Automated Production Flow Line Failure Rate Mathematical Analysis with Probability Theory

Transcription

1 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) Automated Prodution Flow Line Failure Rate Mathematial Analyi with Probability Theory Tan Chan Sin* 1, Rypek Uubamatov 2, C.C.Lee 3 # Shool of Manufaturing Engineering, Univerity Malayia Perli Arau, Perli, Malayia. * t5077@gmail.om Abat Automated line have been widely ued in the induie epeially for ma prodution and to utomize produt. Produtivity of automated line i a ruial indiator to how the output and performane of the prodution. Failure or breakdown of tation or mehanim i ommonly our in the automated line in real ondition due to the tehnologial and tehnial problem whih i highly affet the produtivity. The failure rate of automated line are not expre or analye in term of mathemati form. Thi paper preent the mathemati analyi by uing probability theory toward the failure ondition in automated line. The mathemati expre for failure rate an produe and foreat the output of produtivity aurately Keyword- Automated Flow Line, Probability Theory, Failure Rate I. INTRODUCTION In virtual, for all modern manufaturing ytem, mot of the atual numerou proeing or aemblie operation i aomplihed by mahine or tool in prodution line. The prodution line an be laified a manually, emi-automated and automated. Automated prodution line are typially ued for ma prodution that reuired multiple proeing operation. It onit of numerou worktation that are automated and linked together by a work handling ytem to anfer part from one tation to another tation.[1] Automated prodution line ha a wide variety of potential advantage. One of the mot ruial advantage i the inreaed ability to repond for hange in demand, whih i eential in today view of hort prodution yle. Other advantage inluded the dereae of lead time, redution in the work-in-proe level and improved mahine utilization. The typial deign of induial automated line an be preented uing linear or rotary arrangement. All thee arrangement are preented by three type of uture: erial, parallel ation and erial-parallel ation. [2] The erial prodution line of linear arrangement ha been the mot ommon method of prodution and the anfer line refer to part that are moved from one tation to the next upon ompletion in a aight line. The tation anfer their part from one tation to another at the ame time and erie ytem i produtive when all the tation in the line are up and operating. Normally, a erial automated line will be divided into etion with eual reliability and have a different number of erial tation. It i poible to deign uh line if level of reliability of tation i known. Small variation in the reliability of tation will not have a big influene on the reult of the output from a erial automated line [3-4]. By the way, the model of alulation i ame with the rotor-type erial ation ine the tehnologial and tehnial atibute are imilar and only different in the arrangement. The ingle rotor-type automati mahine i a multi-tation' mahine with parallel ation. Eah ingle rotary-type automati mahine i euipped with a anport and work mahine feeder. A parallel ytem of linear arrangement i produtive when at leat one of the tation i operating. In the parallel arrangement of worktation, tation perform the ame operation. The proeing rate of the parallel ytem doe not hange a the number of operating tation hange in time. A parallel ation of multi-tation prodution line ontain idential parallel tation with the ame reliability. The ytem parallelim inluded deigning of independent prodution line in parallel with an independent material-handling ytem erviing it tation. [5,6] Otherwie, the produtivity rate euation for rotor-type automati with parallel tation doe not have an exeme of the funtion. Normally, manufaturer of variou induie produe automated line with a different number of parallel p and erial tation where the deign preent peuliaritie of tehnologial proee and reition in mahine deign. Two type of mahine with omplex uture repreent the deign of automated line with erial parallel ation. The firt type ha a rotor-type arrangement where appliation i found in variou induie like preing, oining, filling of bottle and an and other. Parallel-erial uture i baially deigned with two, and very rarely deigned with three parallel flow. Thi uture an ombine different number of erial tation and uh an automated line i the mot omplex in deign. [7,8] The eond type of automated prodution line of erial parallel ation ha a linear arrangement, whih i applied for proee that ISSN : Vol 6 No 6 De 2014-Jan

