Residual Life Prediction for a System Subject to Condition Monitoring and Two Failure Modes
In this paper, we investigate the residual life prediction
problem 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 with
unknown parameters. The parameter estimation procedure based on
an EM algorithm is developed and the formulas for the conditional
reliability function and the mean residual life are derived, illustrated
by a numerical example.
[1] 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.
[2] 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.
[3] X. Wang, V. Makis, and Y. M, "A wavelet approach to fault diagnosis of
agearbox under varying load conditions,” Journal of Sound and Vibration,
vol. 329, p. 15701585, 2010.
[4] 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.
[5] R. Jiang, "System availability maximization and residual life predictioni
under partial observations,” Ph.D. thesis, University of Toroto, 2011.
[6] 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.
[7] V. Makis and A. Jardine, "Optimal replacement in the proportional
hazards model,” INFOR, vol. 30, no. 1, pp. 172–183, 1992.
[8] F. Nelwamondo, T. Marwala, and U. Mahola, "Early classifications of
bearing faults using hidden markov models, gaussian mixture models,
mel-frequency cepstral coefficients and fractals,” International Journal
of Innovative Computing Information and Control, vol. 2, no. 6, p.
12811299, 2006a.
[9] M. Dong and D. He, "Hidden semi-markov model-based methodology
for multi-sensor equipment health diagnosis and prognosis,” European
Journal of Operational Research, vol. 178, no. 2, pp. 858–878, 2007.
[10] K. M. J. Jiang, R. and V. Makis, "Maximum likelihood estimation for a
hidden semi-markov model with multivariate observation,” Quality and
Reliability Engineering International, 2012.
[11] M. Kim, V. Makis, and R. Jiang, "Parameter estimation in a
condition-based maintenance model,” Statistics and Probability Letters,
vol. 80, no. 21-22, pp. 1633–1639, 2010.
[12] J. Yang and V. Makis, "Dynamic response of residual to external
deviations in a controlled production process,” Technometrics, vol. 42,
pp. 290–299, 2000.
[13] M. Kim, V. Makis, and R. Jiang, "Parameter estimation for partially
observable systems subject to random failure,” Applied Stochastic
Models in Business and Industry, 2012.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] S. Asmussen, O. Nerman, and O. M, "Fitting phase-type distribution via
the em algorithm,” Scan J Stat, vol. 23, pp. 419–44, 1996.
[19] A. Khaleghei GB and V. Makis, "Hsm modeling of a partially
observable system subject to deterioration and random failure using
phase method,” 2012. (Online). Available: http://www.mie.utoronto.ca/
research/technical-reports/reports/report.pdf
[1] 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.
[2] 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.
[3] X. Wang, V. Makis, and Y. M, "A wavelet approach to fault diagnosis of
agearbox under varying load conditions,” Journal of Sound and Vibration,
vol. 329, p. 15701585, 2010.
[4] 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.
[5] R. Jiang, "System availability maximization and residual life predictioni
under partial observations,” Ph.D. thesis, University of Toroto, 2011.
[6] 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.
[7] V. Makis and A. Jardine, "Optimal replacement in the proportional
hazards model,” INFOR, vol. 30, no. 1, pp. 172–183, 1992.
[8] F. Nelwamondo, T. Marwala, and U. Mahola, "Early classifications of
bearing faults using hidden markov models, gaussian mixture models,
mel-frequency cepstral coefficients and fractals,” International Journal
of Innovative Computing Information and Control, vol. 2, no. 6, p.
12811299, 2006a.
[9] M. Dong and D. He, "Hidden semi-markov model-based methodology
for multi-sensor equipment health diagnosis and prognosis,” European
Journal of Operational Research, vol. 178, no. 2, pp. 858–878, 2007.
[10] K. M. J. Jiang, R. and V. Makis, "Maximum likelihood estimation for a
hidden semi-markov model with multivariate observation,” Quality and
Reliability Engineering International, 2012.
[11] M. Kim, V. Makis, and R. Jiang, "Parameter estimation in a
condition-based maintenance model,” Statistics and Probability Letters,
vol. 80, no. 21-22, pp. 1633–1639, 2010.
[12] J. Yang and V. Makis, "Dynamic response of residual to external
deviations in a controlled production process,” Technometrics, vol. 42,
pp. 290–299, 2000.
[13] M. Kim, V. Makis, and R. Jiang, "Parameter estimation for partially
observable systems subject to random failure,” Applied Stochastic
Models in Business and Industry, 2012.
[14] 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.
[15] 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.
[16] 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.
[17] 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.
[18] S. Asmussen, O. Nerman, and O. M, "Fitting phase-type distribution via
the em algorithm,” Scan J Stat, vol. 23, pp. 419–44, 1996.
[19] A. Khaleghei GB and V. Makis, "Hsm modeling of a partially
observable system subject to deterioration and random failure using
phase method,” 2012. (Online). Available: http://www.mie.utoronto.ca/
research/technical-reports/reports/report.pdf
@article{"International Journal of Engineering, Mathematical and Physical Sciences:67506", author = "Akram Khaleghei Ghosheh Balagh and Viliam Makis", title = "Residual Life Prediction for a System Subject to Condition Monitoring and Two Failure Modes", abstract = "In this paper, we investigate the residual life prediction
problem 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 with
unknown parameters. The parameter estimation procedure based on
an EM algorithm is developed and the formulas for the conditional
reliability function and the mean residual life are derived, illustrated
by a numerical example.
", keywords = "Partially observable system, hidden Markov model,
competing risks, residual life prediction.", volume = "8", number = "6", pages = "965-6", }
