Stochastic processes applied in degradation data analysis-literature review
DOI:
https://doi.org/10.61799/2216-0388.301Keywords:
Confiabilidad, Modelo de degradación, Proceso estocástico en degradación, Proceso Gamma en degradación, Proceso inverso Gaussiano en degradación, Proceso Wiener en degradaciónAbstract
Improving, calculating and projecting the reliability of products is a fundamental task nowadays in the industry. The most common stochastic process models in the literature and applications are the Gamma and Wiener processes. However, both models are insufficient to adjust all degradation data. There are applications where they do not fit at all and can lead to erroneous conclusions. In this manner, the Gaussian inverse process is a very attractive option for degradation data. In order to compare the Wiener, gamma and Gaussian inverse processes, we searched for written literature (books and articles) and online data-bases (virtual libraries, Academic Google and different data bases) for which some applications were obtained in different areas of study and the tendency of the use of the different processes through the last years. In addition, to identify characteristics and differences between each of the stochastic processes.
Keywords: Reliability, Degradation model, Stochastic process degradation, Gamma processes degradation, Inverse Gaussian Process degradation, Wiener Process degradation
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References
[1] G. Rueda-Vera, S. Thomas-Manzano y Y. Casadiego Duque, “La valoración de empresas aplicada en las Mipymes de confecciones textiles de Cúcuta”, Respuestas, vol. 18, n.º 1, pp. 43-49, jun. 2013.
https://doi.org/10.22463/0122820X.396Ç
[2] L. Cely-Illera y R. Bolívar-León, “Materia prima para la industria cerámica de Norte de Santander. II. Evaluación del comportamiento térmico y su incidencia en las propiedades tecnológicas”, Respuestas, vol. 20, n.º 1, pp. 84-94, ene. 2015.
https://doi.org/10.22463/0122820X.260
[3] J.Uzcátegui-Gutiérrez, A. Varela-Cárdenas, y J. Díaz-García, "Aplicación de herramientas de clase mundial para la gestión de mantenimiento en empresas cementeras basado en la metodología MCC", Respuestas, vol. 21, n.º 1, pp. 77-88, ene. 2016.
https://doi.org/10.22463/0122820X.639
[4] R. Monroy-Sepúlveda, B. Ramón-Valencia y Y. Romero-Arcos, "Efecto de la concentración de silicato de sodio y ácido fosfórico en la reducción de la temperatura de cocción de las baldosas cerámicas", Respuestas, vol. 19, n.º 2, pp. 25-31, jul. 2014.
https://doi.org/10.22463/0122820X.434
[5] A. Sarabia-Guarin, J. Sánchez-Molina y J. Leyva-Díaz, "Uso de nutrientes tecnológicos como materia prima en la fabricación de materiales de construcción en el paradigma de la economía circular", Respuestas, vol. 22, n.º 1, pp. 6 - 16, ene. 2017.
https://doi.org/10.22463/0122820X.815
[6] J. Pabón-León, L. Bastos-Osorio, y J. Mogrovejo-Andrade, “Valor económico agregado en las empresas del sector industrial manufacturero de Cúcuta periodo 2008-2012”, Respuestas, vol. 20, n.º 2, pp. 54-72, 2015. https://doi.org/10.22463/0122820X.442
[7] M. Riaño-Solano, "Administración del Capital de Trabajo, Liquidez y Rentabilidad en el Sector Textil de Cúcuta, Periodo 2008-2011", Respuestas, vol. 19, n.º 1, pp. 86-98, 2014.
https://doi.org/10.22463/0122820X.11
[8] A. V. Miranda, "La industria automotriz en México: Antecedentes, situación actual y perspectivas," Contaduría y administración, pp. 209-246, 2007.
[9] F. J. Droguett Jorquera, "Calidad y satisfacción en el servicio a clientes de la industria automotriz: análisis de principales factores que afectan la evaluación de los clientes," 2012.