2 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) are having long mahining time like mahining of houing part, haft of omplex deign and other. A multitation' automated line with erial parallel ation and linear deign ha everal part feeder eual to the number of parallel tation. The erial automated line i divided into everal etion with eual reliability, whih may have a different number of erial tation. [9] Produtivity i onidered a an important indiator to how the performane in an induy [10]. In the perpetive of eonomi, produtivity an be defined a the ratio of output (good and ervie) divided by the input (reoure uh a labour and apital) [11]. Failure or breakdown of tation or mehanim i ommonly our in the automated line in real ondition due to the tehnologial and tehnial problem whih i highly affeted the produtivity. The produtivity rate of automated line inluded tehnologial parameter (mahine time), tehnial parameter (auxiliary time, idle time and apaity of buffer) and utural parameter (number of erial and parallel tation and number of etion of automated line). The urrent euation of produtivity only inluded the tehnologial and tehnial apet of the automated line. Apet of management or maintenane of automated line at preribed planned overhaul repair time are not inluded in the euation. The onept of management onider the uality of the prodution proe while the onept of maintenane onider the planned repair and ervie of mahine that are topped for overhaul proee. The aggrandizement of manufaturing ytem uh a omplex deign of automated line ha inreaed the probability of failure problem. The failure of any ingle tation an lead to toppage of the entire automated line. The random toppage in omplex deign of automated line oniting of independently operated tation are alulated by uing probability theory. [12] The mathematial form of produtivity with average reliability for tation and mehanim i till not very aurate to expre the atual produtivity ine the different failure rate during automated line are not onidered in the mathematial form. Therefore, different type of failure have to be invetigated before to enhane the mathematial form of produtivity with average reliability to a more robut and aurate foreat for produtivity in automated line. Thi paper preent a mathematial approah to expre the failure rate and failure type of the automated line with probability theory to preent the failure rate aurately and learly. II. METHODOLOGY An eay way to omply with the onferene paper formatting reuirement i to ue thi doument a a template and imply type your text into it. There are everal publiation that preented the uage of probability theory for further analyi of failure or freueny in different type of area uh a biology and hemial[13-16]. Appliation of probability theory to the failure rate of automated are reuired to differentia and expre the failure rate of working automated in term of mathemati. In the probability theory, there are few bai axiom that reuired to math before uing the theory and the bai axiom are preented a below[17]: Probability Bai Axiom 1. P(A) 0 for all event A 2. P(Ω) = 1 3. P(A B) = P(A) + P(B) for dijoint event A and B 4. P(A B) = P(A) + P(B) - P(A B) for joint event A and B 5. P(A B) = P(A) x P(B) for joint or dijoint event A and B Firt axiom preent the probability of event A mut eual or more than zero. The bai theory of probability for any event tated that no negative probability exit. For ondition of an automated line, there mut be an ourrene of failure or breakdown during the automated line working time. Sine there are ertain type of automated line failure ( f i ) whih i not zero, the probability for ertain type failure of automated line, P( f i ) i more than zero and no negative figure. Therefore, the failure for automated line i fulfil the bai reuirement of probability theory. The eond axiom preent the total ample pae (Ω) whih i the total overage of event in the onideration boundary mut be obtained the total probability i eual to one or P(Ω) = 1. Total of the failure rate or breakdown i onider a total ample pae whih preent the total of probability for failure rate in automated line i eual to one or P( f ) = 1. With the ombination of firt and eond axiom, probability of total event for all type of failure in automated line i eual to the probability of total ample pae or total of failure in automated. Following axiom whih are third, fourth and fifth axiom that tated above are diued about the mathematial expre between both or more event relationhip. If the ondition of event in the ample ize an our independently, thi mean that the probability i in or ondition and the probability mathematial expre i P(A B). For or ondition, there are two ondition might be happened whih are dijoint event or joint event. The Fig 1(a) and 1(b) below will preent the both ondition of or in term of hemati diagram. ISSN : Vol 6 No 6 De 2014-Jan

3 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) 1(a) 1(b) Fig 1: (a) P(A B) our independently with dijoint event. (b) P(A B) our independently with joint event. For the P(A B) our independently or or ondition with dijoint event i expreed to P(A) + P(B) ine the probability i onidered either A or B event to our. P(A B) our independently with joint event i expreed a P(A) + P(B) - P(A B) whih preent probability i either A or B event ourred but reuired to minu the ubet part between A and B. For dependently ondition, thi i onidered a and ondition whih preent the probability i onidered when A and B event our together. The probability for dependent or and ondition i expreed a P(A B) = P(A) x P(B) whih i uing probability event A multiply with probability event B and figure 2 below i howing the dependent or and ondition. Fig 2. P(A B) our dependently between both A and B event with joint event. Third axiom whih preent the relationhip of different of probability between two or more event. The finding of mathing with the ae of failure rate of automated line i fulfill the firt and eond axiom. Then, the failure of automated line i happened independently to aue the failure or breakdown of the whole line. The independent failure uh a failure of firt tation, anport ytem or onol ytem are ourred itelf without aue by other. One there i any failure happened in the automated, it will aue whole line to top. Thi mean that any failure will aue the inreaing of the total probability of failure. Therefore, the ondition of third axiom i mathed with the ondition of failure of automated line whih our independently with dijoint event. The euation 1 and 2 below will how the relationhip of failure of automated line with the third axiom. (Ω) = ( B) = ( ) + ( ) (1) Where P(Ω) = Total Probability of Sample Spae P(A) = Probability of A event P(B) = Probability of B event ( ) = ( ) = ( ) + ( ) (2) Where P( f ) = Total Probability of failure in automated line P( f 1) = Probability of firt event failure, P( f 2 ) = Probability of eond event failure, The third axiom whih i A and B or f 1 and f 2 are our independently in the ondition of Union ( ) that how in euation 1 and 2 preent the meaning of the reult of the ondition Union i the um of the independent ISSN : Vol 6 No 6 De 2014-Jan

