Remaining Useful Life Estimation Based on Detection of Explosive Changes: Analysis of Bearing Vibration
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Published
Jun 4, 2023
Diana Barraza Barraza
Víctor G. Tercero-Gómez
A. Eduardo Cordero-Franco
Mario G. Beruvides
Abstract
The monitoring of condition variables for maintenance purposes is a growing trend amongst researchers and practitioners where decisions are based on degradation levels. The two approaches in Condition-Based Maintenance (CBM) are diagnosing the level of degradation (diagnostics) or predicting when a certain level of degradation will be reached (prognostics). Using diagnostics determines when it is necessary to perform maintenance, but it rarely allows for estimation of future degradation. In the second case, prognostics does allow for degradation and failure prediction, however, its major drawback lies in when to perform the analysis, and exactly what information should be used for predictions. This encumbrance is due to previous studies that have shown that degradation variable could undergo a change that misleads these calculations. This paper addresses the issue of identifying explosive changes in condition variables, using Control Charts, to determine when to perform a new model fitting in order to obtain more accurate Remaining Useful Life (RUL) estimations. The diagnostic-prognostic methodology allows for discarding pre-change observations to avoid contamination in condition prediction. In addition the performance of the integration methodology is compared against adaptive autoregressive (AR) models. Results show that using only the observations acquired after the out-of-control signal produces more accurate RUL estimations.
##plugins.themes.bootstrap3.article.details##
Keywords
Remaining useful Life, condition-based maintenance, EWMAST, AR models
References
Alwan, L. C., & Roberts, H. V. (1988). Time-Series Process Modeling for Statistical Control. Journal of Business & Economic Statistics, 6(1), 87–95.
Barraza-Barraza, D. (2015). An adaptive ARX model to Estimate an Asset Remaining Useful Life (Unpublished doctoral dissertation). Texas Tech University.
Barraza-Barraza, D., Tercero-Gómez, V. G., Beruvides, M. G., & Limón-Robles, J. (2017). An adaptive ARX model to estimate the RUL of aluminum plates based on its crack growth. Mechanical Systems and Signal Processing, 82, 519–536. doi: 10.1016/j.ymssp.2016.05.041
Barraza-Barraza, D., Tercero-Gómez, V. G., Limón-Robles, J., & Beruvides, M. G. (2016). Statistical Monitoring of Condition Degradation in Maintenance : A State-of-the- Art Review. In Proceedings of the 2016 industrial and systems engineering research conference.
Ben-Daya, M., & Rahim, M. A. (2000). Effect of maintenance on the economic design of x-control chart. European Journal of Operational Research, 120(1), 131–143. doi: 10.1016/S0377-2217(98)00379-8
Bouslah, B., Gharbi, A., & Pellerin, R. (2015). Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint. Omega, 1–17. doi: 10.1016/j.omega.2015.07.012
Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
Capizzi, G., & Masarotto, G. (2007). The EWMAST Control Charts with Estimated Limits : Properties and Recommendations. In Proceedings of the 2007 ieee ieem (pp. 1403–1407).
Cassady, R. C., Bowden, R. O., Liew, L., & Pohl, E. A. (2000). Combining preventive maintenance and statistical process control: a preliminary investigation. IIE Transactions, 32(6), 471–478. doi: 10.1080/07408170008963924
Chan, L.-Y., & Wu, S. (2009). Optimal design for inspection and maintenance policy based on the CCC chart. Computers & Industrial Engineering, 57(3), 667–676. doi: 10.1016/j.cie.2008.12.009
Chen, N., & Tsui, K. L. (2013, sep). Condition monitoring and remaining useful life prediction using degradation signals: revisited. IIE Transactions, 45(9), 939–952. doi: 10.1080/0740817X.2012.706376
Croux, C., Gelper, S., Mahieu, K., & Croux, C. (2011). Robust control charts for time series data. Expert Systems with Applications, 38(11), 13810–13815.
Escobet, T., Quevedo, J., & Puig, V. (2012). A Fault / Anomaly System Prognosis using a Data- driven Approach considering Uncertainty. In Ieee world congress on computational intelligence (pp. 10–15). Brisbane.
