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An Optimal Bayesian Maintenance Policy for a Partially Observable System Subject to Two Failure Modes

Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

Abstract:

In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed, illustrated by a numerical example.

Keywords: Partially observable system, hidden Markov model, competing risks, multivariate Bayesian control.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094729

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References:


[1] W. Jianmou and V. Makis, "Economic and economic-statistical design of a chi-square chart for cbm,” European Journal of Operation Research, vol. 188, no. 2, pp. 516–529, 2008.
[2] B. Liu, "Vibration data monitoring and design of multivariate ewma chart for cbm,” Ph.D. Dissertation, University of Totonto, 2006.
[3] M. Kim and V. Makis, "Joint optimization of sampling and control of partially observable failing systems,” Operation Research, vol. 61, no. 3, pp. 77–790, 2013.
[4] V. Makis, "Multivariate bayesian control chart,” Operation Research, vol. 56, pp. 487–496, 2008.
[5] ——, "Multivariate bayesian process control for a finite production run,” European Journal of Operation Research, vol. 194, pp. 795–806, 2009.
[6] R. Jiang and V. Makis, "Arl criterion in bayesian process control using hidden markov model,” IEEE, 2009.
[7] Z. Yin and V. Makis, "Economic and economic-statistical design of a multivariate bayesian control chart for condition-based maintenance,” IMA Journal of Management Mathematics, vol. 22, pp. 47–63, 2010.
[8] R. Jiang, J. Yu, and V. Makis, "Optimal bayesian estimation and control scheme for gear shaft fault detection,” Computers & Industrial Engineering, vol. 63, pp. 754–762, 2012.
[9] M. Kim, R. Jiang, V. Makis, and L. C., "Optimal bayesian fault prediction scheme for a partially observable system subject to random failure,” European Journal of Operational Research, vol. 214, pp. 331–339, 2011.
[10] R. Jiang, M. Kim, V. Makis, and C. Lee, "A bayesian model and numerical algorithm for cbm availability maximization,” Annals of Operations Research, vol. 196, no. 1, pp. 333–348, 2012.
[11] X. Liu, J. Li, K. Al-Khalifa, A. Hamouda, andW. Coit, "Condition-based maintenance for continuously monitored degrading systems with multiple failure modes,” IIE Transactions, vol. 45, no. 4, pp. 422–35, 2013.
[12] I. Tumer and E. Huff, "Analysis of triaxial vibration data for health monitoring of helicopter gearboxes,” Journal of Vibration and Acoustics, vol. 125, pp. 120–128, 2003.
[13] V. Makis, J. Wu, and Y. Gao, "An application of dpca to oil data for cbm modeling,” European Journal of Operational Research, vol. 174, no. 1, pp. 112–123, 2006.
[14] X. Wang, V. Makis, and Y. M, "A wavelet approach to fault diagnosis of agearbox under varying load conditions,” Journal of Soundand Vibration, vol. 329, p. 15701585, 2010.
[15] R. Jiang, "System availability maximization and residual life predictioni under partial observations,” Ph.D. thesis, University of Toroto, 2011.
[16] R. Palivonaite, K. Lukoseviciute, and M. Ragulskis, "Algebraic segmentaion of short nonstationary time series based on evolutionary prediction algorithms,” Neurocomputing, vol. 121, pp. 354–364, 2013.
[17] H. Aksoy, A. Gedikli, N. Unal, and A. Kehagias, "Fast segmentation algoirthms for long hydrometeorological time series,” Hydrological Processes, vol. 22, pp. 4600–4608, 2008.
[18] J. Yang and V. Makis, "Dynamic response of residual to external deviations in a controlled production process,” Technometrics, vol. 42, pp. 290–299, 2000.
[19] A. Snoussi, M. Ghourabi, and M. Limam, "On spc for short run autocorrelated data,” Communication in Statistics-Simulation and Computation, vol. 34, pp. 219–234, 2005.
[20] M. Ghourabi and M. Limam, "Residual responses to change patterns of autocorrelated processes,” Journal of Applied Statistics, vol. 34, no. 7, pp. 785–798, 2007.
[21] V. Makis and J. X, "Optimal replacement under partial observations,” Mathematics of Operation Research, vol. 28, no. 2, pp. 382–394, 2003.
[22] S. Provost and E. Rudiuk, "The exact distribution of indefinite quadratic forms in noncentral normal vectors,” Annals of the Institute of Statistical Mathematics, vol. 48, no. 1, pp. 381–394, 1996.