Economic aspects of component importance analysis for complex marine systems

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1 Scentfc Journals of the Martme Unversty of Szczecn Zeszyty Naukowe Akadem Morskej w Szczecne 2017, 51 (123), ISSN (Prnted) Receved: ISSN (Onlne) Accepted: DOI: /231 Publshed: Economc aspects of component mportance analyss for complex marne systems Leszek hybowsk, Katarzyna Gawdzńska Martme Unversty of Szczecn, Faculty of Marne Engneerng 1-2 Wały hrobrego St., Szczecn, Poland emal: {l.chybowsk, k.gawdznska}@am.szczecn.pl correspondng author Key words: mportance analyss, complex system, senstvty analyss, marne system, economc aspects, computer smulaton Abstract The paper presents the applcaton of cost-based, component-mportance measures for complex techncal systems. A stern tube sealng system nstalled on a sea vessel was used as an example of a complex techncal system. Selected statstcs of a shp s operaton losses were calculated. Selected, known-mportance measures were presented and the authors own approach to cost-based, component-mportance analyss was shown. The followng measures were dscussed: the operaton-nterrupton cost ndex, the mantenance potental, the smulaton-based mantenance ndex, and mantenance and operatonal costs. A descrpton of factors nfluencng the mportance of the techncal system components was provded. Introducton Whle analysng the actvty of complex techncal systems (TS), t s often necessary to determne not only whch components requre an upgrade of relablty to mprove overall system stablty, but also whch components, f damaged, trgger the most sgnfcant losses n terms of recovery costs and downtme, the latter beng hghly mportant for an operator. The analyss of component mportance n a relablty structure may be consdered n economc terms. Several such economc measures have been descrbed n the lterature (Hlber & Bertlng, 2004). These measures dffer from ndcators presented n (hybowsk, 2014; hybowsk & Gawdzńska, 2016) by beng more mult-factoral. One of the prmary dfferences s that nterruptons n the operaton of the system may ncur contractual penaltes whch are not necessarly lnearly dependent on the duraton of the nterrupton (Hlber, 2005; Paska, 2013). Fnancal losses are dfferent n terms of ther assumptons and ponts of reference; for example, losses due to electrcal power outage wll be dfferent for gven end recpents, and dfferent for the power-plant. It s also necessary to specfy the components of total operatonal nterrupton costs, whch comprse losses ncurred by the operator due to nterrupton of the system s operaton, as well as costs of carryng out repars (purchase and transport of replacement parts, worker costs, etc.) (Woropay, 1983; Karanta, 2011; Kuo & Zhu, 2012; hybowsk, 2014; hybowsk & Gawdzńska, 2016). The operaton nterrupton cost ndex I H uses the total costs assocated wth a dsabled and non-functonal system as a measure of relablty nstead of usng the probablty of falure. These costs are, however, a result of the value of the system component relablty functon. Ths ndex s based on the falure ntensty of components, nstead of the relablty of components, and s defned as follows (Hlber, 2005): H s I [EUR/falure] (1) Zeszyty Naukowe Akadem Morskej w Szczecne 51 (123) 59

2 Leszek hybowsk, Katarzyna Gawdzńska where: s s the total yearly cost of system operaton nterrupton [EUR/year]; and λ s the falure frequency of the -th component of the system [falures/year]. The nterrupton cost ndex of the system s -th component s dependent on the falure frequency of the system s other components, restoraton tme of the -th component, and locaton of the component wthn the system s relablty structure (hybowsk & Gawdzńska, 2016; Derlukewcz, Ptak & Kozołek, 2016; hybowsk & Żółkewsk, 2016). The mantenance potental I MP s the measure whch descrbes the total predcted annual system repar cost reducton, when the -th component s replaced wth an deal one (not subject to falure). Ths ndex descrbes the total predcted annual nterrupton cost caused by falure of the -th component. The mantenance potental s defned as follows (Hlber, 2005): I MP H I [EUR/year] (2) The smulaton-based mantenance ndex s a measure whch uses the ndcators n Equatons (1) and (2). Ths