Prediction of Aviation Equipment Readiness Rate Based on Exponential Smoothing Method. Yan-ming YANG, Yue TENG and Chao-ran GUO

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1 7 nd Inrnonl Confrnc on Informon chnology nd Mngmn Engnrng (IME 7) ISBN: Prdcon of Avon Equpmn Rdnss R Bsd on Exponnl Smoohng Mhod Yn-mng YANG, Yu ENG nd Cho-rn GUO Nvl Aronucl nd Asronucl Unvrsy Qngdo Cmpus; Qngdo 664; Chn Kywords: Prdcon, Exponnl smoohng mhod, Avon qupmn rdnss r. Absrc. Avon qupmn rdnss r s n mporn prmr o s h bl bly of ronucl qupmn, nd s lso n mporn prmr of ronucl qupmn RMS. h rdnss r rflcs h rlbly, mnnbly, supporbly, von suppls, logscs suppor, mngmn lvl nd ohr spcs of ronucl qupmn. In hs ppr, h dfnon of von qupmn rdnss nd s clculd formuls r gvn. hn h prdcon mhods of von qupmn rdnss r usng sngl xponnl smoohng nd doubl xponnl smoohng r proposd, nd h dffrn prdcon mhods r comprd. h smulon rsuls show h h mhods r fsbl nd ffcv. Inroducon In h mngmn of von mnnnc hs mor prdcon problm, h chncl s of h qupmn, von qupmn rdnss, spr prs consumpon, h numbr of fuls o mk scnfc prdcon, o mprov von mnnnc work prdcbly, counrmsurs nd scnfc, nd mprov von qupmn rdnss nd wrm ulzon lvl plys vry mporn rol. h von qupmn rdnss r s rflcon msurmn chnology for rcrf quly lvl. Avon qupmn rdnss r s n mporn mnfson of bl ffcvnss for h ronucl qupmn. hrfor, s mporn o sudy h von qupmn rdnss r. h Dfnon of Equpmn Rdnss R h qupmn vlbly rfrs o h bly of h qupmn o rspond o comb rnng sks upon rcp of comb rnng ordr. I s h srngh of h qupmn n h complon of qupmn, qupmn vlbly, rnng nd ohr fcors combnd ffc of h rsuls. Avon qupmn rdnss r s ssc h dscrbs h s of ronucl qupmn vlbly. A prsn, h rdnss r s usully dfnd s h ro of h numbr of nc qupmn o h ol numbr of qupmn n h ronucl qupmn. h rdnss r s shown n quon (). P OR = k () n whr P OR s h qupmn rdnss r; k s h numbr of nc qupmns; n s h ol numbr of qupmns. h Exponnl Smoohng Prdcon Mhod m srs s sscl ndcor vlu, ccordng o h chronologcl ordr o h formon of h squnc. Avon qupmn rdnss r s ypcl m srs. m srs prdcon s o nlyz h m srs, ccordng o h m srs rflcs h dvlopmn procss, drcon nd rnd, nlogy or xnson, o prdc h nx prod of m or fw yrs lr my rch h lvl. m srs prdcon cn b usd for shor-rm prdcon, mdum-rm prdcon nd long-rm 47

