alarm state A. NA NA Normal data Abormal data A NA p() q() A X T Process variable value A m Fig.. Probability distributios of process data i ormal ad abormal status. Fig. 4. Markov chai diagram of -m-order alarm delaytimers. Copyright 05 IFAC 67

3 AAD Probability desity FAR IFAC ADCHEM 05 Jue 7-0, 05, Whistler, British Columbia, Caada The ROC curves of alarm delay-timers (i Figs. 5 ad 6) show that the MAR ad FAR sigificatly reduce whe the delay-timer order icreases, yet the average alarm delay (AAD) is also icreased dramatically (Xu et al., 0). The essece of delay-timers is to icrease the accuracy by sacrificig o the detectio delay. 0% NH q q( ) (5) T AH q3 q( ) (6) NH P p S (7) N P p S q S (8) N A P p S q S (9) 3 3 N A = =3 =4 0 0 MAR 0% Fig. 5. The ROC curves of alarm delay-timers. P q S (0) 4 3 A where p() ad q() are probability desity fuctios of alarm tag i ormal ad abormal situatios, respectively, with arbitrary distributios with differet meas. where NL NH deote low ad high limits of ormal distributio, ad AL 0% ad AH deote low ad high limits of abormal distributio. S N ad S A are the statistical probabilities of process operatig i ormal ad abormal states, respectively, ad S N +S A =. Normal data Abormal data p() q() =4 =3 = X NL p X AL p q q 3 q p 3 X X T NH Process variable value X AH Setpoit Fig. 6. AADs of alarm delay-timers with differet orders. 3. IMPROVED DELAY-TIMERS For a improved alarm delay-timer, Fig. 7 shows the probabilities ad probability desity fuctios of process values i ormal ad abormal situatios. Equatios (-0) give the results of these probabilities. AL p p( ) () NL T p p( ) () AL NH p3 p( ) (3) T T q q( ) (4) AL Fig. 7. Probability distributios of process data i ormal ad abormal status,. Through aalysis of the alarm delay-timer topology, we otice oe cause of the sigificat icrease of AAD. Whe the process variable eceeds X NH suddely, the process has bee i a abormal state, ad thus the alarm tag should immediately switch to the alarm state; however, the traditioal alarm delay-timer has to wait for state trasitios through all the sub-states step by step ( steps). I the improved alarm delay-timer, the trasitio from o-alarm state to alarm state i this case is immediate (oe step). For the improved alarm delay-timer, we aalyse the probability space o the basis of the traditioal alarm delay-timer, ad add two direct state trasitios betwee the alarm state ad the o-alarm state. 3. Improved Alarm O-Delay-Timers Fig. 8 shows a improved o-delay-timer. The differece is additioal jumps from each o-alarm sub-state to the alarm state compared with the traditioal alarm o-delay-timer. Copyright 05 IFAC 67

4 IFAC ADCHEM 05 Jue 7-0, 05, Whistler, British Columbia, Caada P+ P NA NA A P3 + P4 3. Improved Alarm Off-Delay-Timers Fig. 9 shows a improved off-delay-timer Markov chai. The differece is additioal jumps from each alarm sub-state to the o-alarm state compared to the traditioal alarm offdelay-timer. NA 3 + A A NA P3 + + NA A 3 Fig. 8. Markov chai diagram of the -order improved alarm o-delay-timers. + ( ) ( ) For the Markov chai i Fig. 8, the matri Q R of oe step trasitio probability is P P P P4 P P 0 P P 4 P P 0 0 P3 0 0 P 4 P P P3 0 P4 Q P P P3 P4 P P P3 P 4 P P3 P4 () Here, the elemet locatig at the ith row ad the jth colum of the matri Q is the oe step trasitio probability of the