ndex specfes the total cost of system operaton nterrupton caused by the down state of the -th component as determned through stochastc smulaton, and s defned mathematcally as follows (Hlber, 2005): M ( a) I [EUR/year] (3) where: (a) s the total accumulated cost of the system s operaton nterruptons durng tme τ due to falure of the -th component [EUR]; and τ s the smulaton tme (tme horzon) [years]. The I M ndex makes t possble to determne the components whose falure wll comprse the largest share of the total costs assocated wth an nterrupton of the system s operaton. The nterrupton cost ndex and mantenance potental are analytcally determned measures, whle I M s determned by means of a stochastc smulaton. Due to the contrbuton of varous types of costs ncurred by the operator and/or user of the system, n practce t s more useful to dvde the total costs nto fractons, and conduct the analyss n phases correspondng to the parts that are sgnfcant from the perspectve of the overall system operaton assessment (Bajkowsk & Zalewsk, 2014; Zalewsk & Szmdt, 2014). System operaton cost measures When conductng an mportant economc evaluaton, t s extremely mportant to descrbe the boundary condtons and assumptons due to the fact that many factors contrbute to the fnal result. The total costs assocated wth a system s relablty, called relablty costs accordng to (hybowsk, 2014), are dvded nto the followng components: P, the system purchase and nstallaton costs assocated wth producton costs, [EUR]; and SK, the costs assocated wth nterruptons of operaton (Ptak & Konarzewsk, 2015) due to correctve and preventve mantenance [EUR]. The sum of costs s also mportant n the evaluaton of the nfluence of component falures on the system s operaton, as shown n the followng equaton: [EUR] (4) SE SK SP where: SE s the operatonal loss assocated wth operaton nterruptons [EUR]; SK s the cost of correctve mantenance (repars, renovatons) [EUR]; SP s the cost of preventve mantenance (planned preventve works) [EUR]; and s operatng work costs [EUR]. When analysng the nfluence of a gven component s falure, t should be noted that operatonal losses assocated wth dsablng the system because of the falure of the -th component durng operatng tme t can be dependent on the crtcal operaton nterrupton tme coeffcent: SE DTI SE I d t [EUR] (5) SEH d DTI where: I s the crtcal operaton nterrupton tme coeffcent of the -th component [%]; d SEH s the hourly cost of system operaton nterrupton [EUR/h]; and t d s the tme of system operaton nterrupton [h]. The lost profts assocated wth total operatonal losses for a system comprsed of n components can be expressed by the followng formula: n 1 SE SE [EUR] (6) The mean total costs assocated wth carryng out restoraton of the -th component for falures causng nterrupton of the system s operaton may be determned by the crtcal falure number ndex, a parameter whch s descrbed by the followng formula: FI SK I dskm f t [EUR] (7) where: I FI s the crtcal falure number ndex of the -th component [%]; d SK s the average repar cost of the -th component, ncludng purchase and delvery 60 Scentfc Journals of the Martme Unversty of Szczecn 51 (123)

3 Economc aspects of component mportance analyss for complex marne systems of replacement parts, energy and personnel [EUR/ falure]; m f s the total number of system falures recorded durng the tme t [falures/h]; and t s the operatng tme [h]. The costs assocated wth restorng all components, ncludng those whch are unrelated to the nterrupton of the system s operaton, wll be hgher than the ones descrbed by Equaton (7). For a gven component, restoraton costs are as follows: SK total dskmt [EUR] (8) where: d SK s the average repar cost of the -th component, ncludng purchase and delvery of replacement parts, energy and personnel [EUR/falure]; m s the total number of falures of the system s -th component wthn tme t [falures/h]; and t s operaton tme [h]. The total restoraton cost for a system consstng of n components wthn tme t can be estmated by the followng equaton: n 1 SK SK total [EUR] (9) Smlarly, the average total cost assocated wth carryng out correctve and preventve mantenance for the -th component n stuatons related to nterrupton of the system s operaton can be