4 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) event. In other word, the reult Union ondition i onider the when either event A or event B our. In the term of failure rate ( ) whih preent the failure of any tation or mehanim in automated prodution line with repet to time i alo our independently due to any tation or any mehanim whih will top the automated prodution line. Failure rate i an important parameter in reliability theory for alulation and explanation purpoe [18-19]. Sine that all or any of the failure rate i onibute to the failure of prodution line, o that thi ondition i math to the Union ondition or or ondition in probability theory whih preent the um reult in mathematial expre. The mathematial expreion of failure rate that baed on the probability theory with Union or or ondition i preent in euation 3 below. =( ) = + (3) = Total failure rate in automated prodution line 1 = Failure rate for firt event 2 = Failure rate for eond event III. RESULT AND DISCUSSION In order to expre the probability theory toward the automated line failure rate, the reognition of the type of automated line in induy i very important ine there are different of the probability mathematial failure expreion due to different working propertie of automated line. There are two type of arrangement of automated line in urrent induy whih are linear type and rotor type and eah type onit of three different working ation whih are erial, parallel, and erial parallel ation[9,20]. The firt type of arrangement i linear with erial working ation whih i hown in Fig. 3 below. Sine eah of the worktation onit of different of operation and type of proee, the failure probability of eah tation i different. However, the failure of anport ytem and onol ytem i ame due to the ame anport line and main onol. The euation 4 below will preent the mathematial expreion of total probability of failure and failure rate expreion in euation 5 for linear type with erial ation automated line. Fig. 3. Linear Type Automated Line with Station of Serial Worktation ( f ) P f ) + P( f ) + P( f ) P( f ) + P( f ) P( f ) P + = (4) ( = (5) Where P ( f ) = Probability for total failure rate P ( f ). 1 = Probability for failure of worktation 1 P ( f ). 2 = Probability for failure of worktation 2 P ( f. 3) = Probability for failure of worktation 3 P ( f. ) = Probability for failure of worktation P ( f ) = Probability for failure of anport ytem P ( f ) = Probability for failure of automated line onol ytem = Total of failure rate of automated line.1 ` = Failure rate of worktation 1.2 = Failure rate of worktation 2.3 = Failure rate of worktation 3. = Failure rate of worktation ISSN : Vol 6 No 6 De 2014-Jan

5 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) = Failure rate of anport ytem = Failure rate of automated line onol ytem For linear type with parallel and erial-parallel ation that how in the Fig. 4(a) and 4(b) below onit of different mathematial expreion due to different working propertie. 4(a) Fig 4. (a) Parallel Ation of Linear Arrangement Automated Line with P Station, (b) Linear-Type of Serial Parallel Ation Automated Line with Serial Station and p Parallel Station For parallel ation with linear arrangement automated line, all the mahine are the ame in all apet o that thi automated i expreed in one of probability time p tation with the failure of anportation ytem due to feeder or anport ytem in thi type of line. The probability of thi type of line i expreed in euation 6 while euation 7 preent the failure rate expreion and p i the number of parallel tation in automated line. ( f ) p P( f ) + P( f )] P( f ) P + = (6) = p + ] + [ [ (7) For the erial parallel ation with linear arrangement onit of different failure rate in the erial worktation but ame failure rate in p parallel worktation. The mathematial expreion for erial parallel ation i how in euation 8 inluding the anportation ytem and onol ytem. Failure rate of erial parallel for linear automated line i how in euation 9. ( ) P p P( ) + P( ) + P( ) P( )] + P( ) + P( ) = (8) 4(b) [ = p ] + [ (9) For rotor-type erial ation, the model of alulation i ame with the linear-type erial ation ine the tehnologial and tehnial atibute are imilar and only different in arrangement. The probability expreion of rotor-type erial ation automated line i ame with the linear type erial ation. The eond working ation for rotor type i parallel ation where all the worktation in the automated line i ame and the failure rate i multiple with p tation. Rotor-type parallel ation automated line i hown in Fig. 5 below and the probability expreion i preented in euation 10 and failure rate expre in euation 11 below. P ( ) p P ) + P( ) + P( ) ( Fig 5. Rotor-Type in Single Pure Parallel Ation Automated Line = (10) p + + = (11) ISSN : Vol 6 No 6 De 2014-Jan

