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Impact of Statistical Process Control (SPC) on the Performance of Production Systems M. Colledani, T. Tolio Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione Slide 2 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione Outline of the presentation 1- Literature review 2- Problem definition 3- Isolated machine with local monitoring 4- Two machines one buffer with local monitoring 5- Two machines one buffer with remote monitoring 6- Long lines with local monitoring 7- Numerical results 8- Conclusion and future research Slide 3 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 1- Literature Review - Montgomery,D.C, Introduction to Statistical Process Control, John Wiley and Sons, Inc, 1991. - Ho C., Case K., Economic Design of Control Charts: A Literature Review for 1981-1991, Journal of Quality Technology, 26,: 39-53,1994. - Raz T., A Survey of Models for Allocating Inspection Effort in Multistage Production Systems, Journal of Quality Technology, 18-239-246, 1986. - Dallery, Y.,Gershwin, S.B., Manufacturing Flow Line Systems: A Review of Models an Analytical Results, Queueing Systems Theory and Applications, Special Issue on Queueing Models of Manufacturing Systems, 12(1-2). 1992. - Gershwin S.B., Matta A. and Tolio T., Analisys of Two Machine Lines with Multiple Failure Modes, IIE Transaction, 34(1) : 51 - 62, 2002. - Gershwin S.B., Kim J.,Integrated Quality and Quantity Modeling of a Production Line, OR Spectrum, 2005. - Colosimo B.M., Semeraro Q. and Tolio T. Designing X bar Control Charts in Multistage Serial Manufacturing System, CIRP Journal of Manufacturing Systems, 31-6, 2002 - Tempelmeier H., Burger M, Performance Evaluation of Unbalanced Flow Lines with General Distributed Processing Times, Failures and Imperfect Production, IIE Transactions,33,293-302, 2000. - Helber S. Performance Anaiysis of Flow Lines with Non-Linear Flow of Material, Springer, 1999. - Inman R., Blumenfeld D., Huang N. and Li J.., Designing Productivity Systems for Quality: research opportunities from an automotive industry perspective, IJPR, 41(9), 2003. Slide 4 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione t Example 2- Process in Statistical control PROCESS IN CONTROL PROCESS IN CONTROL each quality measure is in a statistical control state. STATISTICAL CONTROL STATE STATISTICAL CONTROL STATE is a state where all the variations within the observed data can be related to a set of causes not identifiable which do not change over time (i.e. the distribution is stable) Slide 5 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 2- Specifications and bad parts t Lower Specification Limit - LSL Upper Specification Limit - USL Even if the process is in control it can produce bad parts. However, if the process goes out of control the number of bad parts produced changes (in general, infinite out of control modes are possible). LSL USL t Slide 6 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 2- Detecting out of control states In order to understand if the process is in control or out of control, we can sample the produced parts (in the extreme case we can have 100% inspection). Then we measure the parts in the sample and we perform a statistical test with the following hypotheses. H 0 : the process is in control H 1 : the process is out control The outcome of the test is subject to two types of errors: error: the process is in control but the test detects an out of control (false alarm) error : the process is out control but the test does not detect it (out of control not detected) Slide 7 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione If the process is out of control 2- Detecting out of control states If we repeat the test many times and each test has the same and errors than we can evaluate the average number of samples we have to take in order to have an alarm (ARL = Average Run Length). t t If the process is in control For example: Slide 8 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 2- Detecting out of control states If we consider a single machine in isolation and a control chart attached to it then how many parts does the machine produce before getting an alarm? Let us define: mthe sample size. hthe number of parts produced between two samples. If the process is out of control If the process is in control Slide 9 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 2- Inspection stations Testing allows to draw information on the process but also on the inspected parts. Inspected parts which are within the specification limits may proceed downstream (if testing does not destroy the parts). Inspected parts which are outside the specification limits may be either scrapped or reworked Therefore the logic at an inspection station decides two things: control charts which send the alarms related to the out of control conditions scrap/rework policies which decide the final destination of the inspected parts scrap rework good (If m=1 and h=0 than 100% inspection is performed). Out of control Slide 10 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 2- Some Assumptions of the Model -The flow of material in the system is considered as discrete. -Each machine is characterized by the same processing time, scaled to time unit. -Buffers have finite capacity. -Machines can be of three types: manufacturing machines, inspection machines or integrated machines. -Inspection machines are perfectly accurate. -Failures and shifts to out of control are Operation Dependent. -Once an out of control has been detected, the time to repair it is geometrically distributed. -Machines can fail in different modes. We identify two classes of failures: -f type local failures: are those for which the repairing intervention also set the machine to the in control state; type local failures: are those for which the repairing intervention reset the machine to conditions it had before the failure occurred. Slide 11 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 3- Modelling a single machine in isolation W i : operative in control D i,fi : f type local down state D i, i : type local down state A i 1 : out of control detected but not real A i 2 : out of control detected and real O i : out of control non detected Quality link equations: Slide 12 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione 3- The Isolated Machine Case Once the Markov chain has been solved and all the state probabilities have been calculated, the performance measures for the single machine case can be derive as follows: Total average production rate: Effective average production rate: System yield (fraction of conforming parts produced): Average production rate of parts to be scrapped: Average production rate of parts to be reworked: Slide 13 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione scrap rework scrap 4- The General Case Quality has an impact on production system performance: - Control charts allow to identify out of control states. The search for a cause for the out of control reduces the up time of the machine. - Scrap/rework policies allow to identify defective parts and to decide whether to scrap or to rework them. The system architecture impacts on the quality system performance: - The presence of buffers causes a delay in the transmission of the quality signal. Total throughput Yield Total throughput Yield Slide 14 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione CONVERGENCE 4- Two machine one buffer with local monitoring This system is formed by two machines M 1 and M 2 locally controlled by C 1,1 and C 2,2. M U (1) M D (1) B Markov chain solution Stationary state probability distribution New failure probabilities calculation Upstream pseudo-machine M U(1) Building Block evaluation Gershwin, Matta, Tolio 2002 New blocking and starvation probabilities Upstream machine M 1 Downstream machine M 2 Slide 15 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione Total average throughput: System yield:Average buffer level: Blocking (starvation) probabilities equations Monitored machine model Stationary state probability distribution Transition probabilities False alarm state: Detected out of control state: Pseudo-machine model 4- Two machine one buffer with local monitoring Slide 16 Dipartimento di Meccanica Sezione Tecnologie Meccaniche e Produzione C 1,2 M 2 B 1,1 p 1,1 r 2,1 p 2,1 r 1,1F p 1,1F r 1,2 p 1,2 r 2,2 p 2,2 r 2,2F p 2,2F r M 1 Monitored machine M i Control chart C i,q (i

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