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1 Uiversity of Huddersfield Repository Shagluf, Abubaker, Logstaff, Adrew P. ad Fletcher, Simo Derivatio of a cost model to aid maagemet of CNC machie tool accuracy maiteace Origial Citatio Shagluf, Abubaker, Logstaff, Adrew P. ad Fletcher, Simo (2015) Derivatio of a cost model to aid maagemet of CNC machie tool accuracy maiteace. Joural of Machie Egieerig, 15 (2). pp ISSN This versio is available at The Uiversity Repository is a digital collectio of the research output of the Uiversity, available o Ope Access. Copyright ad Moral Rights for the items o this site are retaied by the idividual author ad/or other copyright owers. Users may access full items free of charge; copies of full text items geerally ca be reproduced, displayed or performed ad give to third parties i ay format or medium for persoal research or study, educatioal or ot for profit purposes without prior permissio or charge, provided: The authors, title ad full bibliographic details is credited i ay copy; A hyperlik ad/or URL is icluded for the origial metadata page; ad The cotet is ot chaged i ay way. For more iformatio, icludig our policy ad submissio procedure, please cotact the Repository Team at: E.mailbox@hud.ac.uk.

2 Joural of Machie Egieerig, Vol. 15, No.2, 2015 Abubaker SHAGLUF 1* Adrew P. LONGSTAFF 1 Simo FLETCHER 1 dowtime cost, machie tools, predictive calibratio, accuracy DERIVATION OF A COST MODEL TO AID MANAGEMENT OF CNC MACHINE TOOL ACCURACY MAINTENANCE Maufacturig idustries strive to produce improved compoet accuracy while ot reducig machie tool availability or productio throughput. The accuracy of CNC productio machies is oe of the critical factors i determiig the quality of these compoets. Maitaiig the capability of the machie to produce i-tolerace parts ca be approached i oe of two ways: ru to failure or periodic calibratio ad moitorig. The problem is aalogous to geeral machie tool maiteace, but with the clear distictio that the failure mode of geeral machie tool compoets results i a loss of productio, whereas that of accuracy allows parts to be produced, which are oly later detected as o-coformig as part of the quality cotrol processes. This distictio creates problems of cost-justificatio, sice at this poit i the maufacturig chai, ay resposibility of the machie is ot directly evidet. Studies i the field of maiteace have resulted i cost calculatios for the dowtime associated with machie failure. This paper addresses the aalogous, uaswered problem of maitaiig the accuracy of CNC machie tools. A mathematical cost fuctio is derived that ca form the basis of a strategy for either ruig util o-coformig parts are detected or schedulig predictive CNC machie tool calibratios. This is sufficietly geeric that it ca cosider that this decisio will be based upo differet scales of productio, differet values of compoets etc. Therefore, the model is broke dow to a level where these variables for the differet iputs ca be tailored to the idividual maufacturer. 1. INTRODUCTION Maufacturig compaies across the globe are icreasigly cocered about their ability to iovate ad compete i the fast-chagig techology world. Complex ad highvalue maufacturig ofte requires a high level of accuracy; the demads of cosumers ad ed-users are for lower cost, more efficiet ad resource-lea products. CNC machie tools used for productio are required to operate withi accepted limits of tolerace, which become ever tighter with the availability of ew eablig techology ad greater customer drive. Notwithstadig this ambitio for higher accuracy, icreased availability of productio machies is a fudametal requiremet to maitai competitiveess. These two goals ca be perceived as havig coflictig requiremets; time to maitai accuracy 1 Cetre for Precisio Techologies, Uiversity of Huddersfield, UK * abubaker.shagluf@hud.ac.uk

3 18 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER ca be at the expese of time for producig parts. However, the push for icreased availability must take ito accout the eed that this availability is to produce parts withi tolerace, ot o-coformig parts. Therefore, a suitable strategy is eeded to maitai accuracy without imposig too oerous a regime i terms of lost productio durig measuremet. Machie tool failures i idustrial orgaisatios iterrupt productio operatios ad cause productio loss, which has a direct cost-to-busiess ad potetially a sigificat detrimetal impact to future productio. These failures of mechaical or electrical elemets are ofte biary, where the machie either works or is uable to produce. Here, the eed for repair is clear. However, the failure mode for accuracy is somewhat more complex. No part is ever made perfectly ad o measuremet is exactly correct. Therefore, achievig toleraces o maufactured compoets is oly assured if the sum of all sources of iaccuracies does ot exceed the total tolerace. This i itself cotributes to the discussio of machie accuracy, sice it represets oly oe compoet of the total error budget ad solutios are ofte foud by makig compesatig adjustmets i other areas. For example, by compesatig with small offsets to the CNC program or work-piece offsets, modificatios to part aligmet or fixtures, etc. Herei lies the mai argumet agaist regular maiteace of the machie to preserve accuracy; a machie ca cotiue to produce parts by adaptig the process to suit chagig coditios. There is therefore ofte a resistace to sped time uderstadig the error budget at a graular level if the overall statistical process cotrol (SPC) results show good cosistecy. There are a umber of ways i which the machie ca remai reliably capable: usig a machie with sigificatly better accuracy tha required to meet compoet tolerace, although this requires a higher capital ivestmet makig frequet, mior corrective actios, although this ca reduce traceability ad ca itroduce uwated variability predictive maiteace, focusig o the accuracy aspects of the machie, although this ca impact o machie availability I fact, applicatio of each of these strategies ca be justified for differet circumstaces. This paper does ot seek to provide a uiversal aswer to the questio of the best strategy, but rather provides the derivatio of a mathematical tool that ca be applied to a wide sample of machiig processes to uderstad better the cost of maitaiig machie accuracy, but also the implicatios of o-coformace. Predictive maiteace for accuracy, or predictive calibratio (PdC), is oe possible way of esurig the machie is capable of achievig toleraces ad ca form part of a cotiuous improvemet process i maiteace [11]. This would allow schedulig of time to carry out measuremet tasks to esure that accuracy levels were maitaied. The coverse is true; where high productio rates are demaded, the this ca affect the ability to meet PdC requiremets. The problem is exacerbated where two idepedet departmets have owership of the coflictig Key Performace Idices (KPIs); the maiteace departmet is required to esure accuracy, while the productio departmet is measured agaist productio rate. This is why a compay-wide uderstadig ad approach is vital [16].