[10] R. A. Dovich, Reliability Statistics: ASQC Quality Press, 1990.
[11] S.-T. Tseng and H.-F. Yu, "A Termination Rule for Degradation Experiments," IEEE TRANSACTIONS ON RELIABILITY, pp. 130-133, 1997.
[12] W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data: Wiley, 1998.
[13] X. Wang and D. Xu, "An Inverse Gaussian Process Model for Degradation Data," Technometrics, vol. 52, pp. 188-197, 2010/05/01 2010.
[14] R. R. Zhou, N. Serban, and N. Gebraeel, "Degradation modeling applied to residual lifetime prediction using functional data analysis " The Annals of Applied Statistics, vol. 5, pp. 1586-1610, 2011.
[15] E. Zio and F. Di Maio, "Fatigue crack growth estimation by relevance vector machine," Expert Systems with Applications, vol. 39, pp. 10681-10692, 2012/09/15/ 2012.
[16] X. Wang, "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, vol. 101, pp. 340-351, 2010/02/01/ 2010.
[17] G. Jin, D. E. Matthews, and Z. Zhou, "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering & System Safety, vol. 113, pp. 7-20, 2013/05/01/ 2013.
[18] A. Widodo, M.-C. Shim, W. Caesarendra, and B.-S. Yang, "Intelligent prognostics for battery health monitoring based on sample entropy," Expert Systems with Applications, vol. 38, pp. 11763-11769, 2011/09/01/ 2011.
[19] K. Javed, R. Gouriveau, N. Zerhouni, and P. Nectoux, "Enabling Health Monitoring Approach Based on Vibration Data for Accurate Prognostics," IEEE Transactions on Industrial Electronics, vol. 62, pp. 647-656, 2015.
[20] P. K. Kankar, S. C. Sharma, and S. P. Harsha, "Rolling element bearing fault diagnosis using wavelet transform," Neurocomputing, vol. 74, pp. 1638-1645, 2011/05/01/ 2011.
[21] Z. Liu, H. Cao, X. Chen, Z. He, and Z. Shen, "Multi-fault classification based on wavelet SVM with PSO algorithm to analyze vibration signals from rolling element bearings," Neurocomputing, vol. 99, pp. 399-410, 2013/01/01/ 2013.
[22] X.-S. Si, W. Wang, M.-Y. Chen, C.-H. Hu, and D.-H. Zhou, "A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution," European Journal of Operational Research, vol. 226, pp. 53-66, 2013/04/01/ 2013.
[23] Z. S. Ye, Y. Wang, K. L. Tsui, and M. Pecht, "Degradation Data Analysis Using Wiener Processes With Measurement Errors," IEEE Transactions on Reliability, vol. 62, pp. 772-780, 2013.
[24] C. Graham, "Stochastic Process Algebra Structure for Insensitivity," In Proc. of 7th International Workshop on Process Algebras and Performance Modeling, PAPM, pp. 63-82, 1999.
[25] L. A. Rodríguez Picón, M. I. Rodríguez Borbón, and A. Flores Ortega, "Estimación de confiabilidad para productos con dos características de desempeño basada en un modelo de degradación estocástico bivariado," CULCyT, 2016.
[26] S. Yáñez and R. A. Granada, "Comparación de metodologías para el análisis de datos de degradación para trayectorias lineales," Revista Colombiana de Estadística, pp. 133-151, 2006.
[27] C. J. Lu and W. Q. Meeker, "Using Degradation Measures to Estimate a Time-to-Failure Distribution," Technometrics, vol. 35, pp. 161-174, 1993.
[28] D.-G. Chen, Y. Lio, H. K. T. Ng, and T.-R. Tsai, Statistical Modeling for Degradation Data, 1 ed.: Springer Singapore, 2017.
[29] L. A. Escobar R., E. R. Villa D., and S. Yañez C., "Confiabilidad: historia, estado del arte y desafíos futuros," Dyna, vol. 70, pp. 5-21, 2003.
