A Budget Based Optimization of Preventive Maintenance in Maritime Industry

Transcription

1 Amercan Journal of Engneerng Research (AJER) e-issn: p-issn : Volume-4, Issue-9, pp Research Paper Open Access A Budget Based Optmzaton of Preventve Mantenance n Martme Industry 1 Akpan, W. A., 2 Ogunsola, T.M. 1 Mechancal Engneerng Department, Unversty of Uyo (234) P.M.B 1017 Uyo, Akwa Ibom State, Ngera 2 Boat and Shpbuldng Department, Martme Academy of Ngera, Oron Abstract : Ths research work nvestgates preventve mantenance management of desel engne generators at the Martme Academy of Ngera, Oron. A budget based optmzaton methodology takng cognsance of the age of the equpment was appled on falure data of desel engne generators obtaned from the nsttuton mantenance data base to provde cost effectve mantenance management / replacement programme for crtcal components of desel engne generators. The results were analyzed usng Matlab. The results provde effectve cost and relablty template whch can be used to perform a budget based mantenance plannng programme n the Martme Industry. Keywords: Budget; optmzaton; mantenance; modelng;; relablty; desel engnes; martme ndustry. I. Introducton The Martme Academy of Ngera Oron n Akwa Ibom State Ngera started as Nautcal college of Ngera n 1979 wth a mandate to tran shpboard offcers, ratngs and shore-based management personnel (Wkpeda, 2014). In 1988 the college was upgraded to the present status and the mandate was expanded to tranng all levels and categores of personnel for all facets of the Ngeran martme ndustry. The poor power supply n Ngera country has prompted the academy to generate ts electrcty for the admnstratve actvtes of the nsttuton usng the desel engne generators. The desel engne s popular n martme ndustres. Ths can be attrbuted to ts, hgh performance. It has hgh relablty and a better fuel economy than gasolne engne and s more effcent at lght and full loads. The desel generator emts fewer harmful exhaust pollutants and s nherently safer because desel fuel s less volatle than gasolne. However, desel engnes can be neffectve wth poor mantenance method. Mantenance s all actons whch have the obectve of returnng a system back to another state. Accordng to Moubray, (1995) and Tsang et al. (1999) mantenance has the ablty to brng back the system quckly to ts normal functonal state and reduces equpment down tme. Paz, (1994) categorzed mantenance nto two: correctve mantenance and preventve mantenance. Mantenance s very mportant n the lfe of any physcal asset. The fundamental bass of any planned mantenance system s decdng n advance. : The ndvdual tems of the plant and equpment to be mantaned; The forms, method and detals of how each tem s to be mantenance; The tools, replacements, spares, tradesmen and tme that wll be requred to carry out ths Mantenance; The frequency at whch these mantenance operaton must be carred out; The method of admnsterng the system and; The method of analyzng the results. I The ntroducton of planned mantenance scheme n an organzaton nvolve tme, money and consderable amount of work. It has been shown that the benefts obtaned from planned mantenance are numerous Koboa-Aduama (1991). Mantenance provdes freedom from breakdown durng operatons. Mantenance of equpment s essental n order to: keep the equpment at ther maxmum operatng effcences; keep equpment n a satsfactory condton for safe operatons; and reduce to a mnmum, mantenance cost consstent wth effcency and safety (Koboa-Aduma (1991). w w w. a e r. o r g Page 13