4 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 19 Maiteace programs such as Total Productive Maiteace (TPM), recommed what is called autoomous maiteace, which aims to icrease the skill levels of maiteace persoel so they ca better uderstad, maage ad improve their machies ad the productio process. The objective is to chage workers from beig reactive to proactive, to achieve optimal coditios that elimiate stops as well as reducig the productio of o-coformace parts, rejects ad machie failures [16]. Predictive maiteace (PdM) is oe approach that has bee successfully applied to mitigate the effects of uexpected failure by schedulig cotrolled productio stoppages [20], rather tha reactig to a breakdow. Predictive maiteace is a tool that has bee adopted i some idustries to improve operatioal efficiecy ad reduce maiteace cost [3]. As a result, moitorig equipmet that provides iformatio about the coditio of maufacturig systems has evolved rapidly over recet years. Calibratio is a fudametally accepted process required to maitai the quality of measurig machies [14]. It ca also be applied to the productio process to help cotrol output quality ad maitai the credibility of the machie tool for measuremet, such as iprocess probig [2]. Full machie tool calibratio requires measuremet of a umber of error sources; there are 21 sources of error for a 3-axis machie tool, with may more o complex machies, typically takig up to oe week of measuremet time o large machies. The reaso for repeatedly calibratig a istrumet, machie tool or ay other machie is that their performace ca drift over time ad usage i both their mechaical ad electrical respose. Whe cosiderig machie tool accuracy, beddig i, wear of compoets ad collisio are some reasos for this chage. The prescribed iterval betwee calibratios teds to be subjective; a fixed aual calibratio is sometimes adopted as part of a quality paper-trail, but more likely calibratio is udertake as a reactio to chage i the cosistecy of the machie s output. Buildig a database of ispectio history by measurig the machie o a regular basis, ideally with relatively o-ivasive methods, would make the decisio of schedulig the more extesive calibratio a better-iformed process. Successful measuremet depeds o accurate metrology systems (equipmet ad software) that are traceable to iteratioal stadards, a uderstadig ad miimisatio of measuremet ucertaity assisted by applicatio of good measuremet practice. Schweke ad Kapp [15] stated that whe reportig the error parameters of a machie, a ucertaity must be coected to the reported umbers. Thus the usefuless of the measuremets ca be determied; parameters ca be compared to their specificatios, takig the measuremet ucertaity ito accout. Ucertaity is defied as a o-egative parameter characterisig the dispersio of the quatity values beig attributed to a measurad, based o the iformatio used [1]. The effect of ucertaity ca have a sigificat impact o productio quality cotrol. Fig. 1 1 illustrates the coformity ad o-coformity zoes based o the ucertaity value ad the lower ad upper specificatios limit. The remaider is ucertai. From this illustratio oly measuremet values that fall withi the coformace zoe are certai, withi the give cofidece level, to be withi the tolerace. Miimisig the ucertaity of measuremet ca icrease the coformace zoe, reducig false acceptace ad rejectio [12].

5 20 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER Fig. 1. The effect of measuremet ucertaity o reducig the specified tolerace bad whe examiig coformity, U is the measuremet ucertaity [1] However, this is where potetial coflict ca arise; miimisig dowtime might icrease ucertaity, which is to say reduce data quality. Maufacturig idustries eed their productio machie tools to be measured quickly. However, quick checks ca cause iaccuracy if they are ot well performed. Measuremets should be reliable i idetifyig the dimesios of cocer to the degree of accuracy required ad should be sufficietly robust to elimiate false positives. Measuremets should be coducted i accordace with stadard procedures. These could be accordig to iteratioal (ISO), atioal, compay or origial equipmet maufacturer (OEM) stadards to allow the ease of traceability of the test method. This will eable test reproducibility for differet users ad improve efficiecy [19]. As discussed, PdC ca be used as part of a hybrid maiteace strategy. However, the egative factors are the cost of the metrology equipmet eeded ad the ecessary skilled labour ad traiig costs required to use them effectively. Additioally, such measuremets ca oly be take whe the machie is ot producig parts, thus the opportuity cost must be cosidered. Establishig a optimised PdC strategy is a o-trivial task that must be rolled out as a cotrolled process programme, takig ito accout the available techology ad their relative merits. Table 1 provides brief compariso betwee differet calibratio ad measuremet approaches. Sice may prevetative (ispectio, calibratio) tasks for maitaiig the accuracy of CNC machie tools require them to be removed from productio, the evaluatio of dowtime cost has become a key issue i optimisig the frequecy of calibratio ad maiteace actios [22]. The dowtime of the machie is a importat part of the cost calculatio. I the product maufacturig cycle, several egieerig tasks like machiig desig, process plaig ad machie maiteace/calibratio schedulig have to be performed. The implemetatio of these tasks, i particular calibratio actios, maily ivolves iformatio processig ad decisio-makig. If this ca be performed i parallel to part

