An Optimal Bayesian Maintenance Policy for a Partially Observable System Subject to Two Failure Modes
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:68007", author = "Akram Khaleghei Ghosheh Balagh and Viliam Makis and Leila Jafari", title = "An Optimal Bayesian Maintenance Policy for a Partially Observable System Subject to Two Failure Modes", 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.", volume = "8", number = "9", pages = "1600-5", }