2 prdcon. Accordng o dffrn d nlyss mhods, cn b dvdd no movng vrg, wghd movng vrg, xponnl smoohng, ssonl rnd forcsng. On-Prmr Exponnl Smoohng Prdcon Mhod Exponnl smoohng s commonly usd mhod o produc smooh m srs, nd s lso mhod of curv fng. h bsc d of xponnl smoohng forcsng mhod s: n h nx prod of h forcs d, consdrng h d of hs cycl, nd kng no ccoun h prvous d. h obsrvon of rcn d gv hghr wgh, h wgh s rlvly low wh h rlr d, wghs r usully gomrclly dcrsng ro consn, h rcn d on h prdcon of h fuur grr rol, so s o obn br fng curv nd h prdcon rsuls. Accordng o dffrn prmrs, cn b dvdd no on-prmr xponnl smoohng mhod nd wo-prmr xponnl smoohng mhod. On-prmr xponnl smoohng s subl for h m srs d wh sbl chrcrscs, nd wo-prmr xponnl smoohng s subl for h m srs d wh h rnd chrcrscs. On-prmr xponnl smoohng hs smoohng prmr, whch s bsd on h smoohnss of h numbr of ms, ncludng lnr xponnl smoohng mhod, qudrc xponnl smoohng mhod nd cubc xponnl smoohng mhod. h Lnr Exponnl Smoohng Prdcon Mhod. h lnr xponnl smoohng y wh ( ) y s ( ) prdcon mhod s knd of forcsng mhod of wghng h m srs { } h wgh( < < ). h wgh of clculon formul s s follows: + y s, h wgh of s,..., nd so on, h yˆ = S = y + S () whr, y rprsns h cul vlu h -h prod; y ˆ+ rprsns h prdcd vlu h (+)-h prod;, S S rprsn h sngl xponnl smoohng vlus h (-)-h nd -h prods; ( < < ) rprsns h smoohng coffcn. h nl vlu S s h frs m of h m srs. If h smpl d s smll, h vrg vlu of h hsorcl d cn b slcd s h nl vlu. h Qudrc Exponnl Smoohng Prdcon Mhod. Whn h m srs shows lnr rnd, usng lnr xponnl smoohng mhod o prdc, hr r sll sgnfcn lg dvons. hrfor, h ncssry mndmns should b md. On h bss of lnr xponnl smoohng squnc, xponnl smoohng s prformd gn wh h sm smoohng coffcn, whch s qudrc xponnl smoohng. h formul s s follows: ( ) S = y + S S S S yˆ + = + b = + () = ( ) = S S b S S whr S rprsns n xponnl smoohng vlu h -h prod; (4) S rprsns qudrc xponnl smoohng vlu h -h prod; y rprsns n cul vlu h -h prod; y ˆ+ 48

3 rprsns prdcd vlu h (+)-h prod; nd ( < < ) rprsns smoohng coffcn. h nl vlu of S s h sm s h of S. h Cubc Exponnl Smoohng Prdcon Mhod. Whn h m srs shows nonlnr rnd, h cubc xponnl smoohng mhod cn b usd o prdc h m srs. h bsc prncpl s h n h qudrc xponnl smooh bss, nd hn n xponnl smoohng, whch s cubc xponnl smoohng. h formul s s follows: ( ) ( ) S = y + S S = S + S S S S yˆ + = + b + c ( ) ( ) = + (5) ( ) = S S + S ( ) b = (6 5 ) S (5 4 ) (4 ) S + S ( ) ( ) c = S S + S ( ) (6) whr S rprsns n xponnl smoohng vlu h -h prod; S rprsns qudrc xponnl smoohng vlu h -h prod; ( ) S rprsns cubc xponnl smoohng vlu h -h prod; y rprsns h cul vlu h -h prod; y ˆ+ rprsns h (+)-h Prod prdcon vlu; nd ( < < ) rprsns smoohng coffcn. In gnrl, h nl vlu ( ) S = S = S s h frs rm of h m srs. wo-prmr Exponnl Smoohng Prdcon Mhod wo-prmr xponnl smoohng mhod, lso known s h Hol xponnl smoohng mhod, s lnr xponnl smoohng mhod. On-Prmr xponnl smoohng formul s no subl for fng nd prdcng h m srs wh rnd. Doubl xponnl smoohng nroducs nw prmr, whch s subl for fng nd prdcng h m srs wh rnd. h formul s s follows: ( )( ) ( γ ) S = y + S + = γ S S + (7) yˆ = S + whr S s h lvl vlu m ; s h wgh of S. s h rnd m ; γ s h wgh of ; y s h d vlu m ; y ˆ s h fd vlu m (h prdcd vlu o h prvous sp). In quon (6), h smoohng vlu S n h frs formul dds h ls smoohng vlu o h rnd fcor h prvous m. hs lmns h hysrss nd djuss S o rsonbl vlu. h scond formul s h xprsson for h ls wo djcn smoohng vlu dffrncs nd s n upd formul rprsnng h rnd. By ddng rnds o h smoohng d, you cn smooh h m srs d wh rnds. hus, whn h sysm s smd by nroducng h rnd componn, h vlu of h sysm cn vod h sngl dpndnc of h xponnl s on h sysm, whch cn rflc h moon chrcrscs of h sysm mor rlsclly. 49