6 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 21 productio the the cost has less impact tha if it is sequetial ad requires the machie to stop outputtig parts. Therefore, dowtime for calibratio is ofte see as a o-valueadded cost. Table 1. Compariso betwee calibratio approaches [17] Aspect Quick check tests Full calibratio O-machie artefact probig Post-process measuremet Typical Duratio 30 miutes [21] 2 to 5 days [9] 5 to 10 miutes A few hours Target Measure ad moitor Measure ad compesate Check, aalyse ad rework to icrease part quality Ispect the work piece Eviromet Data suitable for compariso Workshop eviromet Statistics ad process cotrol Workshop eviromet Statistics ad process cotrol. More skilled iterpretatio Workshop eviromet Statistics ad process cotrol Cotrolled eviromet Statistics ad process cotrol Process Occurs while the machie is ruig but machiig process iterrupted Occurs while the machie is out of productio Performed as part of machiig procedures Occurs after machiig ad off the machie Access Operator Skilled Operator Skilled Risk of missig importat data High risk due to low coverage Low risk due to high coverage Low to Medium risk depedig upo relevace of artefact to part Low risk Machie dowtime ca be uderstood as the time whe the machie is ot producig saleable parts. However, Yam defied dowtime as: The amout of time a machie or system is ot fuctioig due to stoppages i a give shift or time period. He stated that dowtime should ot iclude idle time or time the machie or system is waitig for iputs. Therefore dowtime depeds o stoppages ad compay policies [24]. Whether plaed or uplaed, such lost productio is ituitively costly to maufacturig orgaisatios [6]. It is essetial to estimate dowtime costs i order to support maufacturig decisio-makig. Crumrie ad Post [5] stated that factories could lose from 5% up to 20% of their productive capacity because of dowtime. They also estimate that 80% of idustrial facilities are uable to estimate their dowtime accurately, ad suggested that may facilities uderestimate their total dowtime costs by as much as %. The great majority of machie tool uavailability is the result of plaed dowtime that occurs due to required maiteace. Although uplaed dowtime may accout for 10% of all dowtime, its uexpected ature meas that ay sigle dowtime icidet may be more damagig to the idustry, physically ad fiacially, tha may occurreces of plaed

7 22 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER dowtime [4]. To put this ito a fiacial cotext, typical hourly rates for machie tools are estimated betwee 90 ad 175 per hour. Justificatio is eeded if this time is spet i calibratio rather tha productio. Jatue ad Baglee [7] stated that; Very little is kow or published about the importace ad the role of various failure models i differet idustrial sectors. Thus, if failure models are ot uderstood ad hadled properly, the use of coditio-based maiteace caot lead to fiacial beefits. Existig studies i the field of predictive maiteace have resulted i cost calculatios for the dowtime associated with machie failure [13]. However, there is a lack of the availability of a global model that could be used for ay machie tool sceario. It could be said that although PdC ad PdM are differet applicatios, they ca follow the same dowtime cost calculatio process to decide their applicability for a give asset. The surveyed literature was commoly foud to be focused o specific idustries ad coditios ad oly ivestigated dowtime costs associated with productio loss ad igored other possible added costs due to dowtime [18]. This paper presets a derivatio of a cost model to aid maagemet of machie tool accuracy maiteace, with variable iputs depedig upo the levels of productio ad product value, cost of labour iputs ad dowtime required for calibratio actios. 2. COST MODEL APPROACH The proposed methodology is to cosider the machie tool accuracy problem ad error measuremet related costs from istallatio. This algorithm is iteded to lead to a calculator that could predict the beefits of differet maiteace regimes based upo differet factors such as volume ad value of maufacturig. This algorithm ca be used as part of a optimisig techique to determie the most appropriate of these calibratio approaches, adoptio of which could also icrease the mea time to failures (MTTF) of machies. This work will ultimately lead to a techical-drive maagemet tool that ca optimise the frequecy of calibratio to reduce uecessary dowtime while maitaiig the machie at the required tolerace. It is worth statig explicitly that the optimal umber of PdC actios ca be zero i some cases; there are scearios where PdC is ot the most suitable approach. The emphasis i this sectio will be o the idetificatio of the elemets of direct ad idirect costs related to the machie tool accuracy problem. Sice the majority of practical models i maiteace field are based o ambiguous data e.g. (subjective data, expert opiios), it is importat to expose i the model cost factors that could otherwise be overlooked, or be otherwise form part of a lumped model. Reasoable assumptios of those factors that have a idirect cotributio to the dowtime cost should ot cause major problems [23]. Total costs of machie tool dowtime are composed of several differet cost elemets. Breakig dow the factors that cotribute to determiig the dowtime cost is ecessary to cover a broad rage of machie tool assets, productio types ad scales. Dowtime costs must be calculated per evet. Thus; calculate/record the time from the first occurrece