determned by the crtcal number of operaton nterruptons ndex: DEI I dmdt [EUR] (10) where: I DEI s the crtcal number of nterruptons ndex of the -th component [%]; d s the average cost of mantenance of the -th component [EUR/ mantenance]; m d s the total number of system operaton nterruptons recorded n tme t [operaton/h]; and t s operaton tme [h]. The costs assocated wth the mantenance of all components, ncludng those whch are not assocated wth the system s operaton nterrupton, wll be hgher than the costs descrbed by Equaton (10), and wll be gven by the followng expresson: total dskmot [EUR] (11) where: d SK s the average mantenance cost of the -th component [EUR/mantenance]; m o s the total number of mantenance events for the -th component wthn tme t [mantenance/h]; and t s operaton tme [h]. The total mantenance cost of a system consstng of n components wthn a duraton of t can be expressed by the formula: n 1 Object of analyss total [EUR] (12) An llustraton of selected monetary quanttatve mportance measures of components was performed for the lubrcaton system of the stern tube shaft sealng of a contaner shp wth 6500 TEU capacty (Hyunda Heavy Industres, 2003). Ths system s desgned to mnmse frcton durng normal operaton of the shp propulson system, and to provde a sealng of the propeller shaft at the stern such that seawater s excluded from the machne room. The relablty structure of the system was modelled usng the relablty block dagram shown n Fgure 1. The structure assumes a decomposton level consstng of man system components, takng ther functon n the system nto account and consdered as separate machnes or devces. Ol crculaton n the system s carred out by one of the crculaton pumps (P1, P2), whch takes ol from the crculaton tank T3 through a flter (F1, F2), and delvers the ol through the cooler nto one of gravty tanks T1, T2. Selecton of the actve gravty tank s dependent on the draught of the vessel; when the vessel s suffcently drafted, the upper gravty tank T1 s selected as the actve one, whle tank T2 s used durng low draught condtons. The ol from the gravty tank flows freely nto the stern tube seals to provde sealng, lubrcaton and coolng of the shafts, thus ensurng proper operatng condtons. From the seals, ol outflows nto the crculatng tank T3. Because the crculatng pump works contnuously, excess ol n the gravty tank T1 s draned back to tank T2 usng a ppelne system, and from tank T2 agan to the crculaton tank T3. Basc characterstcs of relablty system components are summarsed n Table 1. Ths table reflects the assumpton that all components are reparable objects. The dstrbuton of probablty of tme to damage and recovery tme are exponental dstrbutons. Assumng falure ntensty λ [damage each 10 6 hours], the average renewal tme T D [h] s taken from publcatons (Duda-Gwazda, 1995; hybowsk, 2014). The crcut of the pump-flter s reserved, so the analyss uses an average value of damage and renewal process parameters because of the perodc replacement of these devces between operatng and Zeszyty Naukowe Akadem Morskej w Szczecne 51 (123) 61

4 Leszek hybowsk, Katarzyna Gawdzńska a) T1 b) R T2 FWD SEAL TANK S S/T L.O. OOLER c) T1 S T3 R P1 F1 P1 F1 P2 S/T L.O. PUMP F2 T2 P2 F2 T3 S/T L.O. SUMP TANK Fgure 1. Shp s lubrcaton system of stern tube shaft sealng: a) system dagram; b) fore sealng vew; c) relablty structure of the system (Hyunda Heavy Industres, 2003; hybowsk, 2014) Table 1. Relablty system component characterstcs of shp s lubrcaton system of stern tube shaft sealng (Duda-Gwazda, 1995; hybowsk, 2014) omponent markng omponent descrpton Falure ntensty λ [damage/106 h] Average renewal tme TD [h] S Stern tube shaft sealng wth bearngs and sealng tank T1 Gravty ol tank (top) T2 Gravty ol tank (bottom) Lubrcaton ol cooler T3 rculaton ol tank R Ppes, valves and fttngs P1 Lubrcaton ol pump No P2 Lubrcaton ol pump No F1 Lubrcaton ol flter No F2 Lubrcaton ol flter No Table 2. Summary of planned mantenance works to the stern tube sealng lubrcaton system of the contaner shp (Duda- Gwazda, 1995; hybowsk, 2014) omponent markng omponent descrpton, type of servce Average tme between mantenance procedure [h] Average duraton of system downtme [h] S Stern tube shaft sealng wth bearngs and sealng tank annual nspecton Stern tube shaft sealng wth bearngs and sealng tank nspecton every 5 years (n dry dock) T1, T2, T3 Lubrcaton ol tanks annual nspecton P1, P2 Lubrcaton ol pumps annual nspecton Lubrcaton ol cooler cleanng Scentfc Journals of the Martme Unversty of Szczecn 51 (123)

