SAFETY OPTIMIZATION OF A FERRY TECHNICAL SYSTEM IN VARIABLE OPERATION CONDITIONS ABSTRACT

Transcription

1 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS Krzysztof Kolowrocki Joanna Soszynska-Budny Gdynia aritime University Gdynia Poland katmatkk@am.gdynia.l joannas@am.gdynia.l ABSTRACT The general model of the safety of comlex technical systems in variale oeration conditions linking a semi-arkov modeling of the system oeration rocess with a multi-state aroach to system safety analysis and linear rogramming are alied in maritime transort to safety and risk otimization of a ferry technical system. INTRODUCTION ost real technical systems are very comlex and it is difficult to analyze and otimize their safety. Large numers of comonents and susystems and their oerating comlexity cause that the evaluation and otimization of their safety is comlicated. The comlexity of the systems oeration rocesses and their influence on changing in time the systems structures and their comonents safety characteristics is often very difficult to fix and to analyze. A convenient tool for solving this rolem is a semi-markov (Graski 00) modeling of the system oeration rocesses linked with a multi-state aroach to the system safety analysis (Kolowrocki Soszynska 00 Kolowrocki Soszynska 009) and a linear rogramming for the system safety otimization (Kolowrocki Soszynska 00). This aroach to system safety investigation is ased on the multi-state system reliaility analysis considered for instance in (Aven 9 Kolowrocki 00) and on semi-markov oeration rocesses modeling discussed for instance in (Soszynska 00 Soszynska 00). An alication of the roosed aroach to safety analysis and otimization of maritime ferry technical system is resented in this aer. THE FERRY TECHNICAL SYSTE SAFETY AND RISK The considered maritime ferry is a assenger Ro-Ro shi oerating in Baltic Sea etween Gdynia and Karlskrona orts on regular everyday line. We assume that the ferry is comosed of a numer of main susystems having an essential influence on its safety. These susystems are illustrated in Figure. On the scheme of the ferry resented in Figure there are distinguished its following susystems: S - a navigational susystem S - a roulsion and controlling susystem S - a loading and unloading susystem S - a hull susystem S - an anchoring and mooring susystem S - a rotection and rescue susystem S - a social susystem. 9

2 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch In our further analysis of the ferry safety we omit the rotection and rescue susystem S and the social susystem S and we consider its strictly technical susystems S S S S and S only further called the ferry technical system (Kolowrocki Soszynska 009). S S S S S S S S S S S S S S Figure. Susystems having an essential influence on the ferry technical system safety We assume that the ferry technical system safety structure and the susystems and comonents safety deend on its changing in time oeration states (Kolowrocki Soszynska 00). Taking into account the exerts oinion on the oeration rocess of the considered ferry we distinguish the following as its eighteen oeration states: an oeration state z loading at Gdynia Por an oeration state z unmooring oerations at Gdynia Por an oeration state z leaving Gdynia Port and navigation to GD uoy an oeration state z navigation at restricted waters from GD uoy to the end of Traffic Searation Scheme an oeration state z navigation at oen waters from the end of Traffic Searation Scheme to Angoring uoy an oeration state z navigation at restricted waters from Angoring uoy to Verko Berth at Karlskrona an oeration state z mooring oerations at Karlskrona Por an oeration state z unloading at Karlskrona Por an oeration state z9 loading at Karlskrona Por an oeration state z0 unmooring oerations at Karlskrona Por an oeration state z ferry turning at Karlskrona Por an oeration state z leaving Karlskrona Port and navigation at restricted waters to Angoring uoy an oeration state z navigation at oen waters from Angoring uoy to the entering Traffic Searation Scheme an oeration state z navigation at restricted waters from the entering Traffic Searation Scheme to GD uoy an oeration state z navigation from GD uoy to turning area an oeration state z ferry turning at Gdynia Por an oeration state z mooring oerations at Gdynia Por an oeration state unloading at Gdynia Port. z 9