2 Studes on mperfect mantenance can be found n Pharm and Wang (1996) and Nakagawa (1987). The Martme Academy of Ngera Oron has 500KVA, 600KV and 800KVA desel engne generators to generate power for the admnstratve needs of the academy The mantenance costs of desel engne generators n the academy s rsng daly. Ths s caused by lack of clear mantenance methodology by the nsttuton to mantan these generators. The obectve of ths research s to conduct a budget based mantenance methodology on 500KVA, 600KVA and 800KVA desel engne generators own by the academy and to suggest ways mantenance and replacement actons should be performed on the generators wth the obectve of reducng the cost of mantenance wth the requred relablty of the generators gven any stpulated budget. II. Methodology Data for ths research work were collected from both prmary and secondary sources. The prmary nformaton was obtaned from mantaners, supervsors, engneers and managers. Ths nformaton nclude: mantenance cost, falure cost and replacement cost of each part The man data were obtaned from the log book for a perod of fve years. Ths data nclude the tme of falure of the desel engne generator, the components causng the falure and also when the faled components were repared or replaced.. Ten crtcal parts were selected for the study. Ths data formed nput nto a mantenance and replacement model developed by Kamran (2008).The nformaton was used to predct future mantenance plannng for the three desel generators n the next fve years wth a gven budget and the obectve of reducng mantenance cost and ncreasng the relablty of the desel generators used by the nsttuton. The methods used n solvng the problem are generalzed reduced gradent (GRG) and smulatng annealng (SA). III. Optmzaton model The model by Kamran (2008) provdes a general framework that was appled on the study. In the relablty maxmzaton equaton, the constrants for the soluton of the equaton are as follows: () Constrants that address the ntal age of each component at the begnnng of plannng horzon. Thus; ἰ = 0; = 1 N (1 ) where component, = perod& N=No of components () Effectve age of the components based on preventve mantenance actvtes recursvely. (1 m )(1 r ) m ( ) ( 2), = 1 N and = 2... T T J = 1, N and = 1... T (3) m r,, 1; = 1... N and = 1... T Where:, Effectve age of component at the start of perod, of perod. T = No. of perods, J = No. of ntervals, : Effectve age of component at the end m, : f component at perod s mantaned, otherwse. r, : f component at perod s replaced, otherwse, : Improvement factor of component () Condton/constrant preventng occurrence of smultaneous mantenance and replacement actons on the components. N 1 T e ( ( ) ( ),, RRseres (4) m,,, r, = 0 or 1; = 1... N and = 1... T (5) = 1, N and = 1... T (6) : Characterstc lfe (scale) parameter of component : Shape parameter of component,, RR seres: Requred relablty of the seres system of components. w w w. a e r. o r g Page 14

3 Consder the case where component s mantaned n perod. For smplcty, t s assumed that the mantenance actvty occurs at the end of the perod. The mantenance acton effectvely reduces the age of component at the begnnng of the next perod. That s: +1 = for = 1,, N; =1,,T and (0 α 1) (7) The term α s an mprovement factor, smlar to that proposed by Malk (1979), Jayabalan (1992). Ths factor allows for a varable effect of mantenance on the agng of a system. When α = 0, the effect of mantenance s to return the system to a state of good-as new. When α = 1, mantenance has no effect, and the system remans n a state of bad-as-old. The mantenance acton at the end of perod results n an nstantaneous drop n the ROCOF of component. Thus at the end of perod, the ROCOF for component s v ( ). At the start of perod + 1 the ROCOF drops to v (0) If component s replaced at the end of perod, the followng apples: =0 for = 1,,N; =1,,T (8) 10.e., the system s returned to a state of good-as-new. The ROCOF of component nstantaneously drops from v ( ) to v ( ) If no acton s performed n perod, there s no effect on the ROCOF of component and thus : =, for = 1,, N; =1,,T (9) 1 =, for = 1,, N; =1,,T (10) v ( +1 ) = v ) for = 1,, N; =1,,T (11) (, T = No. of perods, J = No. of ntervals, ROCOF = Rate of Occurrence of Falure For a new system, the cost assocated wth all component levels of mantenance and replacement actons n perod, remans as a functon of all the actons taken durng that perod. The expected number of falures of component n perod, E[ N. ] v ( t) dt for = 1,, N; = 1,, T (12) Under the Non- homogenous posson process assumpton (NHPP) the expected number of component falures n perod s E [ N ] ( ) ( ) for = 1,, N; = 1,, T ( 13) If the cost of each falure s F (n unts of #/falure event), whch n turn allows the computaton of, F, the cost of falures attrbutable to component n perod s: F = F E ] for = 1,, N; = 1,, T (14) [ N, Hence regardless of any mantenance or replacement actons (whch are assumed to occur at the end of the perod) n perod, there s stll a cost assocated wth the possble falures that can occur durng the perod. If mantenance s performed on component n perod, a mantenance cost constant M ἰ s ncurred at the end of the perod. Smlarly If component s replaced, n perod, the replacement cost s the ntal purchase prce of the component denoted by R. w w w. a e r. o r g Page 15

