IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v18y2018i1d10.1007_s12351-016-0254-9.html
   My bibliography  Save this article

Moment-based approximations for first- and second-order transient performance measures of an unreliable workstation

Author

Listed:
  • Farhood Rismanchian

    (Yonsei University)

  • Young Hoon Lee

    (Yonsei University)

Abstract

Performance measures of manufacturing systems have been intensively researched. However, little attention has been paid to the transient performance analysis of non-Markovian production systems. Therefore, this paper proposes a method to approximate the properties of a two-state non-Markovian system. In particular, an unreliable workstation with two states, operating and failed states, is considered. This system is a simplified version of an industrial manufacturing system. Moment-based approximations for the expected output quantity of the workstation at any arbitrary time is derived and discussed. In addition, an upper bound approximation for the variation of the produced amount is proposed. Failure and repair times are assumed to be arbitrarily distributed. The proposed approximations are compared with a simulated model using the ARENA 10 free version software to demonstrate the accuracy of the method. These approximations are nonparametric, easy to implement and depend only on the first three moments of the underlying distributions without recourse to the functional form of the distributions.

Suggested Citation

  • Farhood Rismanchian & Young Hoon Lee, 2018. "Moment-based approximations for first- and second-order transient performance measures of an unreliable workstation," Operational Research, Springer, vol. 18(1), pages 75-95, April.
  • Handle: RePEc:spr:operea:v:18:y:2018:i:1:d:10.1007_s12351-016-0254-9
    DOI: 10.1007/s12351-016-0254-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-016-0254-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12351-016-0254-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. G. J. Miltenburg, 1987. "Variance of the number of units produced on a transfer line with buffer inventories during a period of length T," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 811-822, December.
    2. Tan, Baris, 1998. "Effects of variability on the due-time performance of a continuous materials flow production system in series," International Journal of Production Economics, Elsevier, vol. 54(1), pages 87-100, January.
    3. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    4. Tan, Baris, 1997. "Variance of the throughput of an N-station production line with no intermediate buffers and time dependent failures," European Journal of Operational Research, Elsevier, vol. 101(3), pages 560-576, September.
    5. Bruce Lindsay & Ramani Pilla & Prasanta Basak, 2000. "Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 215-230, June.
    6. Chen, Chin-Tai & Yuan, John, 2004. "Transient throughput analysis for a series type system of machines in terms of alternating renewal processes," European Journal of Operational Research, Elsevier, vol. 155(1), pages 178-197, May.
    7. Altiok, Tayfur & Ranjan, Raghav, 1989. "Analysis of production lines with general service times and finite buffers: A two-node decomposition approach," Engineering Costs and Production Economics, Elsevier, vol. 17(1-4), pages 155-165, August.
    8. Barış Tan, 2000. "Asymptotic variance rate of the output in production lines with finite buffers," Annals of Operations Research, Springer, vol. 93(1), pages 385-403, January.
    9. Papadopoulos, Hrissoleon T., 1996. "An analytic formula for the mean throughput of K-station production lines with no intermediate buffers," European Journal of Operational Research, Elsevier, vol. 91(3), pages 481-494, June.
    10. Kevin B. Hendricks, 1992. "The Output Processes of Serial Production Lines of Exponential Machines with Finite Buffers," Operations Research, INFORMS, vol. 40(6), pages 1139-1147, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shiyong Li & Wei Sun & Huan Liu, 2022. "Optimal resource allocation for multiclass services in peer-to-peer networks via successive approximation," Operational Research, Springer, vol. 22(3), pages 2605-2630, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. He, Xin-Feng & Wu, Su & Li, Quan-Lin, 2007. "Production variability of production lines," International Journal of Production Economics, Elsevier, vol. 107(1), pages 78-87, May.
    2. Tan, Baris, 1998. "Effects of variability on the due-time performance of a continuous materials flow production system in series," International Journal of Production Economics, Elsevier, vol. 54(1), pages 87-100, January.
    3. Kiesmüller, G.P. & Sachs, F.E., 2020. "Spare parts or buffer? How to design a transfer line with unreliable machines," European Journal of Operational Research, Elsevier, vol. 284(1), pages 121-134.
    4. Tan, Bar[iota]s, 1999. "Variance of the output as a function of time: Production line dynamics," European Journal of Operational Research, Elsevier, vol. 117(3), pages 470-484, September.
    5. Konstantinos S. Boulas & Georgios D. Dounias & Chrissoleon T. Papadopoulos, 2023. "A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 823-852, February.
    6. Chen, Chin-Tai & Yuan, John, 2004. "Transient throughput analysis for a series type system of machines in terms of alternating renewal processes," European Journal of Operational Research, Elsevier, vol. 155(1), pages 178-197, May.
    7. Tan, Baris, 1997. "Variance of the throughput of an N-station production line with no intermediate buffers and time dependent failures," European Journal of Operational Research, Elsevier, vol. 101(3), pages 560-576, September.
    8. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    9. Hautphenne, Sophie & Kerner, Yoav & Nazarathy, Yoni & Taylor, Peter, 2015. "The intercept term of the asymptotic variance curve for some queueing output processes," European Journal of Operational Research, Elsevier, vol. 242(2), pages 455-464.
    10. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.
    11. Dhouib, K. & Gharbi, A. & Landolsi, N., 2009. "Throughput assessment of mixed-model flexible transfer lines with unreliable machines," International Journal of Production Economics, Elsevier, vol. 122(2), pages 619-627, December.
    12. Papadopoulos, H. T., 1998. "An approximate method for calculating the mean sojourn time of K-station production lines with no intermediate buffers," International Journal of Production Economics, Elsevier, vol. 54(3), pages 297-305, May.
    13. Belmansour, Ahmed-Tidjani & Nourelfath, Mustapha, 2010. "An aggregation method for performance evaluation of a tandem homogenous production line with machines having multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1193-1201.
    14. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    15. Yang Woo Shin, 2022. "An Algorithm for Asymptotic Mean and Variance for Markov Renewal Process of M/G/1 Type with Finite Level," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 195-212, March.
    16. Korporaal, R. & Ridder, A.A.N. & Kloprogge, P. & Dekker, R., 1999. "Capacity planning of prisons in the Netherlands," Econometric Institute Research Papers EI 9909-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Lutz, Christian M. & Roscoe Davis, K. & Sun, Minghe, 1998. "Determining buffer location and size in production lines using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 301-316, April.
    18. Tan, BarIs & Gershwin, Stanley B., 2009. "Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer," International Journal of Production Economics, Elsevier, vol. 120(2), pages 327-339, August.
    19. Sumi Kim & Seongmoon Kim, 2015. "Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing," Annals of Operations Research, Springer, vol. 230(1), pages 35-55, July.
    20. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:operea:v:18:y:2018:i:1:d:10.1007_s12351-016-0254-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.