3 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch Additionally as in (Kolowrocki Soszynska ) we assume that susystems S... of the ferry technical system are comosed of five-state comonents and their safety states are 0 and. Consequently the comonents conditional multi-state safety function is the vector (Kolowrocki Soszynska 009) [ s ( ) ( )] ( ) ( ) ( ) = [ [ s ( ) ( ) ( )] [ s ( ) ( ) ( )] [ s ( ) ( ) ( )] [ s ( )] ]... with the exonential co-ordinates [ ( ) ( ) s ( ) ( ) ( )] ex[ [ ()] t] ( ) ( ) [ s ( ) ( ) ( )] ex[ [ ] t] [ ( ) ( ) [ s ( ) ( ) ( )] ex[ [ ()] t]... ( ) ( ) s ( ) ( ) ( )] ex[ [ ()] t] Further assuming that the ferry technical system is in the safety state suset { u u...} u 0 if all its susystems are in this suset o safety states we conclude that the ferry is five-state series system (Kolowrocki Soszynska 009) of susystems S S S S S and S. The ferry oeration rocess is very regular in the sense that the oeration state changes are from the articular state z... to the neighoring state z... and from z to z only. Therefore the roailities of transitions etween the oeration states are given y (Kolowrocki Soszynska 009) [ l ] On the asis of statistical data coming from exerts the matrix of the density functions of the ferry technical system oeration rocess conditional sojourn times l l... defined in (Kolowrocki Soszynska 009) can e evaluated. Nex the mean values l E[ l ] l... l of the system oeration rocess conditional sojourn times l in articular oeration states can e determined and they are: Hence according to (Kolowrocki Soszynska 00) the mean values of the unconditional sojourn times in the oeration states are:

4 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch Since from the system of equations given in (Kolowrocki Soszynska ) taking here the form we get 0.0 for.... [ ] x [ ] v x [ ] l x Thus according to the results contained in (Kolowrocki Soszynska ) the long term roortion of transients at the oerational states z can e aroximated y () Under the assumtion that the changes of the ferry oeration states have an influence on the S... comonents safety and on the ferry technical system safety structures susystems as well on the asis of exert oinions and statistical data given in (Soszynska et al. 009) the ferry technical system safety structures and their comonents safety functions and the ferry technical system conditional safety functions at different oeration states can e determined (Kolowrocki Soszynska 00). Namely in the case when the system oeration time is large enough the unconditional fife-state safety function of the ferry technical system is given y the vector s ( ) = [ s () s ( ) s () s ( ) ] t 0 where after considering the values of... given y () its co-ordinates are u) 0.0 [ () 0.00 [ 0.0 [ () 0.0 [ () 0.[ () 0.0 [ () 0.00 [ () 0.0 [ () 0.0 [ (9) 0.00 [ (0) 0.00[ () 0.0 [ () 0. [ () 0.0 [ () 0.0 [ () 0.00[ () 99

5 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch () () 0.00[ 0. 0 [ () () for t 0 u where [ u )]... are the system conditional safety functions at articular oeration states z... determinedd in (Kolowrocki Soszynska 00). The safety function of the ferry f technical system is resentedd in Figure Figure. Grah of the safety function [ )] ] coordinate es Fromm () the mean values of the ferryy technical system unconditional state susets {} {} {} {} resectively are: lifetimes in the safety (). 0 years years () (). years (). 9 years. From the aove (Kolowrocki Soszynska ) the mean values of the system lifetimes in the articular safety states are: ( ) () ( ) 0.9 ( ) ( ) () 0. years If we assume that the critical safety state is r = then the system s risk Soszynska ) is given y where ( ) ( ) () 0. () (). 9 years. r(t) = ) ) is given y () for u. () function (Kolowrocki () 00