4 For a mult-component system, the cost structure s defned as stated above, the problem can be reduced to a smple problem of fndng the optmal sequence of mantenance, replacement, or do-nothng for each component, ndependent of all other components. That s, one could smply fnd the best sequence of actons for component 1 regardless of the actons taken on component 2 and so on. Ths would result n N ndependent optmzaton problems. Such a model seems unrealstc, as there should be some overall system cost penalty when an acton s taken on any component n the system. It would seem that there should be some logcal advantage to combne mantenance and replacement actons, e.g., whle the system s shutdown to replace one component, t may make sense to go ahead and perform mantenance/replacement of some other components, even f t s not at ts ndvdual optmum pont where mantenance or replacement would ordnarly be performed. Under ths scenaro, the optmal tme to perform mantenance/replacement actons on ndvdual components s dependent upon the decson made for other components. As such, a fxed cost of downtme, Z, s charged n perod f any component (one or more) s mantaned or replaced n that perod. Consderaton of ths fxed cost makes the problem much more nterestng, and more dffcult to solve, as the optmal sequence of actons must be determned smultaneously for all components. From the vantage pont, at the start of perod = 0, t s good to determne the set of actvtes,.e., mantenance, replacement, or do nothng, for each component n each perod such that total cost s mnmzed. In order to have age of component at the end of perod by usng equaton 2. Frst, defne m, and r, as bnary varables of mantenance and replacement actons for component n perod as: m, f component at perod s mantaned, otherwse. (15) r, f component at perod s replaced, otherwse. (16) The followng recursve functon of,, m, r, α, wth a constrant are constructed: ( 1 m )(1 r ). m ( ) ( 17) T J (18) m, + r, 1 (19) In addton, the ntal age for each component s equal to zero:, =0 for =1,,N (20) If component replacement occurs n the prevous perod then, r = m =0, (21) 1, r 1 =, = 1. If a component s mantaned n the prevous perod then m =1 (22 ) 1, ( 23) and fnally f nothng s done, r 1 =o, m. = 0 and, = 1 (24) The formulaton of a budget constrant, GB s ntroduced. The obectve of ths model s to maxmze the system relablty, through our choce of mantenance and replacement decsons, such that we do not exceed the budgeted total cost. Ths model s formulated as: Max Relablty = (25) Subect to = 1... N (26) = (1-1) (1 1) ( -1) (27) = 1... N and = 2... T (28) w w w. a e r. o r g Page 16

5 = + = 1... N; and = 1... T 29) + 1; = 1... N; and = 1... T (30) (31), =0 or 1 ἰ =1 N and = 1 T (31) 0 ἰ =1 N and = 1 T (32) M ἰ,, r = 0 or 1; = 1... N and = 1... T (33) = 0; N and 1... T (36) Wheree: Effectve age of component at the start of perod, : Effectve age of component at the end of perod.t = No. of perods, J = No. of ntervals m ἰ, : f component at perod s mantaned, otherwse., r ἰ, : f component at perod s replaced, otherwse : Characterstc lfe (scale) parameter of component : Shape parameter of component, RR seres: Requred relablty of the seres system of components. : Improvement factor of component : Summaton, П: Multplcaton, ἰ:unexpected falure cost of component n perod N: No. of components, M : mantenance cost of component, R : Replacement cost of component, Z : Fxed cost of the system Decson varables M ἰ, : r ἰ, : f component at perod s mantaned, otherwse. f component at perod s replaced, otherwse. Ths obectve functon computes the maxmum relablty subect to a gven budget cost wth stated constrants and nput parameters from tables 1, 2and 3. The generalzed reduced gradent and the smulated annealng algorthms were used to solve the cost mnmzaton usng Matlab software and the results presented n tables 4, 5 and 6. Tables 1, 2 and 3 were generated based on data obtaned from mantenance log book and nformaton from mantenance engneers. IV. + Results and dscusson The characterstc lfe, shape factor, mantenance factor, falure cost, mantenance cost, and replacement cost are presented n tables 1, 2 and 3 for 500KVA, 600KVA and 800KVA desel generators respectvely for the selected components shown n tables 1.2 and 3. Table :1. Parameters for 500KV a desel generator w w w. a e r. o r g Page 17