[30] J. Acuña Acuña, Ingeniería de Confiabilidad. Costa Rica Editorial Tecnológica de Costa Rica, 2003.
[31] E. A. Elsayed, Reliability engineering vol. 88: John Wiley & Sons, 2012.
[32] L. W. Condra, Reliabilty improvement with design of experiments. New York: Marcel Dekker, 1993.
[33] E. E. Lewis, "Introduction to reliability engineering," 1987.
[34] P. P. Cabezas O, "La Función Gamma y sus Aplicaciones," 2008, vol. 3, 2008-05-30 2008.
[35] P. Ibarrola Muñoz and V. Quesada Paloma, "Simulación de trayectorias en procesos gamma-exponenciales," Estadística Española, pp. 7-30, 1982.
[36] N. J. Lasprilla, "Teoría de la ruina y el proceso de Wiener," Revista Colombiana de Estadística, vol. 4, 1983.
[37] U. Cárcamo C, "Procesos de Wiener," Revista Universidad EAFIT, vol. 110, pp. 39-51, 1998.
[38] Z.-S. Ye and N. Chen, "The Inverse Gaussian Process as a Degradation Model," Technometrics, vol. 56, pp. 302-311, 2014/07/03 2014.
[39] F. Duan and G. Wang, "Optimal design for constant-stress accelerated degradation test based on gamma process," Communications in Statistics - Theory and Methods, pp. 1-25, 2018.
[40] C. Peng and S. Tseng, "Mis-Specification Analysis of Linear Degradation Models," IEEE Transactions on Reliability, vol. 58, pp. 444-455, 2009.
[41] J. D. Esary and A. W. Marshall, "Shock Models and Wear Processes," Ann. Probab., vol. 1, pp. 627-649, 1973/08 1973.
[42] J. Lawless and M. Crowder, "Covariates and random effects in a Gamma process model with application to degradation and failur," Kluwer Academic Publishers, pp. 2013-227, 2004.
[43] W. Kahle, S. Mercier, and C. Paroissin, Degradation Processes in Reliability vol. Volume 3: Wiley, 2016.
[44] I. Iervolino, M. Giorgio, and E. Chioccarelli, "Gamma degradation models for earthquake-resistant structures," Structural Safety, vol. 45, pp. 48-58, 2013/11/01/ 2013.
[45] J. M. van Noortwijk, "A survey of the application of gamma processes in maintenance," Reliability Engineering & System Safety, vol. 94, pp. 2-21, 2009/01/01/ 2009.
https://doi.org/10.22463/0122820X.396Ç
[2] L. Cely-Illera y R. Bolívar-León, “Materia prima para la industria cerámica de Norte de Santander. II. Evaluación del comportamiento térmico y su incidencia en las propiedades tecnológicas”, Respuestas, vol. 20, n.º 1, pp. 84-94, ene. 2015.
https://doi.org/10.22463/0122820X.260
[3] J.Uzcátegui-Gutiérrez, A. Varela-Cárdenas, y J. Díaz-García, "Aplicación de herramientas de clase mundial para la gestión de mantenimiento en empresas cementeras basado en la metodología MCC", Respuestas, vol. 21, n.º 1, pp. 77-88, ene. 2016.
https://doi.org/10.22463/0122820X.639
[4] R. Monroy-Sepúlveda, B. Ramón-Valencia y Y. Romero-Arcos, "Efecto de la concentración de silicato de sodio y ácido fosfórico en la reducción de la temperatura de cocción de las baldosas cerámicas", Respuestas, vol. 19, n.º 2, pp. 25-31, jul. 2014.
https://doi.org/10.22463/0122820X.434
[5] A. Sarabia-Guarin, J. Sánchez-Molina y J. Leyva-Díaz, "Uso de nutrientes tecnológicos como materia prima en la fabricación de materiales de construcción en el paradigma de la economía circular", Respuestas, vol. 22, n.º 1, pp. 6 - 16, ene. 2017.