6 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) Where P = Number of parallel worktation in a rotor P ( ) = Probability for total failure P( ) = Probability for one worktation failure in rotor P( ) = Probability for anport failure in rotor P( ) = Probability for automated line onol ytem failure in rotor = Total of failure rate of automated line = Failure rate of one worktation in rotor = Failure rate of anport ytem = Failure rate of automated line onol ytem Sine the pure parallel ation automated line are eldom exit in ingle line, the third rotor-type whih i erial-parallel ation i widely ue in the induial prodution ytem for ma and fat prodution. The erialparallel ation of rotor-type automated line i hown in Fig. 6 below. Fig. 6. Serial-parallel Ation of Rotor-type Automated Prodution Line Thi rotor-type with erial parallel ation i onidered a ompliated or omplex deign of automated line in induy. Thi line i the ombination of erial ation and parallel rotor to inreae the produtivity. The number of working rotor and anport rotor in erial arrangement onit of different failure rate due to the different worktation and working propertie. However, the p number of worktation in eah of rotor i onidered a parallel ation whih i working for all imilar worktation with the ame working proe. The failure rate for working rotor and anport rotor are reuired to multiply by the number of parallel tation, p. The failure of onol ytem for thi type i onidered in one group of probability due to the ame onol ytem in the whole automated line and the euation of probability failure for erial parallel of rotor type i expre in euation 12 while euation 13 how the failure rate euation below. P = p P( ) + P( ) P( ) + P( ) + P( ) P( )] + P( ) (12) ( ) [ = p ] + [ (13) Where: P( ). 1 = Probability for erial rotor 1 failure ISSN : Vol 6 No 6 De 2014-Jan

7 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) P( ). 2 = Probability for erial rotor 2 failure P( ). 3 = Probability for erial rotor 3 failure P ) = Probability for erial rotor failure (. P( ). 1 = Probability for anport rotor 1 failure P( ). 2 = Probability for anport rotor 2 failure P( ). 3 = Probability for anport rotor 3 failure P ) = Probability for anport rotor failure (..1 = Failure rate of erial rotor 1.2 = Failure rate of erial rotor 2.3 = Failure rate of erial rotor 3. = Failure rate erial rotor.1 = Failure rate of anport rotor 1.2 = Failure rate of anport rotor 2.3 = Failure rate of anport rotor 3. = Failure rate of anport rotor Sine the theory of probability i applied in the apet of reliability, it an how learly the different level of reliability regarding to the worktation, anportation and onol ytem in rotor-type automated line. The analyi of the failure rate for all ommon type of automated line in induy i ueful for further reearh about produtivity. The reliability part of mathematial model whih i availability i applied by thi probability methodology to improve the urrent mathematial model with average level of reliability. IV. CONCLUSION Analyi of the failure rate or breakdown in automated line by uing the theory of probability ha been done to expre the probability of failure and failure rate of the automated line into probability mathematial euation. The probability euation for eah type of automated line i learly tated and expreed regarding to the working ation and type of arrangement of worktation. The expreion of euation in term of mathematially i ueful for engineer or reearher to alulate or foreat the failure rate of the automated line and for improvement of produtivity mathematial model to obtain a more robut model due to the onideration of failure rate in ditinguihe ategorie. Simulation and validation are reuired in future to be applied to the probability failure rate model expreion.improvement of the probability in term of failure rate in automated line i important a future work. ACKNOWLEDGMENT I would like to thank my PhD upervior, Prof Rypek Uubamatov to give me a lot of guidane for my reearh. Beide that, I would like to expre my appreiation to my reearh partner who are Mr. Fidzwan, Low and Teh that alway help me to olve ome tehnial problem. REFERENCES [1] Mikell P. Groover Automation, Prodution Sytem, and Computer-Integrated Manufaturing, Third Edition, by Pearon Eduation, In., Upper Saddle River, NJ. [2] Jouni Smed, Mika Johnon, Tommi Johtela & Olli Nevalainen. Tehniue and Appliation of Prodution Planning in Eleoni Manufaturing Sytem.(1999) [3] B. Tan, An Analytial Formula for Variane of Output from a Serie-Parallel Prodution Sytem with No Intertation Buffer and Time-Dependent Failure, Turkey,1997. [4] AdarA.Kalir, SubhahC.Sarin, A Method for Reduing Inter-departure Time Variability in Serial Prodution Line, Int. J. Prodution Eonomi 120 (2009) [5] Bari Tan, Variane of The Throughput of An N-tation Prodution Line with no Intermediate Buffer and Time Dependent Failure, European Journal of Operational Reearh 101 (1997) [6] Theodor Freiheit, Yoram Koren, S. Jak Hu, Produtivity of Parallel Prodution Line With Unreliable Mahine and Material Handling, IEEE Tranation on Automation Siene and Engineering, Vol. 1, No. 1, July 2004 [7] Rypek Uubamatov & A. M. Ahmed Alwaie & Z. M. Zain, Produtivity and optimization of etion-baed automated line of parallel erial uture with embedded buffer Springe r-verlag London Limited 2012 ISSN : Vol 6 No 6 De 2014-Jan