6 (Vol.) 0 arch is Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS The moment when the system risk function exceeds a ermitted level for instance = 0.0 = r ()) 0. year. () Figure. Grah of the ferry technical system risk function OPTIIZATION OF THE FERRY TECHNICAL SYSTE OPERATION PROCESS Considering thee equation ()( it is natural to assume that the system oeration rocess has a significant influence on the system safety. This influence is also clearly exressed in the equation () for the mean values of the system unconditional lifetimes in the safety state susets. The ojective function defined in (Kolowrocki Soszynska 00) in this case as the system critical state is r takes the form r (t) Since the lower and uer ounds of the unknown transient roailities... coming from exerts are resectively: ()

7 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch then we assume for the ojective function defined y () the following ounds constraints (9) Now in order to find the otimal values of the transient roailities... that maximize the ojective function () w arrange the system conditional lifetimes mean values... in non-increasing order 9 and we sustitute 0 x 0.0 x 0.0 x 0.0 x x 0.0 x 0.0 x 0.0 x 0. x 0.0 x 0. x 0.0 x x 0.00 x 0.0 x 0.00 x 0.00 x 0.00 x (0) 0 Afterwards we maximize with resect to x i i... the linear form () that after considering the sustitution (0) takes the form = x. 9 x. 9 x. x. x. 90 x. 90 0

8 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch x.0 x. 0 x9. 0 x0. 0 x. 0 x. x. x. x. x. x. x. () with the following ound constraints 0.00 x x x 0.00 x x x x x x x x x x x x x x x 0.00 x i i. Further according to the rocedure given in (Kolowrocki Soszynska 00) we calculate x x i i 0.0 y x = = 0.9 () and we find x 0 0 x x 0 x 0 x 0.00 x 0.0 x x 0. 0 x 0.00 x 0.0 x x 0.0 x 0.00 x 0. x x 0. x 0.00 x 0. x x 0. x 0.0 x 0. x x 0. x 0.09 x 0.99 x x 0.9 x 0.0 x 0. x x 0. 0

9 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch x 0. x.0 x x 0.. () From the aove as according to () after considering the inequality x I x I 0.9 () it follows that the largest value I {0...} such that this inequality holds is I. Therefore we fix the otimal solution that maximize linear function () according to the rule given in (Kolowrocki Soszynska 00). Namely we get x x 0. 0 x x 0. 0 x x 0. 0 x x 0. 0 x x x 0. 0 x x 0. 0 x x y x x x x 9 x x 0 x0 0. x x 0.0 x x x x x x 0.0 x x 0.00 x x x x 0.00 x x Finally after making the sustitution inverse to (0) we get the otimal transient roailities x x 0. 0 x 0. 0 x 0.0 x 0. 0 x 0.0 x 0.0 x 0.9 x x 0 0. x 0.0 x x 0.00 x 0.0 x 0.00 x x 0.00 x 0.00 () that maximize the system mean lifetime in the safety state suset { } exressed y the linear form () giving its otimal value () 0

10 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch THE FERRY TECHNICAL SYSTE OPTIAL SAFETY CHARACTERISTICS Further using the otimal transient roailities () we otain the otimal solution for the mean value of the system unconditional lifetime in the safety state suset { } { } and { } ().9 ( ).9 ( ). () and the otimal solutions for the mean values of the system unconditional lifetimes in the articular safety states and are as follows ( ) 0. ( ) 0. ( ) 0. ( ).. () oreover according to the corresonding otimal function of the system is of the form of the vector unconditional multistate safety s ( ) = [ s () s ) s ()] t 0 (9) with the coordinates given y s () 0. 0 [ () 0.00[ () 0.0 [ 0. 0 [ ()( 0.9 [ 0.0 [ () (9) () () 0.0[ [ ] 0. 0 [ (0) () 0.00[ [ ) 0. 0 [ () ()) 0. [ () () () 0.0 [ t 0. 0 [ u) ] [ () 0.00 [ () 0.0[ u )] () (0) () for t 0 u where [ u )]... are the system conditional safety functions at articular oeration states z... given in (Kolowrocki Soszynska a 00). The safety function of the ferry f technical system is resentedd in Figure. Figure. Grah of the otimal safety function [s ( )] coordinates 0

