Research on the Rework Strategies of RMS Based on Process Reliability

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1 A publicatio of CHEMICAL ENGINEERING TRANSACTIONS VOL., 0 Guest Editors: Erico Zio, Piero Baraldi Copyright 0, AIDIC Servizi S.r.l., ISBN ; ISSN The Italia Associatio of Chemical Egieerig DOI: 0.0/CET087 Research o the Rework Strategies of RMS Based o Process Reliability Wei Dai*, Ji A, Yu Zhao School of Reliability ad System Egieerig, BeiHag Uiversity, BeiJig,Chia dw@buaa.edu.c Rework Strategies are idispesable i order to improve the process reliability of recofigurable maufacturig system (RMS). Process reliability is a itegrated measuremet of productio ability of RMS, which serves as a performace idicator of the productio process uder specified techical costraits, icludig time, cost ad quality. The process reliability of RMS with rework process is studied, ad the rework process is decomposed ito oe geeral processig path ad several reworkig processig paths. A ovel model ad algorithms is itroduced to obtai the iputs, outputs, costs, ad process reliability of each machie, as well as the rework strategies uder differet batch size of RMS based o process reliability is preseted. Case study o machiig process of slide valve is employed to illustrate the proposed algorithm, which shows that the proposed methodology ca make the rework strategies of RMS effectively ad efficietly.. Itroductio How to respod chages i market demads quickly ad ecoomically is a huge challege for today s maufacturig, which is trasformed gradually from mass productio mode to multi-varieties mode. The Egieerig Research Ceter of the Uiversity of Michiga, USA proposed the cocept of recofigurable maufacturig system (RMS) (Kore et al., 999). Recofigurability is a egieerig techology that deals with cost-effective, quick reactio to market chages. Recofigurable maufacturig systems, whose compoets are recofigurable machies ad cotrollers, as well as methodologies for their systematic desig ad rapid ramp-up. For differet batch size, RMS ca adjust productio fuctio ad capability of maufacturig system through lower coversio costs ad higher equipmet utilizatio, ad adapt to the dyamic maufacturig eviromet cosequetly. I the research of RMS, reliability is a very importat idicator to measure system performace (Zhag, 009). Cosiderig the system reliability is coducive to estimate ad distribute the iteded target ad missio. The settig of rework strategies is recofigurig maufacturig process ad it is commo meas of RMS. I order to accomplish the productive missio with low cost ad high quality, a ovel model ad algorithms is itroduced to obtai the iputs, outputs, costs, ad process reliability of each machie, as well as the rework strategies uder differet batch size of RMS based o process reliability is preseted i the paper.. Literature review. Reliability of maufacturig process,. (978) from the Soviet Uio gave the defiitio of equipmet s process reliability: withi the prescribed scope ad time, the ature that equipmet was able to maitai the decisive quality idicator values of process. He also stressed the eed to defie equipmet s reliability accordig to the purpose of aalysis. Sog (99) cosidered the process system reliability is the ability that process is made to meet the techical requiremets. Zhag ad Guo (009) provided the defiitio of process system reliability: the ability that respose maufacturig systems quickly to achieve process quality parameters of desig documets withi specified coditios ad time. Barriger (000) gave the defiitio of process Please cite this article as: Dai W., A J., Zhao Y., 0, Research o the rework strategies of rms based o process reliability, Chemical Egieerig Trasactios,, 57-5 DOI: 0.0/CET087 57

2 reliability: the poit o a Weibull probability plot where the demostratio productio lie shows a distict cusp because of cutbacks ad /or crash ad bur problems.. Reliability of maufacturig process Rework is the actio o a ocoformig product to make it coform to the requiremet (ISO 9000:000). The pheomea of productio batch chages, machie failures, defects, multiple rework loops, etc., results i much difficulty i aalyzig process modelig of RMS, ad therefore the performace aalysis of such systems has bee ivestigated limitedly i the past. Buscher ad Lider (007) has developed a optimizatio method to determie the ecoomic productio ad rework quatity as well as the correspodig batch size for both activities. Liu et al. (008) foud simultaeously the optimal umber of productio ad rework setups i a cycle, their sequece, ad the ecoomic productio quatity of each setup. Cao ad Subramaiam (0) came up with the decompositio aalysis of rework systems requirig the developmet of a three-machie ad oe-buffer lie (MB) model i additio to the MB models (Gershwi, 99). This model is developed specifically for rework systems, ad is capable of characterizig multiple rework loops. Li ad Chag (0) revised a maufacturig system with reworkig actios as a stochastic-flow etwork i which the capacity of each machie is stochastic. But they assumed the ocoformig products ca rework oly oce o the same machie. I actual productio, rework times is ot limited to oce. But reworkig too may times will cost more, ad the reworkig machie may ot bear the processig tasks. So it is ecessary to fid optimal rework strategies ad realize the target of low cost ad high quality.. Rework strategies based o process reliability of RMS. Reliability of RMS Reliability of recofigurable maufacturig system is a itegrated measuremet of productio ability of RMS, which serves as a performace idicator of the productio process uder specified techical costraits, icludig time, coditio, task, cost etc. The specified time are the give cotiuous processig cycles; the specified productio coditios iclude evirometal coditios, maitaiig coditios ad applicatio coditios i process; the specified tasks are give productio itesity, which is cosist of throughput ad its techical specificatios required to achieve. Basic reliability is used to describe the ability of machies to complete specified productio task stregth, amely R( x) = P( ξ > x) ad x meas productio task stregth. Missio reliability is used to estimate the ability of products i process to complete specified productio task stregth. I the paper, it ca be calculated by the ratio of output to iput. With the icrease of reworkig frequecy, the machies eed rework ocoformig products will process more uits. Whe the machies processig amout is more tha they could afford, the process reliability falls sharply. Accordig to daily product data of a certai machie withi a year, distributio law ca be give as Table : Table : Distributio law of daily product data Daily product data W W W probability P P P pi = Based o the defiitio of basic reliability ad daily product data, equipmet s basic reliability presets the followig variatio tred show i Figure.. Figure. Variatio tred of equipmet s basic reliability I Figure., the curve is usually Weibull distributio (Barriger, 000). 58

