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A Markov Quality Control Process Subject to Partial Observation

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  • Chelsea C. White

    (University of Virginia)

Abstract

This paper studies the problem of optimally controlling a discrete-time production process with countable state space which is subject to one of three control settings at each time interval: produce, inspect while producing, or repair (revise) the process. The cost of the item produced and the inspection and repair costs are assumed dependent on the state of the production process. It is assumed that the inspector-decisionmaker receives imperfect on-line observations of the production process at both times of production and inspection. Bounds on optimal cost are obtained. For the two-state case, several results associated with observation quality are determined which are sufficient for particularly simple characterizations of an optimal policy. Generalizations of several results due to Ross are also presented.

Suggested Citation

  • Chelsea C. White, 1977. "A Markov Quality Control Process Subject to Partial Observation," Management Science, INFORMS, vol. 23(8), pages 843-852, April.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:8:p:843-852
    DOI: 10.1287/mnsc.23.8.843
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    Citations

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    Cited by:

    1. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    2. Gong, Linguo & Tang, Kwei, 1997. "Monitoring machine operations using on-line sensors," European Journal of Operational Research, Elsevier, vol. 96(3), pages 479-492, February.
    3. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    4. Wallace J. Hopp & Sung‐Chi Wu, 1988. "Multiaction maintenance under markovian deterioration and incomplete state information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 447-462, October.
    5. Kuo, Yarlin, 2006. "Optimal adaptive control policy for joint machine maintenance and product quality control," European Journal of Operational Research, Elsevier, vol. 171(2), pages 586-597, June.
    6. V. Makis & X. Jiang, 2003. "Optimal Replacement Under Partial Observations," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 382-394, May.
    7. White, Chelsea C. & Cheong, Taesu, 2012. "In-transit perishable product inspection," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 310-330.
    8. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    9. Armando Z. Milioni & Stanley R. Pliska, 1988. "Optimal inspection under semi‐markovian deterioration: Basic results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 373-392, October.
    10. Jue Wang, 2016. "Minimizing the false alarm rate in systems with transient abnormality," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 320-334, June.
    11. Abraham Grosfeld‐Nir & Eyal Cohen & Yigal Gerchak, 2007. "Production to order and off‐line inspection when the production process is partially observable," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 845-858, December.
    12. Hao Zhang & Weihua Zhang, 2023. "Analytical Solution to a Partially Observable Machine Maintenance Problem with Obvious Failures," Management Science, INFORMS, vol. 69(7), pages 3993-4015, July.
    13. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.

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