5 Economc aspects of component mportance analyss for complex marne systems backup system. It was also assumed that both subsystems (pump systems) are damaged n the same way. A smlar assumpton s made for gravty ol tanks. The characterstcs of planned mantenance works of the system descrbed are presented n Table 2. Due to the confdentalty of nformaton regardng costs ncurred by freghters, as well as many factors whch affect the results, general nformaton regardng system repar costs was used to show the vablty of the aforementoned ndces. It s assumed that the cost of a shp s operaton nterrupton s 15,000 EUR/day, whle the ndvdual average costs assocated wth system component restoraton are presented n Table 3. Table 3. Average restoraton cost of the propeller shaft tube seal lubrcaton system components of a contaner shp (generc data) (hybowsk, 2014) omponent desgnaton omponent descrpton Restoraton cost d SK [EUR] S Propeller shaft tube seal wth bearngs and sealng contaner T1, T2, T3 Ol gravty tank (upper) 500 Lubrcatng ol cooler 250 R Ppelnes, valves and other equpment 125 P1, P2 Lubrcatng ol pump No F1, F2 Lubrcatng ol flter No alculaton of monetary measures The 20,000 h operaton tme smulaton was carred out usng the Synthess 9 calculatng platform by RelaSoft. Parameters for the smulaton are: smulaton start tme: 1 h; pont results at every: 100 h; number of smulatons: 100,000; seed value: 1; report sub-dagram: OFF; run throughput smulaton: OFF; report throughput pont results: OFF; use system downtme threshold: OFF. A detaled report from the analyss s presented n (hybowsk, 2014). In the smulaton result, whch encompassed a year of system operaton, the total tme of shp operaton nterrupton was 69 h. Takng nto consderaton that the hourly cost of shp operaton nterrupton s 625 EUR, the estmated operatng losses assocated wth system operaton nterrupton caused by falure of the -th component durng operaton tme t were estmated [EUR]. The effect of falures on the system operaton nterrupton costs calculated wth use of (5) s presented n Fgure 2. Average costs assocated wth restoraton of system components whch caused nterruptons of SE [EUR] S T1 T2 T3 R P1 F1 P2 F2 Element Fgure 2. Operatng losses assocated wth system operaton nterrupton caused by falure of the -th component of the propeller shaft tube seal lubrcatng ol system durng operaton (hybowsk, 2014) SE [0.25 EUR] S T1 T2 T3 R P1 F1 P2 F2 Element Fgure 3. Average yearly restoraton costs of the -th component of the propeller shaft tube seal lubrcatng ol system (crtcal falures) (hybowsk, 2014) SK total [0.25 EUR] S T1 T2 T3 R P1 F1 P2 F2 Element Fgure 4. Average yearly renovaton costs of the -th component of the propeller shaft tube seal lubrcatng ol nstallaton (all falures) (hybowsk, 2014) system operaton calculated wth the use of (7) are presented n Fgure 3. The hghest costs assocated wth system operaton nterrupton caused by falure of a gven component correspond to falures of the T3 crculaton tank, the cooler, and the R ppelnes and ther equpment. These are components for whch the crtcal operaton nterrupton tme ndex reached the hghest value. Zeszyty Naukowe Akadem Morskej w Szczecne 51 (123) 63

6 Leszek hybowsk, Katarzyna Gawdzńska The I DEI ndex can, therefore, consttute a measure whch descrbes the nfluence of component falure on the degree of losses assocated wth nterrupton of the system s operaton. The hghest SK costs are assocated wth repars to the S propeller shaft tube seal, due to the necessty of dockng the shp or hrng dvers for underwater work. Due to the large dfference n repar costs of the S component, compared to other components, the results are presented on a logarthmc scale. In relaton to the yearly operaton tme of the analysed system, the average total restoraton costs of ndvdual system components calculated wth the use of (8) are presented n Fgure 4. The hghest SK total repar cost of the propeller shaft lubrcaton and tube seal