3 . Assumptios The model is based o assumptios below:. Each ispectio statio is perfectly reliable.. The capacity of each machie is a radom variable accordig to a give probability distributio.. The capacities of differet machies are statistically idepedet.. The ocoformig products detected by the ispectio statio are either all reworked, or all scrapped i each path.. Optimizatio method of rework strategies The optimizatio method icludes the followig steps: Step. Rework system of RMS aalysis ad calculatio. First, the paper cosiders a productio lie with machies ad buffers. The r th machie is a ispectio machie, if the ocoformig products are detected by it, they will retur to the machie caused defects for reworkig (see Figure.). I Figure., buffers are idicated by circles, ad machies are idicated by arrows. e e e e e - e rk - - rk er r + e Figure.: The processes with oly oe rework actio We decompose the rework system i Figure. ito oe geeral processig path ad oe reworkig path, it is showed i Figure.. Iput e e e erk - - e rk - er e r + e Output (a) Geeral processig path e e e e r er e e rk - e r- (b) Reworkig path Figure : The decompositio of rework system Whe calculatig the rework system of RMS, geeral processig path ad reworkig path eed to be cosidered at the same time. The iput raw materials/wip (work-i-process) processed by the i th machie ( w w w ) after reworkig m times ca be calculated as Eq(): j- I pi, j=,, L, r-k- i= wj = j- m r- r- t- j- I pi + I pq i r pq i r pi, j= r- k, r-k+,, i= t= i= i= r-k i= r-k () The otatios used i Eq() are as follows: I =the iput uits of raw materials; p i =the yield rate of i th machie; q i =the rework rate of i th machie; r =defective WIP output from r th machie; k =defective WIP are reworked startig from previous k machie. p i eed to be determied by iterative calculatio. Iterative maer is as follows: firstly, o the basis of m variatio of daily productio data, approximate curve ca be fitted out just like Rx ( ) = exp( ( x/ η) ). Secodly, yield rate p ca be achieved by pluggig I ito fittig reliability fuctio, ad the w ca be calculated through Eq(). Based o w ad fittig reliability fuctio, we ca get yield rate p. The rest p i ad wi may be deduced by aalogy. Step. Missio reliability calculatio The output of the system is equal to the sum of geeral processig path s output ad reworkig path s output, whe oly eed rework oce. The formula is as Eq(): 59

4 r - O = I p + I pq p i i r i i= i= i= r-k () I Eq(), O is the output uites of products. Based o the decompositio method, we ca figure out output of the system whe eed rework m times. The results ca be expressed by Eq(): r- r- m- O = O + I pq pq p () m+ m i r i r i i= i= r-k i= r-k Ad the missio reliability of processig system is R / t = Om+ I. Step. Productio costs calculatio The otatios used i this part are as follows: a 0 =uit price of the iput raw materials; b i = processig costs of a part of i th machie; w i the iput raw materials/wip processed by the i th machie. Maufacturig costs of a complete product C iclude raw materials costs C m, processig costs C p, ad schedulig costs of rework C d, it ca be expressed by Eq(): C = Cm + Cp + Cd m () I Eq(), C = m a0i C C C wb + + = C d p s r j j j= ca be give accordig to the practical situatio. Step. Decisio values calculatio Firstly, the calculated missio reliability ad costs are ormalized. The, accordig to the give weight ω, ω of costs ad missio reliability, decisio values ca be obtaied through the ' ' formula Z = Cω R b ω, ad the miimum amog decisio values correspods to the optimal rework strategy.. Case Applicatio Machiig process of slide valve s excircle of servo-valve eed pass through four processes: rough gridig, accurate gridig, beddig-i, lubricatio. Ad these four processes eed four differet machies show i the followig Figure.. I the processig, whether the excircle s dimesios are withi the prescribed limits eed to be ispected whe accomplish the beddig-i. If ocoformig dimesios are detected, they are required to retur to machie e for reworkig, amely r=, k =. e e e e Figure. Machiig process of slide valve s excircle. Suppose that: I =500, uit price of the iput raw materials a 0 = 0, processig costs per part of each machie are : b = b =, b = 5, b = 6. Schedulig costs of rework oce is C d = 5. Accordig to equipmet s daily productio data, reliability fuctio of four processig equipmet ca be fitted. Both the.9 reliability fuctios of e ad e are R ( x) = exp( ( x / 800) ), both the reliability fuctios of e ad.5 e are R ( x) = exp( ( x / 800) ). O the basis of computatioal methods previously put forward, we ca get results show as Table : 50