8 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 23 of machie tool breakdow to the time whe machie tool was back ito full productio. The first step i the cost estimatio is to make a process map for the dowtime related sources of costs. This is show i Table 2. Table 2. Machie tool accuracy related source of costs Source of cost Cost of measuremet equipmet (metrology) Measuremet labour Lost productio Utilities ad tools Measuremet/ Bechmarkig Explaatio Direct or idirect where you metrology eed to be hired. If it is direct, a cost of traiig ad calibratig the measuremet equipmet may eed to be added. Iteral or exteral labour. This icludes the cost of machie operator to drive the machie aroud. Cotractor iductio may be icluded uder this cost. Cost of lost productio durig measurig the machie. Temporary utilities ad tools icludig eergy ad coolig. Start-up of productio Warm-up cycle Cost of pass-off part The cost due to resettig ad warm up period. This icludes offset adjustmet, program selectio ad replacemet of fixtures. This is assumed to be a sigle process. This icludes: Raw material, cuttig tool, eergy, coolat, air compressor, eergy, ad machiig cost. Cost of o-coformace Scrap Rework Late pealties This icludes lost productio, raw material, ad cost of productio processes. Recyclig of the scrap material might be a icome if it could be sold or a loss if it caot be sold. Icludes the ispectio, ivestigatio, quality cotrol extra hours due to rework ad lost productio durig rework. Pealties, fies ad shippig costs due to o-coformace parts. Cost of reactio Cost of reactio This could iclude: Additioal quality cotrol tests, measuremets, maagemet ivolvemet, lost cofidece implies possible additioal quality cotrol, ad reduce throughput. Cost of low accuracy iefficiecy Cost of waitig to react Time for quality cotrol to detect o-coformace Low accuracy iefficiecy This icludes: Icreased tool wear, reduced efficiecy (feed rate), ad cost of shift chage to overcome problems. This will icrease the risk of o-coformace. Lost productio This icludes the time to: Travel to quality cotrol, temperature stabilisatio of the part, time to measure o CMM, ad time to report back to productio maager.

9 24 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER Typical part maufacturig plaig is summarised i Fig. 2, which shows that it is divided ito two stages. The first stage is the part desig, where the study ad preparatio for the desired desig criteria takes place. This is followed by the part maufacturig process, where the material is procured, rough-machied, fiish-machied ad ispected. Fig. 2. Part Maufacturig Plaig 3. COST MODEL DERIVATION The followig amig covetio is used throughout: CV A CR B QV C T D t (i) QC PPI QC IPI QC MC error mappig QC MC verificatio Cost value of A Cost rate of B; per hour. Quatity value C; a umeric, uitless value Time period D (hours) A istat i time Quality cotrol post process ispectio Quality cotrol I-process ispectio Quality cotrol Machie error mappig Quality cotrol Machie verificatio

10 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 25 First, assume a machie tool ru-to-fail sceario for the cost fuctio derivatio. There are o predictive calibratio actios ad detectio of failure oly occurs durig post-process ispectio (PPI) i the quality cotrol departmet. Fig. 33 shows machie tool ru-to-failure sceario ad its related costs. There is a period betwee t 1 ad t 3, betwee PPIs, where there is o feedback o the quality of the product. I this sceario, if the machie goes out of tolerace at time t 2 it could be assumed that the parts betwee t 1 ad t 2 have bee produced accurately but those produced betwee t 2 ad t 3 have ot. However, lack of feedback meas that the value of t 2 is ukow to the productio maagers; it could be aywhere betwee the two PPIs. There is a further amout of time betwee the PPI actio ad t 3, which is the time at which the productio is halted due to o-coformig parts detected. This time period could vary from miutes to days depedig upo the resposiveess of the productio departmet to detectio of o-coformace. There will also be a period of time for ivestigatio, T ivestigatio, icludig delay while the calibratio actio is scheduled, measuremet ad while remedial actio is take. Productio will be iterrupted while the machie is calibrated, the it will start agai at time t 4. Fig. 3. Machie tool; ru to fail sceario ad the related costs 3.1. COST PER PART The value of the part (product), ad therefore the cost of materials, is a importat compoet of the cost model. Material costs ca be divided ito direct ad idirect costs. The latter are those costs that are ot directly added ito the product. For example: coolat oil, lubricats for machies, uts, bolts ad screws. Direct costs are more sigificat for the calculatio because they are directly iput to the product; the cost of raw materials for a particular product is the mai cotributor. It is a fuctio of the amout of iput (raw) material ad its uit cost. The cost value of the part is represeted i more detail i equatio (1).

11 26 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER CV part = CR maufacturig T cycle + CV total iput compoets (1) Where: CV part is the value of the part at the ed of the maufacturig cycle; CR maufacturig is the cost rate of part productio i parts per hour (equatio (2)); T cycle is the cycle time i hours to produce oe part ad; CV total iput compoets is the total value of the raw materials per part (equatio (9)). Factory burde, also referred to as maufacturig overhead, is a idirect maufacturig-related cost that is icurred whe a part is produced. Alog with costs such as direct material ad direct labour, the cost of maufacturig burde must be assiged to each uit maufactured. CR maufacturig = CR total machiest labour + CR burde (2) Where: CR total machiest labour is the rate of total machiist labour, per hour (equatio (3)) CR burde is the cost rate of idirect maufacturig burde icurred durig parts productio per hour (equatio (5)). Direct labour is sometimes cosidered the most obvious loss durig a dowtime icidet [5]. However, if the part value per hour is high the the mai loss ca be the machie ot producig parts. Direct labour cost is the cost of labour applied to a particular product or usig a particular machie. This icludes the wages of labourers maufacturig the product. Some labourers are cosidered to remai idle for the period of dowtime, although the case where oly partial loss of productivity by the worker is cosidered i equatio (4). Direct labour cost ca be calculated by multiplyig the direct labour time ad wage rate. Traiig cost to direct labour cost is ot preseted separately sice it could be icluded i the labour cost itself. Hece, the total labour cost is calculated based upo how much labour is cotributed by differet persoel. It will be represeted as i equatio (3) to reflect differet workers with differet labour rates. The total cost of labour for the machiist could be expressed as: CR total labour machiist = QV i (labour machiist) CR i (labour machiist) i=1 Where: QV i (labour machiist) is the quatity of machiists labour ivolved i the productio process. CR i (labour machiist) is the cost rate of machiist, per hour. The quatity of labour refers to the umber of operators ivolved (machiists) i the productio process. It may or may ot be a iteger umber, depedig upo whether multiple tasks are performed i parallel by idividual workers. For istace, a operator workig o two productio machies i parallel would be cosidered as 0.5 i the umber of operators for each machie, although this divisio could be more accurately reflected depedig upo the itesity of labour required o a particular machie. There might be (3)