https://doi.org/10.22463/0122820X.815
[6] J. Pabón-León, L. Bastos-Osorio, y J. Mogrovejo-Andrade, “Valor económico agregado en las empresas del sector industrial manufacturero de Cúcuta periodo 2008-2012”, Respuestas, vol. 20, n.º 2, pp. 54-72, 2015. https://doi.org/10.22463/0122820X.442
[7] M. Riaño-Solano, "Administración del Capital de Trabajo, Liquidez y Rentabilidad en el Sector Textil de Cúcuta, Periodo 2008-2011", Respuestas, vol. 19, n.º 1, pp. 86-98, 2014.
https://doi.org/10.22463/0122820X.11
[8] A. V. Miranda, "La industria automotriz en México: Antecedentes, situación actual y perspectivas," Contaduría y administración, pp. 209-246, 2007.
[9] F. J. Droguett Jorquera, "Calidad y satisfacción en el servicio a clientes de la industria automotriz: análisis de principales factores que afectan la evaluación de los clientes," 2012.
[10] R. A. Dovich, Reliability Statistics: ASQC Quality Press, 1990.
[11] S.-T. Tseng and H.-F. Yu, "A Termination Rule for Degradation Experiments," IEEE TRANSACTIONS ON RELIABILITY, pp. 130-133, 1997.
[12] W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data: Wiley, 1998.
[13] X. Wang and D. Xu, "An Inverse Gaussian Process Model for Degradation Data," Technometrics, vol. 52, pp. 188-197, 2010/05/01 2010.
[14] R. R. Zhou, N. Serban, and N. Gebraeel, "Degradation modeling applied to residual lifetime prediction using functional data analysis " The Annals of Applied Statistics, vol. 5, pp. 1586-1610, 2011.
[15] E. Zio and F. Di Maio, "Fatigue crack growth estimation by relevance vector machine," Expert Systems with Applications, vol. 39, pp. 10681-10692, 2012/09/15/ 2012.
[16] X. Wang, "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, vol. 101, pp. 340-351, 2010/02/01/ 2010.
[17] G. Jin, D. E. Matthews, and Z. Zhou, "A Bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft," Reliability Engineering & System Safety, vol. 113, pp. 7-20, 2013/05/01/ 2013.
[18] A. Widodo, M.-C. Shim, W. Caesarendra, and B.-S. Yang, "Intelligent prognostics for battery health monitoring based on sample entropy," Expert Systems with Applications, vol. 38, pp. 11763-11769, 2011/09/01/ 2011.
[19] K. Javed, R. Gouriveau, N. Zerhouni, and P. Nectoux, "Enabling Health Monitoring Approach Based on Vibration Data for Accurate Prognostics," IEEE Transactions on Industrial Electronics, vol. 62, pp. 647-656, 2015.
[20] P. K. Kankar, S. C. Sharma, and S. P. Harsha, "Rolling element bearing fault diagnosis using wavelet transform," Neurocomputing, vol. 74, pp. 1638-1645, 2011/05/01/ 2011.
[21] Z. Liu, H. Cao, X. Chen, Z. He, and Z. Shen, "Multi-fault classification based on wavelet SVM with PSO algorithm to analyze vibration signals from rolling element bearings," Neurocomputing, vol. 99, pp. 399-410, 2013/01/01/ 2013.
[22] X.-S. Si, W. Wang, M.-Y. Chen, C.-H. Hu, and D.-H. Zhou, "A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution," European Journal of Operational Research, vol. 226, pp. 53-66, 2013/04/01/ 2013.
[23] Z. S. Ye, Y. Wang, K. L. Tsui, and M. Pecht, "Degradation Data Analysis Using Wiener Processes With Measurement Errors," IEEE Transactions on Reliability, vol. 62, pp. 772-780, 2013.
[24] C. Graham, "Stochastic Process Algebra Structure for Insensitivity," In Proc. of 7th International Workshop on Process Algebras and Performance Modeling, PAPM, pp. 63-82, 1999.