5 Table : Results of example Rework times Output Uit costs Iput raw materials/wip processed by the i th machie Missio reliability zero 9.7 w =6, w =9, w = oe w =9, w =, w = two w =50, w =, w = three w =50, w =, w = Accordig to the results above ad weights ω = 0.8, ω = 0. that maufacturig compay has give, decisio values ca be achieved: Z 0 = Z = Z = Z = Z is the miimum, so the maximal rework times for this productio process is two. Besides, optimal rework strategies are calculated whe iputs are 00, 00, 00, 00, 600 respectively, the results are show i Table : Table : Optimal rework strategies i differet iputs Maximal rework times Iput *the shadows are the optimal rework strategies Whe iput equals 600, the reliability is oly It meas early 0% raw materials are scrapped from e ad it will result i great wastes. From the example, we ca see whe iputs are withi a certai rage, if they are relatively small, o rework is the best rework strategies. With the icrease of iput, the reworkig frequecy has a correspodig icrease. This is because that storage of equipmet will decrease with the icrease of iput, ad yield rate is reducig. So the frequecy of rework eeds to be icreased to meet the egieerig requiremets. This is cosistet with the cocept of process reserve i OCT of the former Soviet stadard. Therefore, the proposed method i this paper is feasible. Note that the iput should be cotrolled withi the capabilities of equipmet. The paper realized this by maitaiig the value of reliability at 0.8 or more. 5. Coclusios This paper geeralizes the model ad algorithms of rework strategies optimizatio of RMS based o process reliability. The paper decomposes the rework system ito oe geeral processig path ad several reworkig paths, ad provides umerical methods to obtai iputs, outputs, costs ad process reliability of each machie. It also gives the computatioal methods of optimal rework strategies uder differet batch sizes. Case study o machiig process of slide valve shows that the proposed methodology ca make the rework strategies of RMS effectively ad efficietly. I this paper, the rework processes are desigated, that is to say that the processes where ocoformig products/wip are detected ad modified are give. I the future research, geetic algorithm will be applied to determie the optimal reworkig process i order to improve computatioal accuracy. Ad the comprehesive rework strategies will be give through exped the proposed methods i this paper. 5

6 Refereces Barriger P., 000, Process reliability ad six-sigma, Natioal Maufacturig Week Coferece Track for Maufacturig Process ad Quality. Buscher U., Lider G., 007, Optimizig a productio system with rework ad equal sized batch shipmets. Elsevier,, Cao Y.X., Subramaiam V., Che R.F., 0, Performace evaluatio ad ehacemet of multistage maufacturig system with rework loops. Elsevier, 6, Gershwi S.B., 99, Maufacturig systems egieerig. Eglewood Cliff: Pretice Hall. Iteratioal Stadardizatio Orgaizatio, 000, ISO9000:000(E), Quality Maagemet Systems Fudametals ad Vocabulary. Kore Y., Heisel U., Jovae F., 999, Recofigurable maufacturig systems. Elsevier, 8, Liu N., Kim Y., Hwag H., 008, A optimal operatig policy for the productio system with rework. Elsevier, 56, Li Y.K., Chag P.C., 0, Evaluate the system reliability for a maufacturig etwork with reworkig actios. Elsevier, 06, 7-7.,.., 978,..:, 59 (i Russia). Sog B.W., Li Z.N., 99, Mechiical maufacturig process reliability. IEEE,,-7 (i Chiese). Zhag J.Y., Xie L.Y., Li B., 009, Reliability aalysis of o-series maufacturig systems based o petri ets, Chiese Joural of Mechaical Egieerig,, 95-00, DOI: 0.90/JME Zhag K.L., Guo B., 009, Study of process system reliability model cosiderig error propagatio. IEEE, 7, -7 (i Chiese). 5

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