12 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 27 cases where two operators workig o the same machie are eeded, although this is ot commo. Uder this circumstace, equatio (3) would iclude multiple idices. 0 < QV i (labour machiist) 1 (4) Maufacturig burde icludes elemets such as electricity ad air supply used to operate the maufacturig machie ad other equipmet, depreciatio o the factory equipmet ad buildig, ad it might iclude factory persoel (other tha direct labour). Factory overhead icludes all maufacturig cost besides direct materials ad direct labour. It is used directly for productio, but it fails to be credited directly to a particular product cost. Most elemets of maufacturig overhead do ot have direct relatioship to processig of the product. I actual productio costig, if the workshop produces oly oe product the the maufacturig costs ca be reckoed directly i the productio cost of the product. Otherwise, the maufacturig cost is reckoed i various products by usig a reasoable allocatio method [10]. The cost rate of burde CR burde is defied as beig already calculated for the legth of time. For overall burde, it is simplified as a total 12 moths divided by a rate per hour time. The machie charge would have to cover all the costs. I order to do this, the umber of hours per year that the machie will be producig parts must be calculated ad divide this figure ito these costs. This will give a machie rate per hour. CR burde = (CR eergy + CR coolat + CR air comp eergy + CR lubricat + CR sudries + CR Machie depreciatio + CR others ) (5) Where: CR eergy is the cost rate of eergy cosumed durig part productio, per hour. The rest are the cost rate of coolat, air compressor, lubricat, ad sudries (other) used durig part productio per maufacturig hour. CR burde is differet durig productio ad o-productio. For example, whe the machie is ruig the air compressor will be active ad have ruig costs. If the machie is completely stopped durig a dowtime period the the cost will ot be icurred. Aother example is the potetially lower cost whe the machie is beig measured; the axes are movig, but the effect of cuttig force, rapid acceleratio, etc. will be much less oerous. For simplificatio, this will be dealt with separately i the assumptios made i the variables for the case studies i future work. To simplify the equatio i this paper, oly the eergy elemet (CR eergy ) of the cost rate of burde CR burde will be varied CR eergy ad the others remai costat for simplificatio. Therefore, the cost rate of burde equatio that will be used i this paper will be simplified to: CR burde = (CR eergy + CR others ) (6) There will be cases where the machie is ot i productio. For example, scheduled or uscheduled maiteace or stoppage due to detected o-coformig parts. Equatio (8) gives the cost value of o-productio CV machie o productio for the whole period where

13 28 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER the machie is ot producig parts. It is aturally a fuctio of the rate of costs (equatio (7)) ad duratio of stoppage. CR machie o productio = CR burde + CR idle labourer (7) Where: CR machie o productio is the cost rate of machie o-productio i per hour due to work stoppage due to ay cause. CR idle labourer is the cost rate per hour of idle labourer waitig for the machie to resume productio, per hour. T o productio is machie idle time, or waitig time. CV machie o productio = CR machie o productio T o productio (8) The cost of iput compoets to the maufacturig process ca be preseted as: CV total iput compoets = QV i(iput compoets) CV i (iput compoets) i=1 (9) Example1: A machie tool pallet that takes three iput compoets at a time to produce oe fiished part (Fig. 4). These compoets are perhaps of differet material or simply have differet values due to the umber of pre-machiig processes. Fig. 4. Example of a machie tool pallet that takes three differet iput compoets

14 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 29 Substitutig equatio (2) ad (9) ito equatio (1) gives the value of the part at the ed of the maufacturig cycle: CV part = ( QV i (labour machiist) CR i (labour machiist) + CR burde ) T cycle i=1 (10) + QV i(iput compoets) CV i (iput compoets) i= COST OF UNCONTROLLED PERIOD Cost of ucotrolled productio has a direct relatioship with the time spet to detect that the machie is producig o-coformig parts due to the machie goig out of accepted performig tolerace. The cost of a scrapped part is directly affected by variable maufacturig parameters such as eergy costs, raw material costs, time to maufacture, etc. For this reaso, the equatio produced i this study must be cosidered a live tool which must be reaalysed as these cost variables chage. CV Ucotrolled = CV scrap uits ucotrolled + CV rework uits ucotrolled (11) Where: CV scrap uits ucotrolled is the cost value of scrapped uits produced durig the ucotrolled period of productio. CV rework uits ucotrolled is the cost value of reworked parts produced durig the ucotrolled time of productio. QV ucotrolled parts maufactured is the quatity of uits maufactured durig the ucotrolled time of productio (equatio (12)). T detectio is the time at which faulty parts are detected (equatio (12)). T cycle is the part maufacturig time (equatio (12)). Defie: QV ucotrolled parts maufactured = T detectio T cycle (12) The: CV scrap uits ucotrolled = P scrap QV ucotrolled parts maufactured CV part (13) Cost value of rework might be a small percetage of the whole maufacturig process for the part. However, this will be decided by the legth of the time of the rework process.