nstallaton are assocated wth the S sealng (over 25,000 EUR), followed by crculaton pumps P1 and P2 (over 17,500 EUR) and other system components (below 875 EUR). onclusons These estmates of mportance measures, encompassng the economc aspect of operaton (Fgures 2, 3 and 4), bascally correspond to results acheved n stochastc smulatons (RelaSoft, 2007; hybowsk, 2014). Weak lnks n the system whch sgnfcantly nfluence operatng costs nclude ppelnes and ther equpment, the ol cooler and the crculaton tank (Fgures 2 and 3). Due to the consequences of falures (hgh restoraton costs and system operaton nterrupton), the most mportant component of the system s the shaft tube seal, for whch the mportance measures reached very hgh values (Fgures 2 and 3). onsderng that the mantenance costs of the shaft tube seal are several tmes hgher than for any of the other components, t s classfed n terms of falure consequences as the most crtcal component n the system despte the fact t s a very relable component. Full assessment of a component s mportance requres knowledge of the consequences of ts falure (hybowsk, 2014; hybowsk, Laskowsk & Gawdzńska, 2015; hybowsk & Gawdzńska, 2016). For example, although the crankshaft of an nternal combuston engne s very relable, the engne wll be out of commsson for a relatvely long tme whenever the crankshaft s damaged. Thus, the component could be consdered very mportant. Therefore, the mportance of complex techncal system components depends on: the relablty characterstcs of the system components; the system relablty structure; and the consequences of damage to system components. A crucal ssue related to the topc s the need to determne the uncertanty of obtaned results. Analysng ths concept s hghly complcated due to the non-lnear relatonshp among costs and nstances of downtme and the necessty of ncludng varous addtonal costs such as duty, taxes, transportaton costs, contractual penaltes, etc. All the above tems create a bass for conductng long-term research amed at establshng detaled methodologes for cost analyses of system senstvty. Due to the complexty of measurement uncertanty and the fact that the man objectve of the paper s to suggest a methodology useful n the ntal analyss of component mportance n mnmsng system explotaton costs, the presented methodology may fnd ts applcaton n varous TSs used daly. References 1. Bajkowsk, J.M. & Zalewsk, R. (2014) Transent response analyss of a steel beam wth vacuum packed partcles. Mechancs Research ommuncatons 60, pp hybowsk, L. (2014) Ważność komponentów w strukturze złożonych systemów techncznych. Szczecn, Radom: ITE. 3. hybowsk, L. & Gawdzńska, K. (2016) On the Present State-of-the-Art of a omponent Importance Analyss for omplex Techncal Systems. In: A. Rocha et al. (eds.) New Advances n Informaton Systems and Technologes. Advances n Intellgent Systems and omputng 445, pp , Sprnger, ham. 4. hybowsk, L., Laskowsk, R. & Gawdzńska, K. (2015) An overvew of systems supplyng water nto the combuston chamber of desel engnes to decrease the amount of ntrogen oxdes n exhaust gas. Journal of Marne Scence and Technology 20, 3, pp hybowsk, L. & Żółkewsk, S. (2016) Basc relablty structures of complex techncal systems. In: A. Rocha et al. (eds.) New ontrbutons n Informaton Systems and Technologes. Advances n Intellgent Systems and omputng 354, pp , Sprnger, ham. 6. Derlukewcz, D., Ptak, M. & Kozołek, S. (2016) Proactve falure preventon by human-machne nterface n remote-controlled demolton robots. In: A. Rocha et al. (eds.) New Advances n Informaton Systems and Technologes. Advances n Intellgent Systems and omputng 445, pp , Sprnger, ham. 7. Duda-Gwazda, J. (1995) Nezawodność okrętowych słown spalnowych. Raport technczny Nr RT-95/T-01. Gdańsk: entrum Technk Okrętowej. 8. Hlber, P. (2005) omponent relablty mportance ndces for mantenance optmzaton of electrcal networks. Lcentate thess. Stockholm: Royal Insttute of Technology. 9. Hlber, P. & Bertlng, L. (2004) Monetary Importance of omponent Relablty n Electrcal Networks for Mantenance Optmzaton. Proceedngs of Probablty Methods Appled to Power Systems, Ames, Iowa, September Scentfc Journals of the Martme Unversty of Szczecn 51 (123)

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