11 (Vol.) 0 arch Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS If the critical safety state is r = then the system risk function (Kolowrocki Soszynska 00) is given y where ) is given y (0) for Hence the moment when instance = 0.0 is r (t) s for t 0 u. the otimal system risk function exceeds = r - ( ) 0. year. () a ermitted level for () Figure. The grah of the ferryy technical system otimal risk function r (t) The comarison of the ferry technical system safety characteristics after its oeration rocesss otimization given y ()-()) with the corresonding characteristics efore this otimization determinedd y -() justifies the sensiilityy of this action. CONCLUSION The joint model of the safety of comlex technical systemss in varialee oeration conditions linking a semi-arkov modeling of the system oeration rocesses with a multi-state aroach to system safety analysis was alied to the maritime ferry technical systemm safety characteristicss evaluation. Nex the final results otained from this joint modell and a linear rogramming weree used to erform this comlex technical system safety otimization. These tools ractical alication to safety and risk evaluation and otimization of a technical systemm of a ferryy oerating in variale oeration conditions at the Baltic Sea waters and the results achieved are interesting for safety ractitioners from maritime transort industry and from other industrial sectors as well. Acknowledgements The aer descries art of the workk in the Poland-Singaore Joint Research Project titled Safety and Reliaility of Comlex Industrial Systems and Processes suorted y grants from the Poland s inistry of Science and Higher Education (SHE grant No. /N-Singaore/00/0) and the Agency for Science Technology and Research of Singaore (A*STAR R SERC grant No ). 0

12 Krzysztof Kolowrocki Joanna Soszynska Budny SAFETY OPTIIZATION OF A FERRY TECHNICAL SYSTE IN VARIABLE OPERATION CONDITIONS (Vol.) 0 arch REFERENCES Aven T. 9. Reliaility evaluation of multi-state systems with multi-state comonents. IEEE Transactions on reliaility -9. Graski F. 00. Semi-arkov odels of Systems Reliaility and Oerations. Warsaw: Systems Research Institute Polish Academy of Science. Kolowrocki K. 00. Reliaility of Large Systems. Elsevier Amsterdam - Boston - Heidelerg - London - New York - Oxford - Paris - San Diego - San Francisco - Singaore - Sydney - Tokyo. Kolowrocki K. Soszyńska J. 00. Reliaility and availaility of comlex systems. Quality and Reliaility Engineering International Vol. Issue J. Wiley & Sons Ltd Kolowrocki K. Soszynska J. 00. A general model of shi technical systems safety. Proc. International Conference on Industrial Engineering and Engineering anagemen IEE 00 Singaore -0. Kolowrocki K. Soszynska J Safety and risk evaluation of Stena Baltica ferry in Variale oeration conditions. Electronic Journal of Reliaility & Risk Analysis: Theory & Alications Vol. No. -0. Kolowrocki K. Soszynska J. 00. Safety and risk otimization of a ferry technical system. Summer Safety and Reliaility Seminars SSARS 00 Journal of Polish Safety and Reliaility Association Vol. 9-. Lisnianski A. Levitin G. 00. ulti-state System Reliaility. Assessmen Otimisation and Alications. World Scientific Pulishing Co. New Jersey London Singaore Hong Kong. Soszynska J. 00. Reliaility evaluation of a ort oil transortation system in variale oeration conditions. International Journal of Pressure Vessels and Piing Vol. Issue 0-0. Soszynska J. 00. Systems reliaility analysis in variale oeration conditions. International Journal of Reliaility Quality and Safety Engineering. System Reliaility and Safety Vol. No -9. Soszyńska J. Kołowrocki K. Kamiński P. Judziński. & ilczek B Data mining for identification and rediction of safety and reliaility characteristics of comlex industrial systems and rocesses WP. Safety and risk analysis and evaluation of a Stena Baltica ferry in variale oeration conditions. WP - Su-Task.. English Poland-Singaore Joint Project. SHE Decision No. /N-Singaore/00/0. 0