15 30 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER CV rework uits ucotrolled = P rework QV ucotrolled parts maufactured CR maufacturig T rework (14) Substitutig equatio (13) ad equatio (14) ito equatio (11) gives: CV Ucotrolled = Pscrap QV ucotrolled parts maufactured CV part + P rework QV ucotrolled parts maufactured CR maufacturig T rework (15) Where P scrapad P rewo1rk are the probabilities of a scrap or part eedig rework respectively. P coformig is the probability that the part coforms despite the omial machie tolerace is beig exceeded. P scrap + P rework + P coformig = 1 (16) Example2: Assumig twelve hours of ucotrolled time before the machie out-oftolerace fault is detected, T detectio, ad that the machie takes two hours to make a part, the: QV ucotrolled parts maufactured = 12 2 = 6 ucotrolled parts maufactured. Example3: A productio of possible 100 parts durig a maufacturig cycle T cycle with probabilities of: P scrap = 10% umber of scrap items = 10 P rework = 70% umber of rework items = 70 P coformig = 20% umber of coformig items = 20 I the remaider of this discussio, the machie tolerace will be assumed to be exact; if the machie is out of tolerace the it is guarateed that parts will be produced out of tolerace). I this case, P coformig = COST OF EXTERNAL IMPACT OF PRODUCING NONCONFORMING PARTS The cost due to producig o-coformig parts may iclude losig cotracts due to reputatioal harm because of customer dissatisfactio [17]. It may also iclude the cost of shippig, fies ad pealties, delayed orders, or delivery of poor quality goods or services. A o-coformig part produced eeds either additioal part rework to maitai customer satisfactio or major activities will be required to rectify the situatio for the customer.

16 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 31 I this work the impact cost value of o-coformig parts customer impact is the additioal cost due to shippig ucotrolled parts. This is the split ito the case where faulty parts are detected upo receipt by the customer ad the case where the faulty part is the used by the customer with cosequetial damage. CV ocoformig parts customer impact = (CV Shippig + CV fies + CV pealties ) (QV ucotrolled parts maufactured (1 P coformig )) (17) Where: CV ocoformig parts customer impact is the cost due to producig o-coformig parts. CV Shippig, CV fies, CV pealties are the cost value of the additioal cost due to shippig ucotrolled parts. This is a simplificatio, as i some cases pealties will be o a time basis rather tha a umber of parts basis. Moreover, the problem of sedig faulty parts is a big cocer related to how much quality cotrol is effective. However, detailed cosideratio of this aspect is outside the scope of this paper. Nevertheless, the overarchig theme of the paper requires cosideratio be give to the value of cosequetial costs. If they are high the every part should be checked ad the eed to have more regular validatio of the machie ca also be justified. If the overall cost is lower the, this requiremet ca be relaxed 3.4. QUALITY CONTROL COST Process cotrol is cocered with moitorig quality while the product or service is beig produced. The costs of quality are essetially the cost of failures or defects ad tryig to avoid the failure of such as ispectio ad traiig [8]. It is very importat to cosider quality cotrol time related to quality ispectio. This usually ivolves seior/skilled persoel to iterpret data to fid fault. CV QC total = CV QC regular + CV QC reactive (18) Where: CV QC total is the total cost value of quality cotrol actios. CV QC regular is the cost value of regular cotrol ispectio which might iclude: CV PPI the cost of ay post process cotrol actio required, ad CV IPI the cost of i process actios take durig part maufacturig process (equatio (19)). CV QC MC error mappig is the cost value of regular machie measuremet.

17 32 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER CV QC MC verificatio is the cost value of ay quality cotrol actio eeded to double check that the machie is fuctioig properly eve after a regular machie measuremet but produced a faulty part. CV QC reactive is the cost value of reactive cotrol actios. It is ot goig to be simplified ay further here ad it will be take a sigle-value. Ad; CV QC regular = CV QC PPI + CV QC IPI + CV QC MC error mappig + CV QC MC verificatio (19) Machie error mappig might iclude both regular (proactive) ad irregular (reactive) machie calibratio. I the case where a critical (highly utilised) machie breaks, rapid reactive maiteace is likely to be demaded. Such a time-sesitive reactio will probably attract a premium o costs to have the fault remedied ad the machie back ito productio as soo as possible. However, QC M/C error mappig will be geeralised ad take as a siglevalue i this stage of the work. The terms required for equatio (18) ad equatio (19) are provided below: CV QC PPI = T totalppi CR PPI (20) Where: CR PPI is the cost rate of post process ispectio actio, per hour. T totalppi is the total time required to execute the post process ispectio evet. T trasport QC is the time required to take the uits to CMM checks. T temp stabilisatio is the time required to stabilise the ambiet temperature prior to the post process ispectio. T schedulig is the time required to schedule ad orgaise for a part or a patch of parts to be ispected. T report is the time to report back to productio maager. Ad; T totalppi = T trasport QC + T temp stabilisatio + T schedulig + (T PPI + T report ) QV PPI umber of parts (21) Where, QV PPI umber of parts is equal to oe ormally. Combiig equatio (20) ad equatio (21) we get: CV QC PPI = (T trasport QC + T temp stabilisatio + T schedulig + (T PPI + T report ) QV PPI umber of parts) CR PPI (22) Quality cotrol time is oe of the mai elemets of this cost fuctio, due to the focus o machie ad part accuracy.

