Implementation of Lean Manufacturing Through Learning Curve Modelling for Labour Forecast

Transcription

1 Ieraioal Joural of Mechaical & Mecharoics Egieerig IJMME-IJENS Vol:09 No:0 35 Absrac-- I his paper, a implemeaio of lea maufacurig hrough learig curve modellig for labour forecas is discussed. Firs, various learig curve models are preseed. The he models are aalyzed i erms of heir advaages ad limiaios. As a case sudy, he learig curve modellig is preseed wih he daa derived from a producio compay. Wih he applicaio of he learig curve, labour eed ca be more accuraely prediced ad scheduled o ime. Idex Term-- Learig Curve. Implemeaio of Lea Maufacurig Through Learig Curve lig for Labour Forecas Forecas, Labour, Lea Maufacurig, ad. INTRODUCTION The erm learig curve describes he relaioship bewee he amou of learig ad he ime ake o do so [2, 3, 5-7]. I his paper, learig curves are used o forecas labour-hours for he purpose of plaig o mee fuure demads. There are may differe models for learig curves. Each will focus o a differe aspec or may be for a differe applicaio. Each compay or idusry will have is ow uique learig curve. Learig curves are based o daa colleced from prelimiary uis so his daa mus be accurae. There are several facors ha may ifluece he learig curve. Chages i saff, desig or procedure will aler he learig curve. Learig curve for workers, idirec labour ad maerial are differe from each oher. Culure of workplace or resource availabiliy may chage curve (i.e. a he ed of asks operaors lose ieres). Whe workig o muliple projecs workers forge ad reduce learig curves. I order o maiai learig curves ad sudy i, he maageme s abiliy o pla, impleme ad corol aciviies of he orgaisaio have o be of a accepable sadard. I he ex secios, omeclaure ad various ypes of learig curve models are discussed. A case sudy i a producio compay is preseed o show he learig curve modellig for labour forecas. Fially, a lis of learig curve models i erms of advaages ad limiaios are summarized. 2. NOMENCLATURE The followig parameers are used i learig curve modellig: = Performace ime o complee h cycle (secods) Idra Guawa Deparme of Mechaical ad Maufacurig Egieerig Aucklad Uiversiy of Techology, Aucklad, New Zealad idra.guawa@au.ac.z = Performace ime o complee s cycle (secods) Φ = Rae of learig (%) b = Learig curve cosa = Cycle umber ^ = Cumulaive average of he ime o complee he h cycle (secods) B = Experiece facor M = Icompressibiliy facor R = Producio rae a R c = Sarig producio rae R f = Seady sae producio rae τ = Time cosa d = Number of imes producio has doubled. = Repeiio umber MAD = Mea Absolue Deviaio MSD = Mea Squared Deviaio A() = Acual daa for f() = Prediced values for 3. LEARNING CURVE MODEL Various ypes of learig curve models are discussed below. 3. Power This basic model was firs described i 936 by Theodore Paul Wrigh i he aircraf idusry as he firs mahemaical model for learig [8]: Where b () 00(2) b This is a basic approximaio of he learig pheomeo. I does o accou for he smoohig of he curve, i.e. learig does o go o forever. Each ime producio is double he performace ime is reduced by fracio b []. 3.2 Arihmeic This is he simples mehod of modelig learig curves: d (2)