state from i to j. Whe the process is i ormal state, we defie S S A N 0 From (-0) ad (), we have 3 () FAR p (3) Whe the process is i abormal state, we defie S S A N 0 (4) From (-0) ad (), the solvig process details ca refer to refereces (Xu. et al., 0), we have q( q ) MAR q 3 3 ( qq + q3) (5) q q +( q q ) q q ADD h( ) (6) A + Fig. 9. Markov chai diagram of the -order improved alarm off-delay-timers. ( ) ( ) For the Markov chai i Fig. 9, the matri Q R of the oe step trasitio probability is P3 P4 P P P3 P4 0 P P P3 P4 0 0 P 0 0 P P3 P P 0 P Q P3 P P P P3 P P P P P P (7) Accordig to the characteristics of the Markov chai, we obtai the performace idicators as follows: p3( p ) FAR p ADD (8) MAR q (9) q h q q Improved Alarm Delay-Timers (0) Fig. 0 is the Markov chai of a -order improved delaytimer. Copyright 05 IFAC 673

5 IFAC ADCHEM 05 Jue 7-0, 05, Whistler, British Columbia, Caada A A NA A NAA 4. SIMULATION STUDY Apply the followig mechaism to produce a sigle-variable data series ivolvig two states. Assume that it follows the N(,) ormal distributio i the ormal coditio, ad the N(3,) ormal distributio i the abormal coditio. Geerate data, icludig ormal data poits ad abormal data poits. ( t) ~ N(,), 00( ) t 50( ) ( t) ~ N(3,), 50( ) t 00 t, N, 000 (5) NA Table. Defiitio of false ad missed alarms Alarm Situatio No alarm(0) Alarm() Normal(0) correct false alarm NA + Abormal() missed alarm correct Fig. 0. Markov chai diagram of the -order improved alarm delay-timers. For the Markov chai i Fig. 0, the matri Q R step trasitio probability is P P P P P P 0 P3 0 0 P P3 0 P P3 P P P P3 P Q P P3 P4 P P P3 P4 0 P 0 0 P P3 P4 0 0 P 0 P P3 P P P P3 P of oe () Accordig to the characteristics of the Markov chai, we obtai the performace idicators as follows: FAR MAR i p3 p i0 i i i p( 3 - p3 p) + p3 p i0 i0 i0 i q q i0 i i i q( -q q) q q i0 i0 i0 3 3 ( qq + q3) () (3) q q +( q q ) q q ADD h( ) (4) Geerate alarm data via a simple setpoit compariso, a 3rdorder covetioal delay-timer, ad a improved delay-timer, ad the calculate MAR, FAR, ad AAD, as show i Table. Table. Performace compariso method MAR FAR AAD Threshold (X T =) rd-order delay-timer (X T =) 3rd-order improved delay-timer(x T =, X NH =4.5 X AL =-0.5) From Table, we see that the improved alarm delay-timer has better performace i all idicators compared to the covetioal alarm delay-timer. It ca make the alarms more accurate ad timely. 5. CONCLUDING REMARKS The proposed improved alarm delay-timers are essetially a uivariate alarm cofiguratio method with multiple orders ad setpoits. The problem of AAD ecessive growth with order icreases is overcome by addig a alarm auciatio setpoit ad a alarm clearace setpoit o the basis of covetioal alarm delay-timers. Improved alarm delaytimers have more parameters to be desiged, ad thus how to improve the alarm system operatig efficiecy by desigig each parameter requires i-depth study. Copyright 05 IFAC 674