18 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 33 Fig. 5. Machie idle durig post process ispectio It icludes the cost of checkig productio parts (samples). The latecy for quality cotrol to detect o-coformace i produced parts icludes the time for the part to travel to the ispectio facility, the time to thermally stabilise, the time to measure (for example o a coordiate measurig machie (CMM)) ad the time for the iformatio to be fed back to the productio maager i the form of a failure report. CV QC reactive = CV QC PPI cofirm + (CV QC PPI umeasured QV umeasured parts ) + CV QC MC error mappig + CV MC verificatio (23) CV QC PPI cofirm is the cost of makig a cofirmatio measuremet i the evet of fidig a o-coformig part; upo fidig a o-coformace the part might be re-ispected to cofirm the results. CV QC PPI cofirm ca be equal to the ormal cost of ispectio, CV QC PPI, or might differ if the cofirmatio process is a reduced subset of the overall measuremets. The time for trasportatio T trasport QC ad/or part stabilisatio, T temp stabilisatio, may be zero for the cofirmatio measuremet if the part did ot leave the ispectio facility. Coversely, this time may be greater if the part has already moved o to aother part of the maufacturig process, which might eve ivolve beig trasported to aother facility. Therefore, to recheck the part or to cofirm that the post process ispectio of the part (Fig. 5) is correct the followig equatio is eeded: CV QC PPI cofirm = (T PPI + T report ) QV umber of parts CR PPI (24) If the ispectio is doe i batches the the time to trasport, T trasport QC, ad time for thermal stabilisatio, T temp stabilisatio, will be uified across the batch, while QV umber of parts is the umber of parts i the batch. Otherwise, i the case where each part is idividually trasported, QV umber of parts=1. I the evet of detectio of o-coformace, further quality cotrol ispectio may be required. Assumig that oly a sample of parts are ispected, the referrig to Fig. 3, the actual time t 2, where the machie wet out of tolerace is ot kow. Therefore the parts that were ot ispected betwee PPI -1 ad PPI should ow be measured. The umber of parts affected is give by equatio (26). The cost of ispectig these umeasured parts is give i equatio (25), where CV QC PPI is give by equatio (22). I this case, the values for trasport ad stabilisatio time may vary from the regular ispectio process sice they will be diverted from their ormal process flow.

19 34 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER CV QC PPI umeasured = CV QC PPI QV umeasured parts (25) QV umeasured parts = ( t 3 t 1 T cycle ) 1 = ( t PPI t PPI( 1) T cycle ) 1 (26) 3.5. MACHINE ERROR MAPPING Machie error mappig is measurig the geometric errors of machie tools ad coordiates measurig machies. The cocept is based o classifyig the machie error mappig ito three stages as represeted i equatio (27). The cost of machie tool error mappig ca be expressed as: CV QC MC error mappig = CV preperatio for machiig part + CV measuremet of machie + CV startup after adjustmet (27) Where: CV preperatio for machiig part ; is the cost of preparatio for machiig a part after measuremet give by equatio (28). CV measuremet of machie is the cost of machie measuremet give by equatio (32). CV startup after adjustmet is the ispectio ad adjustmet eeded eve after machie full measuremet to reach a machie stable productio coditio give by equatio (36) COST OF PREPARATION OF MACHINING A PART CV preparatio for machiig part = T warmup_adjustmets_reloadig prog_applyig fix (CR adjustmet service + CR machie o productio ) (28) Where: T warmup_adjustmets_reloadig prog_applyig fix is the time required for machie warmup, adjustmets, reloadig programs ad applyig ay fixtures required prior to the maufacturig process. CR adjustmet service is the cost rate, per hour of ay adjustmet services might be eeded. This icluded the service workers ad the hire of the equipmet required (equatio (29)). For those maufacturig processes that require computer programmig of the equipmet as part of iitial set-up to produce a ew part, adjustmet ad programmig time as well as establishig work-piece offsets must be icluded i the cost of machiig a part

20 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 35 preparatio. Adjustmets iclude the cost value eeded for adjustig ad modifyig CNC codes ad parameters. CR adjustmet service = CR i (adjustmet service) QV i (adjustmet service) i=1 + CR i (adjustmet labour) QV i (adjustmet labour) i=1 (29) Substitutig equatio (7) ad equatio (29) ito equatio (28) gives: CV preperatio for machiig part = T adjustmets_reloadig prog_applyig fix (( CR i (adjustmet service) i=1 QV i (adjustmet service) + CR i (adjustmet labour) QV i (adjustmet labour) ) i=1 + CR burde + CR idle labourer ) (30) The: CV reactio to detected o coformace = CV QC reactive + CV machie o productio T ivestigatio + CR maagemet T ivestigatio (31) The adjustmet service hire cost per uit time is the rate for measuremet ad repair. This may iclude the daily rate expeses of labour travel, fuel ad accommodatio. The method of calculatio differs depedig upo the maiteace structure of the compay. For istace, this cost should ot be icluded i the fial dowtime cost calculatio where a compay has its ow facilities ad does ot eed to hire this service. I this case it is cosidered as a fixed cost. O the other had, other compaies eed to hire this service, where it is probably beig measured as a variable cost. Discussio of the relative merits of each approach is outside the scope of this paper, but is a fudametal maagemet decisio that must be made with a large umber of other factors take ito accout THE COST OF MACHINE MEASUREMENT The cost of major machie tool measuremet is ot usually accouted as a prime cost, but as part of the burde or factory expeses cost of the total maufacturig cost. The same thig applies for idirect labour for measuremet service, equipmet istallatio,

21 36 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER maufacturig equipmet depreciatio ad eergy costs. However, the cost of machie measuremet is a elemet icluded i the mai equatio of the machie error mappig. CV measuremet of machie = T measure (CR measuremet service + CR machie o productio ) (32) Where: T measure is the time required to fully measure the machie tool. CR measuremet service is the cost per hour of the measuremet service. This is give by equatio (33), where CR measuremet equipmet is the cost per hour of the measuremet equipmet ad CR measuremet labour the cost per hour of the measuremet worker Ad: The: CR measuremet service = CR measuremet equipmet + CR measuremet labour (33) CR measuremet service = CR i (measuremet equipmet) QV i (measuremet equipmet) i=1 + CR i (measuremet labour) QV i (measuremet labour) i=1 (34) Substitutig equatio (7) for CR machie o productio : CV measuremet of machie = T measure (( CR i (measuremet equipmet) i=1 CR i (measuremet labour) i=1 QV i (measuremet equipmet) + QV i (measuremet labour) ) + CR burde + CR idle labourer ) (35) COST OF PRODUCTION START-UP The reaso for performig machie error mappig is to establish the accuracy performace of the machie ad, where ecessary, use umerical compesatio to make the machie as accurate as it is required to be. However, i this work it is assumed that eve after measurig the machie there will be some ispectio ad adjustmet eeded ad a low