8 Tan Chan Sin et al. / International Journal of Engineering and Tehnology (IJET) [8] Nakagawa T (2005) Maintenane Theory of Reliability. Springer, New York [9] Rypek Uubamatov, A. M. Ahmed Alwaie, Z. M. Zain, Produtivity and Optimization of Setion-baed Automated Line of Parallel erial Suture with Embedded Buffer, Int J Adv Manuf Tehnol (2013) 65: [10] G. Chryolouri, Manufaturing Sytem: Theory and Pratie, 2nnd edn. New York: Springer, [11] J. H. & B. Render, Operation Management. New Jerey: Pearon Eduation In., [12] Uabamatov R., Imail K.A., and Shah J.M., 2012, Mathematial model for produtivity and availability of automated line, International Journal of Advaned manufaturing Tehnology. [13] G. Kaiel, Gambler ruin probability A general formula, Stat. Probab. Lett., vol. 83, no. 10, pp , Ot [14] T. Nakajima, Probability in biology: Overview of a omprehenive theory of probability in living ytem., Prog. Biophy. Mol. Biol., vol. 113, no. 1, pp , Sep [15] M. Rédei and S. J. Summer, Quantum probability theory, Stud. Hit. Philo. Si. Part B Stud. Hit. Philo. Mod. Phy., vol. 38, no. 2, pp , Jun [16] N. Frenh, Value and worth: probability analyi, J. Prop. Invet. Finan., vol. 24, no. 4, pp , [17] H. Gaifman, The ure thing priniple, dilation, and objetive probabilitie, J. Appl. Log., vol. 11, no. 4, pp , De [18] D. B.S., Reliability, Quality, and Safety for Engineer. New York: CRC Pre, [19] P. D.T.O Connor, Pratial Reliability Engineering, 4th ed. John Wiley & Son, In, [20] L. Volhkevih, Automation of Manufaturing Proee, Mahinooenie, Moow, AUTHOR PROFILE Tan Chan Sin 1* born in 1988 in loal of Malayia. He i a PhD andidate in Univerity Malayia Perli ine 2012 after he graduate hi Bahelor Degree of Manufaturing Engineering in the ame year of tarting PhD. In the area of PhD reearh, he i work out in Manufaturing Engineering field whih major in Produtivity Mathematial Model and Reliability Analyi. He i alo interet in field of Lean Manufaturing and TQM a well. He i publihed everal paper in International Conferene inluding ASME Digital Library Publiation. Rypek Uubamatov 2 born in Kyrgyztan and urrently work a a Profeor in Shool of Manufaturing Engineering, Univerity Malayia Perli. He wa obtained diploma (Mehanial & Manufaturing Engineering) in Moow State Tehnial Univerity, Ruia. Hi M.S. (Tehnial Siene) i tudied in National Aademy of Siene, Kyrgyztan. While hi Ph.D.(Tehnial Siene) obtained from Moow State Tehnial Univerity, Ruia. He i intereted in variety of area uh a produtivity analyi, mahining, dynami ytem and et. C.C. Lee 3 urrently work a a Senior Leturer in Shool of Manufaturing Engineering in Univerity Malayia Perli. He wa tudied in Univerity Kebangaan Malayia for B.Eng. (Manufaturing). For hi Mater bahelor, he wa alo tudied in Univerity Kebangaan Malayia for M.Eng. (Mehanial & Material Engineering). He obtained hi PhD (Eomaterial Deign & Proe Engineering) in Tohoku Univerity, Japan. Hi interetd reearh field i more on eomaterial development, biomaterial, manufaturing proe improvement and operation management. ISSN : Vol 6 No 6 De 2014-Jan