6 IFAC ADCHEM 05 Jue 7-0, 05, Whistler, British Columbia, Caada ACKNOWLEDGEMENTS The authors would appreciate the fiacial support from the Natioal Natural Sciece Foudatio of Chia (643300) ad the Natioal High-tech Research ad Developmet Program of Chia (03AA04070). REFERENCES Adhitya, A., Cheg, S.F., Lee, Z., et al. (04). Quatifyig the effectiveess of a alarm maagemet system through huma factors studies. Computers & Chemical Egieerig, 67, -. Ada, N.A., Cheg, Y., Izadi, I., et al. (03). Study of geeralized delay-timers i alarm cofiguratio. Joural of Process Cotrol, 3(3), Ada, N.A., Izadi, I., ad Che, T. (0). O epected detectio delays for alarm systems with deadbads ad delay-timers. Joural of Process Cotrol, (9), Ahmed, K., Izadi, I., Che, T., et al. (03). Similarity aalysis of idustrial alarm flood data. IEEE Trasactios o Automatio Sciece ad Egieerig, 0(), Cheg, Y., Izadi, I., ad Che, T. (03). Optimal alarm sigal processig: filter desig ad performace aalysis. IEEE Trasactios o Automatio Sciece ad Egieerig, 0(), Egieerig Equipmet ad Materials Users' Associatio (03). Alarm Systems - A Guide to Desig, Maagemet ad Procuremet (EEMUA 9), 3rd Editio. Iteratioal Society of Automatio (009). Maagemet of Alarm Systems for the Process Idustries (ANSI/ISA ) Izadi, I., Shah, S.L., Shook, D.S., et al. (009), A framework for optimal desig of alarm systems. I Proceedigs of the 7th IFAC Symposium o Fault Detectio, Supervisio ad Safety of Techical Processes, Kodaveeti, S. R., Izadi, I., Shah, S.L., et al. (0). O the use of delay timers ad latches for efficiet alarm desig. I Proceedigs of the 9th Mediterraea Coferece o Cotrol & Automatio (MED), 0, Kodaveeti, S.R., Izadi, I., Shah, S.L., et al. (0). Graphical tools for routie assessmet of idustrial alarm systems. Computers & Chemical Egieerig, 46, Kodaveeti, S.R., Izadi, I., Shah, S.L., et al. (03). Quatificatio of alarm chatter based o ru legth distributios. Chemical Egieerig Research ad Desig, 9(), Naghoosi, E., Izadi, I., ad Che, T. (0). Estimatio of alarm chatterig. Joural of Process Cotrol, (9), Pariyai, A., Seider, W.D., Oktem, U.G., et al. (00). Icidets ivestigatio ad dyamic aalysis of large alarm databases i chemical plats: A Fluidizedcatalytic-crackig uit case study. Idustrial & Egieerig Chemistry Research, 49(7), Schleburg, M., Christiase, L., Thorhill, N.F., et al. (03). A combied aalysis of plat coectivity ad alarm logs to reduce the umber of alerts i a automatio system. Joural of Process Cotrol, 3(6), Wag, J. ad Che, T. (04). A olie method to remove chatterig ad repeatig alarms based o alarm duratios ad itervals. Computers & Chemical Egieerig, 67, Xu J., Wag J., Izadi, I., et al. (0). Performace assessmet ad desig for uivariate alarm systems based o FAR, MAR, ad AAD. IEEE Trasactios o Automatio Sciece ad Egieerig, 9(), Yag, F., Shah, S.L., Xiao, D., et al. (0a). Improved correlatio aalysis ad visualizatio of idustrial alarm data. ISA Trasactios, 5(4), Yag, F., Shah, S.L., ad Xiao, D. (0b). Siged directed graph based modellig ad its validatio from process kowledge ad process data. Iteratioal Joural of Applied Mathematics ad Computer Sciece, (), Yag, Z., Wag, J., ad Che, T. (03). Detectio of correlated alarms based o similarity coefficiets of biary data. IEEE Trasactios o Automatio Sciece ad Egieerig, 0(4), Zag, H. ad Li, H. (04). Optimizatio of process alarm thresholds: A multidimesioal kerel desity estimatio approach. Process Safety Progress, 33(3), Zhu, J., Shu, Y., Zhao, J., et al. (04). A dyamic alarm maagemet strategy for chemical process trasitios. Joural of Loss Prevetio i the Process Idustries, 30, Zhu, Q. ad Geg, Z. (005). A ew fuzzy clusterig-rakig algorithm ad its applicatio i process alarm maagemet. Chiese Joural of Chemical Egieerig, 3(4), Copyright 05 IFAC 675