[25] L. A. Rodríguez Picón, M. I. Rodríguez Borbón, and A. Flores Ortega, "Estimación de confiabilidad para productos con dos características de desempeño basada en un modelo de degradación estocástico bivariado," CULCyT, 2016.
[26] S. Yáñez and R. A. Granada, "Comparación de metodologías para el análisis de datos de degradación para trayectorias lineales," Revista Colombiana de Estadística, pp. 133-151, 2006.
[27] C. J. Lu and W. Q. Meeker, "Using Degradation Measures to Estimate a Time-to-Failure Distribution," Technometrics, vol. 35, pp. 161-174, 1993.
[28] D.-G. Chen, Y. Lio, H. K. T. Ng, and T.-R. Tsai, Statistical Modeling for Degradation Data, 1 ed.: Springer Singapore, 2017.
[29] L. A. Escobar R., E. R. Villa D., and S. Yañez C., "Confiabilidad: historia, estado del arte y desafíos futuros," Dyna, vol. 70, pp. 5-21, 2003.
[30] J. Acuña Acuña, Ingeniería de Confiabilidad. Costa Rica Editorial Tecnológica de Costa Rica, 2003.
[31] E. A. Elsayed, Reliability engineering vol. 88: John Wiley & Sons, 2012.
[32] L. W. Condra, Reliabilty improvement with design of experiments. New York: Marcel Dekker, 1993.
[33] E. E. Lewis, "Introduction to reliability engineering," 1987.
[34] P. P. Cabezas O, "La Función Gamma y sus Aplicaciones," 2008, vol. 3, 2008-05-30 2008.
[35] P. Ibarrola Muñoz and V. Quesada Paloma, "Simulación de trayectorias en procesos gamma-exponenciales," Estadística Española, pp. 7-30, 1982.
[36] N. J. Lasprilla, "Teoría de la ruina y el proceso de Wiener," Revista Colombiana de Estadística, vol. 4, 1983.
[37] U. Cárcamo C, "Procesos de Wiener," Revista Universidad EAFIT, vol. 110, pp. 39-51, 1998.
[38] Z.-S. Ye and N. Chen, "The Inverse Gaussian Process as a Degradation Model," Technometrics, vol. 56, pp. 302-311, 2014/07/03 2014.
[39] F. Duan and G. Wang, "Optimal design for constant-stress accelerated degradation test based on gamma process," Communications in Statistics - Theory and Methods, pp. 1-25, 2018.
[40] C. Peng and S. Tseng, "Mis-Specification Analysis of Linear Degradation Models," IEEE Transactions on Reliability, vol. 58, pp. 444-455, 2009.
[41] J. D. Esary and A. W. Marshall, "Shock Models and Wear Processes," Ann. Probab., vol. 1, pp. 627-649, 1973/08 1973.
[42] J. Lawless and M. Crowder, "Covariates and random effects in a Gamma process model with application to degradation and failur," Kluwer Academic Publishers, pp. 2013-227, 2004.
[43] W. Kahle, S. Mercier, and C. Paroissin, Degradation Processes in Reliability vol. Volume 3: Wiley, 2016.
[44] I. Iervolino, M. Giorgio, and E. Chioccarelli, "Gamma degradation models for earthquake-resistant structures," Structural Safety, vol. 45, pp. 48-58, 2013/11/01/ 2013.
[45] J. M. van Noortwijk, "A survey of the application of gamma processes in maintenance," Reliability Engineering & System Safety, vol. 94, pp. 2-21, 2009/01/01/ 2009.
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2018-07-01
How to Cite
Quezada del Villara, A. V., Rodríguez Picón, L. A., Pérez Olguín, I. J. C., & Rodríguez Borbón, I. (2018). Stochastic processes applied in degradation data analysis-literature review. Mundo FESC Journal, 8(16), 68–77. https://doi.org/10.61799/2216-0388.301
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