4 Applcon Exmpl Anlyss Problm Dscrpon Sscs of von qupmn for monhs of rdnss r d, s shown n bl. h d of h prvous monhs r known smpls nd h Dcmbr d r h vrfcon smpls. h sngl xponnl smoohng mhod nd h doubl xponnl smoohng mhod r usd o prdc h h monh von qupmn rdnss r nd compr h forcsng rsuls. bl. Avon qupmn rdnss r sscs d. Monh Rdnss r Rsul Anlyss Usng h m srs nlyss funcon of Mnb, w cn g h followng prdcon rsuls convnnly, s shown n Fgur nd Fgur. h fgur shows h cul vlu of h Avon qupmn rdnss r, fng vlu nd prdcon of h squnc dgrm, lso ncluds smoohng prmrs, ccurcy msurmn nformon. h ccurcy msur of hr fng modls: mn bsolu prcng rror (MAPE), mn bsolu dvon (MAD) nd mn squrd dvon (MSD). For hs hr msurs, h smllr h vlu, h br h modl f. r s n d.8 R Vrbl Acul vlu Fd vlu Prdcd vlu 95.% prdcon nrvl Smoohng consn Accurcy msurmn MAPE MAD.89 MSD Monh 8 9 Fgur. On-prmr xponnl smoohng prdcon of von qupmn rdnss r. r.9.85 s n.8 d R Vrbl Acul vlu Fd vlu Prdcd vlu 95.% prdcon nrvl Smoohng consn.794 γ.479 Accurcy msurmn MAPE.484 MAD.869 MSD Monh 8 9 Fgur. wo-prmr xponnl smoohng prdcon of von qupmn rdnss r. 5

5 As cn b sn from h Fgur nd Fgur, h sngl xponnl smoohng mhod nd doubl xponnl smoohng mhod prdc h von qupmn rdnss r n Dcmbr r nd h forcsng rsuls r shown n bl. I s obvous h h doubl xponnl smoohng mhod s br hn h sngl xponnl smoohng mhod. bl. Comprson of forcsng rsuls by dffrn forcsng mhods n Dcmbr. Prdcon mhod Acul vlu Prdcv vlu Rsdul On-prmr xponnl smoohng On-prmr xponnl smoohng For h bov prdcon mhod, h hr ccurcy msurs MAPE, MAD nd MSD r shown n bl, snc hs vlus of h wo-prmr xponnl smoohng mhod r smllr, cn b concludd h hs mhod s br fd o hs d. hs s conssn wh h prvous nlyss. bl. Rsdul comprson of dffrn prdcon mhods. Prdcon mhod MAPE MAD MSD On-prmr xponnl smoohng wo-prmr xponnl smoohng I should b pond ou h h bov-mnond prdcon mhod hs no mrs. For dffrn d, s prdcon ffc s dffrn, nd o choos h ppropr mhod ccordng o h spcfc suon. h sm forcsng mhod cn lso ffcvly mprov s prdcon by djusng s smoohng prmrs. Conclusons h pplcon xmpl shows h h m srs nlyss chnqu cn mk full us of hsorcl d nd conrol h mcro-rnd nd h mcro-flucuon. h forcsng rror cn b conrolld whn 5%. A h sm m, h mhod proposd n hs ppr no only ppls o h prdcon of von qupmn rdnss r, bu lso o ohr qupmn ndxs or prmrs wh m srs chrcrscs, such s qupmn flur r, flgh sfy ccdn r nd r mrl spr prs consumpon, whch provds scnfc mhod nd mns for qupmn suppor forcs. Rfrncs [] Ynmng Yng, Yng Go, Rul Zhng. Sscl Anlyss nd Applcon of Quly Mngmn. Bjng, snghu Unvrsy Prss, 5. [] MLA Goodwn, Pul. h Hol-Wnrs Approch o Exponnl Smoohng: 5 Yrs Old nd Gong Srong. Forsgh h Inrnonl Journl of Appld Forcsng 9():-. [] ylor, J W. Shor-rm lcrcy dmnd forcsng usng doubl ssonl xponnl smoohng. Journl of h Opronl Rsrch Socy 54.8(): [4] Osmn, Ahmd Frd, nd M. L. Kng. A nw pproch o forcsng bsd on xponnl smoohng wh ndpndn rgrssors. Monsh Economrcs & Busnss Sscs Workng Pprs (5). [5] Hyndmn, Rob, l. Forcsng wh Exponnl Smoohng. Sprngr 6.(8):4-5. [6] Brown, Robr G. Exponnl Smoohng. Sprngr US,. [7] Informon on hps://n.wkpd.org/wk/exponnl_smoohng. 5