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State estimation of a shop floor using improved resampling rules for particle filtering

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  • Celik, Nurcin
  • Son, Young-Jun
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    Abstract

    Operational inefficiencies in supply chains cost industries millions of dollars every year. Much of these inefficiencies arise due to the lack of a coherent planning and control mechanism, which requires accurate yet timely state estimation of these large-scale dynamic systems given their massive datasets. While Bayesian inferencing procedures based on particle filtering paradigm may meet these requirements in state estimation, they may end up in a situation called degeneracy, where a single particle abruptly possesses significant amount of normalized weights. Resampling rules for importance sampling prevent the sampling procedure from generating degenerated weights for particles. In this work, we propose two new resampling rules concerning minimized variance (VRR) and minimized bias (BRR). The proposed rules are derived theoretically and their performances are benchmarked against that of the minimized variance and half-width based resampling rules existing in the literature using a simulation of a semiconductor die manufacturing shop floor in terms of their resampling qualities (mean and variance of root mean square errors) and computational efficiencies, where we identify the circumstances that the proposed resampling rules become particularly useful.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 134 (2011)
    Issue (Month): 1 (November)
    Pages: 224-237

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    Handle: RePEc:eee:proeco:v:134:y:2011:i:1:p:224-237

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    Web page: http://www.elsevier.com/locate/ijpe

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    Keywords: Sequential Monte Carlo methods Resampling rules Importance sampling Simulation Shop floor state estimation;

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    1. J. Koop, 1962. "On upper limits to the difference in bias between two ratio estimates," Metrika, Springer, vol. 5(1), pages 145-149, January.
    2. Surekha, K. & Ghali, Moheb, 2001. "The speed of adjustment and production smoothing: Bayesian estimation," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 55-65, May.
    3. Roberto Casarin & Domenico sartore, 2008. "Matrix-State Particle Filter for Wishart Stochastic Volatility Processes," Working Papers 0816, University of Brescia, Department of Economics.
    4. Neil Shephard & Thomas Flury, 2008. "Bayesian inference based only on simulated likelihood: particle filter analysis of dynamic economic models," Economics Series Working Papers 413, University of Oxford, Department of Economics.
    5. Meng, Xiao-Li, 1993. "On the absolute bias ratio of ratio estimators," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 345-348, December.
    6. Paul Fearnhead & Peter Clifford, 2003. "On-line inference for hidden Markov models via particle filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 887-899.
    7. Lee, Chih-Ming, 2008. "A Bayesian approach to determine the value of information in the newsboy problem," International Journal of Production Economics, Elsevier, vol. 112(1), pages 391-402, March.
    8. Mula, J. & Poler, R. & Garcia-Sabater, J.P. & Lario, F.C., 2006. "Models for production planning under uncertainty: A review," International Journal of Production Economics, Elsevier, vol. 103(1), pages 271-285, September.
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