2 Ieraioal Joural of Mechaical & Mecharoics Egieerig IJMME-IJENS Vol:09 No:0 36 This model lacks flexibiliy as producio imes ca oly be deermied for quaiies doubled, i.e. 2, 4, ad 8 [4]. Noe he chage of omeclaure i he equaio for arihmeic approach. This was o avoid cofusio of parameers amogs differe models. 3.3 Cumulaive Power This model is based o he relaioship bewee direc labour ma-hours o he cumulaive umber of uis produced: ^ b This model was developed by researchers whe he regressio value wih he power model was uaccepably low. This model dampes ou he wild daa pois because i is a coiually averagig process []. I has higher R 2 values compared o he power model. 3.4 Saford B This is aoher modificaio of he Power model: T ( B) b (3) (4) B is he experiece facor of he operaor (bewee ad 0) ad a ypical value of 4 is usually used. For small values of B his model asympoes fairly rapidly o he regular power model. Clearly his model was ideed for use o learig curves of large producs like aircrafs []. 3.5 DeJog s Learig This model akes io accou he maual ad machie processig imes. I icludes a icompressibiliy facor (M) for asks ha have machie compoes. I is based o he fac ha machie imes do o icrease ad remai cosa regardless of experiece []. M ( M) (5) Where M is he raio of performace ime afer ifiie cycles over performace ime afer s cycle (0 M ). Whe here is o machie coe M = 0. cycles are required o reach he limiig value. There has bee o field daa o suppor his model. 3.6 Dar-El s Modificaio of De Jog s The icompressibiliy facor is redefied as applyig o all ask elemes. By raisig he origial power curve by A, a ew learig curve lie is creaed. ^ A (6) This model elimiaes he drawback of he power model i ha i does o ed zero afer a ifiie umber of repeiios. 3.7 Dar-El/Ayas/Gilad b This was geeraed whe research daa was poorly mached o all kow models. Predicio based o early daa eds o uderesimae ad predicios based o laer daa ed o overesimae. This poor fi occurred due o wo separae ypes of learig occurrig simulaeously, cogiive ad moor learig. Cogiive learig icludes decisio makig, followig isrucios, learig complex sequeces, ierpreig measuremes, ec. This ype of learig is much faser. Moor learig is a lo slower. I cosiss of he physical moveme required i order o complee a ask (i.e. lower b value ha cogiive). Cogiive learig domiaes iiially, afer which moor learig domiaes as he umber of repeiios ges larger. 3.8 Bevis Towill Learig This model uses a expoeial law o show he oupu as a fucio of ime. I has a maximum level which is more realisic ha he power model []. R Rc R f e Where τ = he ime cosa This model is o pracical o apply as he variables o which he model is based are hard o collec. For his reaso here are o applicaios of usig his model. 4. CASE STUDY-COMPANY PRODUCTION Lea maufacurig is a echique ha is commoly implemeed by producio ad projec maagers o improve produciviy ad reduce wasage. Meal Skills Ld is oe of New Zealad s larges maufacurers of shee meal producs. Their cusomers iclude US, Ausralia ad Domesics maufacurers. The objecive of his sudy was o ulimaely improve he compay s abiliy o mee deadlies. This was o be doe hrough he learig curve modellig for labour forecas. I order o fid specific models ha ca be applied o his compay, daa was required o be colleced. The procedure followed was o ge permissio from he maagig direcors o observe he workers afer i was cleared by he shop floor maager. Oce his was doe healh ad safey regulaios eeded o be explaied ad abided by. Fially permissio was gaied from he worker beig observed so ha hey would o feel sigled ou. I order o be able o predic job imes i is esseial ha he curre learig rae be evaluaed. I order o do his, daa was colleced from he shop floor ad compared o he models for learig previously measured. The he model ad learig rae ha is mos applicable o he compay are derived. Learig raes will vary bewee employees, deparmes ad each idividual job. There will be a lo of work ad daa aalysis required if here was o be a differe model se up for every differe variable. Therefore for he scope of his projec a geeral learig curve rae eeds o be foud as a suiable (7)

3 Ieraioal Joural of Mechaical & Mecharoics Egieerig IJMME-IJENS Vol:09 No:0 37 model chose. The required daa was colleced from he foldig deparme as show i Fig.. This deparme was seleced for some of he followig reasos: ) This is oe of he boleecks i he facory. The oher boleeck was he weldig bay, bu due o healh ad safey sadards required, daa collecio would have bee difficul, 2) I has more maual compoes ha ay oher deparmes, excep weldig, 3) I is he mos uilised deparme i he facory, 4) Requires careful schedulig as i has he larges umber of workers ha ay oher deparmes.whe collecig daa i was impora ha he firs cycle ime recorded was ake for he firs cycle of ha bach so ha he value was valid. May ses of daa were colleced bu hree mai baches were used for aalysis. of daa was calculaed, where: MAD MSD BIAS i i i f ( ) A( ) f ( ) A( ) f ( ) A( ) 2 (8) (9) (0) Three ses of daa are colleced ad he highlighed values as he mos accurae daa for ha saisical measure are show i Table I. Fig.. A Press Brake Machie Usig saisical aalysis he accuracy of each model o each se T ABLE. SUMMARY OF LEARNING CURVE MODELS Pow er Cumulaive Saford B De Jog's Learig Arihmeic 96% 95% 97% 96% 96% 97% 84% 82% 99% 98% 89% 88% MAD MSD BIAS Pow er Cumulaive Saford B De Jog's Learig Arihmeic 97% 98% 98% 97% 98% 97% 90% 85% 00% 99% 89% 88% MAD MSD BIAS Pow er Cumulaive Saford B De Jog's Learig Arihmeic 94% 93% 95% 96% 94% 93% 60% 55% 96% 97% 87% 88% MAD MSD BIAS