6 The characterstcs lfe and shape factors were calculated from falure data whle the falure costs. mantenance costs and replacement costs data were obtaned from mantenance engneers. The mantenance factors were assumed based on the frequency of falure of components. Table: 2. Parameters for 600KV a desel generator The falure cost s hgher than replacement cost whch n the same van hgher than the mantenance cost. The costs of components n 500KVA, 600KVA and 800KV generators are dfferent n some cases or smlar n others. Table: 3. Parameters for 800KV a desel generator engne In tables 4, 5 and 6 the gven budget wth maxmum relablty s presented n the thrd and sxth columns by the decson maker, whle a search algorthm of generalzed reduced gradent and smulated annealng calculate the total optmzed cost functon for each component and the optmum relablty n the sxth column usng Matlab software. A gap analyss shows the effectveness of each algorthm. At 98.21% relablty and a gven cost of 800, nara, sx number perods at ten months per perod for the 60 months predcton has a total cost of 800, nara and 792,027.2 nara as shown n table 4. From perods of 36 and above, the calculated total cost s less than the gven budget. The optmzed relablty les between 46.96% and 84.71% for smulated annealng algorthm and 55.42% and 95.06% for generalzed reduced gradent method. Table: 4. Budget Algorthm and Optmzed functon value (OFV) for 500KVA w w w. a e r. o r g Page 18

7 For the 600KVA and 800KVA desel engne generators, the same trend s followed. However, the allocated gven budgets are much more hgher than that of the 500KVA generator Table :5. Budget Algorthm and Optmzed functon value (OFV) for 600KVA Table: 6. Budget Algorthm and Optmzed functon value (OFV) for 800KVA V. Conclusons The results presented from the study show that the formulaton s qute effectve n mantenance decson makng for desel engne generators. The research shows that shorter mantenance nterval s effectve allowng budget surplus for the decson maker. The generalzed reduced gradent gves a lower cost than the smulated annealng. Ths methodology s therefore recommended to the Martme Academy Oron for effectve budget based mantenance management programme for the desel engne generators. References w w w. a e r. o r g Page 19

8 [1] Kamran, S. M(2008) Preventve Mantenance and Replacement Schedulng: Models and algorthms. Ph.D thess, Unversty of Lousvlle, Kentucky, USA. [2] Koboa-Aduma, B. (1991) Mantenance Management of Small scale Industres, n the Proceedngs of the Internatonal Conference Workshop on Engneerng for Accelerated Rural Development (Eds) Anazodo, U. G. N. Chukwuma. G. O. and Chukwueze, H. O.; Faculty of Engneerng, Unversty of Ngera, Nsukka. 243 [3] Jabayalan, V.; Chaudhur D. (1992) Sequental Imperfect Preventve Mantenance Polces: a case study, mcroelectroncs and relablty, V 32, n 3 September pp [4] Malk, M. A.K.(1979) Relable Preventve Mantenance Schedulng, AIIE Transacton, V11, N 3 September, pp [5] Moubray, J. (1995) Mantenance Management A New Paradgm. (Onlne seral) Avalable: [June 18, 2013]. [6] Nakagawa, T. and Yusu K, (1987) Optmum Polces for System wth Imperfect Mantenance, IEEE Transacton on Relablty. Vol. R-36, No. 5, pp [7] Paz, N. M. (1994) Mantenance Schedulng: Issues, Results and Research Needs. Internatonal Journal of Operatons and Producton Management. Vol. 14, No. 8, pp [8] Pharm, H. and Wang, H. (1996) Imperfect Repar, European Journal of Operatonal Research Vol. 94, pp [9] Tsang, A. H. C., Jardne, A. K. S., Kolodry, H. C. (1999) Measurng Mantenance Performance: A Holstc Approach Internatonal Journal of Operatons and Producton Management. Vol ssue 1, pp [10] Wkpeda (2014) Martme Academy of Ngera: Avalable [Onlne] http//en.wkpeda.org. w w w. a e r. o r g Page 20