22 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 37 probability of producig scrap ad rework parts; this assumptio is reasoable, though it should be oted that it does ot always hold true. The time periods that cotribute to the total time to machie a part are illustrated i Fig. 6, while actios betwee stoppig ad resumig productio are show i Fig. 7, Fig. 8. The cost due to the resettig ad warm up period may iclude the cost of all scrap, rejects ad adjustmets util the machie settles dow ad reaches the steady state coditio. Fig. 6. Total time to machie a part CV startup after adjustmet = CV reloadig prog ad reapplyig fix + CV scrap uits startup + CV rework uits startup + CV startup ispectio (36) Fig. 7. Typical actios betwee stoppig ad resumig productio

23 38 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER The setup time accouts for all the time spet repeatig o-productive tasks that are ecessary for the machiig process, such as removig the fiished work-piece, machie tool cleaig, modifyig fixtures, loadig cotrol part program, warm-up cycles required to allow the machie to stabilise, measurig the machie etc. From equatio (12); QV startup parts maufactured = T idle waitig for PPI T cycle 1 (37) Where QV startup parts maufactured is ormally equal to oe, sice it is good practise to validate the first part before proceedig to full productio. I some circumstaces a secod part might be started before the results of the first have bee achieved. This is ruig at risk, but is ofte applied where compoet value is low. The cost of start-up rejects will iclude the cost of all the parts rejected durig the start-up period util the machie reaches steady state coditio. Start-up cost per machie icludes all the parts rejected durig the start-up period util the machie reaches steady state coditio, it also icludes eergy surge costs, set up (materials ad mapower), percet of reduced productio (uits per hour lost), scrap produced icludes rework, recycle costs ad/or scrap value. T startup is equal to T idle waitig for PPI i this case, where the cost icludes ay scrap cost ad additioal ispectio costs. This is to avoid ay double coutig of scrap ad rework uits durig the productio process. From equatio (13): CV scrap uits startup = P scrap start up QV startup parts maufactured CV part (38) P scrap start up is a lower probability of producig scrap uits tha i previous situatio whe producig parts i a ucotrolled period P scrap. Substitutig equatio (14) we get: CV rework uits startup = P rework start up QV startup parts maufactured CR maufacturig T rework (39) Substitutig equatio (38) ad equatio (39) ito equatio (36) gives:

24 Derivatio of a Cost Model to Aid Maagemet of CNC Machie Tool Accuracy Maiteace 39 CV startup after adjustmet = CV reloadig prog ad reapplyig fix + P scrap start up QV startup parts maufactured CV part + P rework startup QV startup parts maufactured CR maufacturig T rework + CV startup ispectio (40) Fig. 8. Productio start-up after machie measuremet This is sometimes called a pass off part process or a sacrificial part process. However, whe producig a high value part this is ot acceptable; advaced maufacturig is ofte strivig for right-first-time TOTAL MACHINE TOOL ACCURACY RELATED COST From equatio (14) the cost value of ucotrolled productio depeds o the umber of icidets. The quatity value of regular calibratio is a variable that depeds o the compay decisio of how may regular calibratios will be established. This is ofte a fixed value that is arbitrarily agreed. For example, aual error mappig of the machie is sometimes scheduled because it fits ito other quality cotrol systems. The the total cost of machie accuracy related cost ca be represeted as: CV total accuracy related cost = CV Ucotrolled + CV ocoformig parts customer impact + CV QC MC error mappig QV regual calibratio + (CV QC IPI QV QC IPI parts + CV QC MC verificatio QV QC MC validatio checks ) + CV reactio to detected o coformace QV icidits of failures (41)

25 40 Abubaker SHAGLUF, Adrew P. LONGSTAFF, Simo FLETCHER Where the quatity of regular calibratios, QV regual calibratio, is the umber of calibratio actios take per year. This value ca be less tha oe if the actios are take less tha oce per year. A total cost of a reactive maiteace strategy i equatio (18) is give by a modified form of equatio (19) that icludes the calibratio of the machie after a o-coformace has bee detected. I the case of o regular calibratio, where the machie rus completely ucotrolled, the machie error mappig i the equatio will be zero ad the machie verificatio will cacel out. If a regular calibratio is always used ad failures ever occur the regular error mappig will be a value ad the other terms of equatio (19) will be assumed zero as o o-coformace parts are detected. For simplificatio, the total cost of o-coformace could be represeted as: CV Total ocoformace = CV Ucotrolled 1 (42) + CV reactio to detected o coformace 1 Where: CV Total ocoformace is the total cost icurred due to producig o-coformig parts. Assume that all icidets are the same, the this ca be simplified to: CV Total ocoformace = CV Ucotrolled + CV reactio to detected o coformace 1 (43) From equatio (19): CV regular machie cotrol = CV QC IPI + CV QC MC error mappig + CV QC MC verificatio 1 (44) Combiig equatio (43) ad equatio (44), equatio (41) ca be simplified to: CV total accuracy related cost = CV regular machie cotrol + CV Total ocoformace (45)