4 Ieraioal Joural of Mechaical & Mecharoics Egieerig IJMME-IJENS Vol:09 No: LIMITATIONS AND SUMMARY OF LEARNING CURVES There are some limiaios of usig learig curves ha a compay eed o be made aware of i order o make proper use of learig curves [4]: Learig curves vary from oe idusry o aoher ad also bewee compaies i he same idusry. So i is impora ha a compay s ow learig curve is developed raher ha jus applyig someoe else s. Learig curves are based o he daa colleced for imes observed. So i is impora ha his daa is cosise ad as accurae as possible. To maiai accuracy re-evaluaio is ecessary as imes progress. The learig curves developed for a compay are uique o ha compay ad he persoel employed a he ime of he daa collecio. As saff chages so will he learig curve. Learig curves are oly applicable o direc labour ad o for idirec labour ad maerials. Learig curves are also affeced by resource availabiliy ad chages i he process as well as culural chages. Learig curve models are summarized below i Table II accordig o heir advaages ad limiaios: From he eigh models ivesigaed oly six were acually compared agais daa colleced a he compay. The Bevis/Towill model was excluded as he parameers are difficul o obai from field daa ad here are o kow examples of his beig used. Dar El s modificaio o De Jog s model was also excluded as he ime i moio ables appropriae for his compay were o made available. Daa se ad 3 demosraed he expeced red. The red of TABLE II COMPARISON OF LEARNING CURVE MODELS Advaages Limiaios Power Cumulaive Saford B DeJog's Learig Dar-El's Modificaio o DeJog's Bevis/Towill Learig Arihmeic Simple ad easy o use Dampes ou 'wild' daa pois Icludes a experiece facor Takes io accou ha machiig ime is o compressible wih respec o experiece Icompressibiliy facor redefied o apply o all asks Elimiaes he drawbacks of power model Accou for separae cogiive learig ad moor learig raes Has a maximum learig rae Simples mehod Performace ime approaches zero as umber of repeiios becomes large Smoohig masks impora chages Ieded for use i idusries wih large producs like aeroplaes Wih small B values i is almos ideical o power model No field daa o suppor his model Whe he umber of repeiios is less ha 50 he icompressibiliy has o effec Complex o apply Requires elecroic spreadshee o fid parameers Grea difficuly i fidig he parameers o apply his model Lacks Flexibiliy Oly fids imes for doubled uis. daa colleced i sample 2 was uexpeced. A reaso for he flucuaig imes was ha he acual cycle ime was so small ha he huma error grealy affecs he daa. The oher wo samples had cycle imes ha were much loger so he huma error made up a smaller compoe of he ime. I order o ge as accurae as possible imes o ormal producio raes i was impora ha he workers were comforable beig imed ad ha hey were made aware of he

5 Ieraioal Joural of Mechaical & Mecharoics Egieerig IJMME-IJENS Vol:09 No:0 39 reasos for he observaios. Workers were imed for he ed of a bach ad he he daa recorded was from he sar of he ex bach. This was doe so ha workers would be accusomed o he daa collecor before he esseial daa was ake, hus reducig some of he error. Usig each model a predicio was made usig several differe learig raes. Each of hese was saisically compared o he acual daa colleced. Each se of daa had differe models ha were mos accurae, bu o he whole he power model was cosisely oe of he mos accurae. Miimizaio of he MSD, MAD ad BIAS were doe usig solver o fid he opimum learig rae for each model. The mos suiable learig curve rae was 96%. 6. CONCLUSION A variey of learig curve models were cosidered ad aalysed. A learig curve has bee ideified o sui he compay s producio. This is he Power wih a learig rae of 96%. This was seleced as i is applicable o a wide rage of producio processes hroughou he facory. The oher models were rejeced afer aalysis as hey were foud o be isufficie o he eeds of he compay. The seleced model was he validaed agais daa colleced i he facory ad hus is applicaio was jusified. Applicaio of his learig curve will beer equip he compay o maage job imes ad herefore be able o schedule more accuraely ad quoed due daes achieved wih higher success rae. REFERENCES [] Dar-El, E. (2000). Huma Learig: From Learig Curves o Learig Orgaisaios: Kluwer Academic Publisher. [2] David A Nembhard, N. O. (200). A Empirical Compariso of Forgeig s. IEEE Trasacios o Egieerig Maageme, 48(3), [3] Eber, R. J. (976). Aggregae Plaig wih Learig Curve Produciviy. Maageme Sciece, 23(2), [4] Heizer, & Reder. (2006). Operaios Maageme (8h ed.): Pearso Preice Hall. [5] Kamisky, P., & Lee, Z.-H. (2008). Effecive o-lie algorihms for reliable due dae quoaio ad large-scale schedulig. Joural of Schedulig, (3), [6] Shabay, D., & Seier, G. (2008). Opimal due dae assigme i muli-machie schedulig eviromes. Joural of Schedulig, (3), [7] Walers, D. (2002). Operaios Maageme-Producig Goods ad Services (Secod ed.). Essex: Pearso Educaio Limied. [8] Wrigh, T. P. (936). Facors affecig he cos of Airplaes. Joural of Aeroauical Scieces (3(4)), Idra Guawa is a Seior Lecurer i he Deparme of Mechaical ad Maufacurig Egieerig a Aucklad Uiversiy of Techology, New Zealad. He obaied his Ph.D. degree i Idusrial Egieerig from Norheaser Uiversiy, USA. His mai areas of research are reliabiliy egieerig, producio ad operaios maageme, applicaio of operaios research, applied saisics, probabiliy modelig, ad projec maageme. His work has appeared i Ieraioal Joural of Projec Maageme; Ieraioal Joural of Reliabiliy, Qualiy ad Safey Egieerig; Reliabiliy Egieerig ad Sysem Safey; Applied Mahemaical lig; Ieraioal Joural of lig ad Simulaio; Ieraioal Joural of Performabiliy Egieerig ad oher publicaios.