Gardner, E. S. (2006). Exponential smoothing: The state of the art—Part II. International journal of forecasting, 22(4), 637–666.
Ho, L. L., & Quinino, R. C. (2012). Integrating on-line process control and imperfect corrective maintenance: An economical design. European Journal of Operational Research, 222(2), 253–262. doi: 10.1016/j.ejor.2012.04.019
Ivy, J. S., & Nembhard, H. B. (2005). A modeling approach to maintenance decisions using statistical quality control and optimization. Quality and Reliability Engineering International, 21(August 2003), 355–366. doi: 10.1002/qre.616
Jammu, N. S., & Kankar, P. K. (2011). A Review on Prognosis of Rolling Element Bearings. International Journal of Engineering Science and Technology, 3(10), 7497–7503.
Kirchg¨assner, G., Wolters, J., & Hassler, U. (2012). Introduction to Modern Time Series Analysis. Springer.
Landau, I. D., & Zito, G. (2006). Digital Control Systems. Design, Identification and Implementation. London: Springer.
Lee, J., Qiu, G., Yu, G., & Lin, J. (2007). IMS Bearing Data Set. Retrieved from https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-epository/
Lei, Y., Li, N., Guo, L., Li, N., Yan, T., & Lin, J. (2018). Machinery health prognostics: A systematic review from data acquisition to rul prediction. Mechanical Systems and Signal Processing, 104, 799–834.
Lim, C. K. R., & Mba, D. (2014). Switching Kalman filter for failure prognostic. Mechanical Systems and Signal Processing, 52-53, 426–435. doi: 10.1016/j.ymssp.2014.08.006
Linderman, K., McKone-Sweet, K. E., & Anderson, J. C. (2005). An integrated systems approach to process control and maintenance. European Journal of Operational Research, 164(2), 324–340. doi: 10.1016/j.ejor.2003.11.026
Liu, L., Yu, M., Ma, Y., & Tu, Y. (2013). Economic and economic-statistical designs of an X control chart for twounit series systems with condition-based maintenance. European Journal of Operational Research, 226(3), 491–499. doi: 10.1016/j.ejor.2012.11.031
Ljung, L., & S¨oderstr¨om, T. (1983). Theory and practice of recursive identification.
Mehrafrooz, Z., & Noorossana, R. (2011). An integrated model based on statistical process control and maintenance. Computers & Industrial Engineering, 61(4), 1245–1255. doi: 10.1016/j.cie.2011.07.017
Montgomery, D. C. (2009). Introduction to Statistical Quality Control. Wiley.
Moubray, J. (1992). RCM II: Reliability-Centered Maintenance (1st ed.). New York: Industrial Press Inc.
NASA. (2008). NASA Reliability-Centered Maintenance Guide for Facilities and Collateral Equipment (Tech. Rep. No. September).
Nectoux, P., Gouriveau, R., Medjaher, K., Ramasso, E., Chebel-Morello, B., Zerhouni, N., & Varnier, C. (2012). PRONOSTIA: An experimental platform for bearings accelerated degradation tests. In Conference on prognostics and health management. (pp. 1–8).
Panagiotidou, S., & Nenes, G. (2009). An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart. Reliability Engineering and System Safety, 94, 732–741. doi: 10.1016/j.ress.2008.07.003
Panagiotidou, S., & Tagaras, G. (2010). Statistical process control and condition-based maintenance: a meaningful relationship through data sharing. Production and Operations Management, 19(2), 156–171. doi: 10.1111/j.1937-5956.2009.01073.x
Panagiotidou, S., & Tagaras, G. (2012). Optimal integrated process control and maintenance under general deterioration. Reliability Engineering and System Safety, 104, 58–70. doi: 10.1016/j.ress.2012.03.019
Pen˜abaena Niebles, R., Oviedo-Trespalacios, O´ ., Va´zques Cabeza, J. G., & Fernández Cantillo, L. M. (2013). Diseño estadístico de cartas de control para datos autocorrelacionados. Ingeniería y Desarrollo, 31(2), 1–50.
Perry, M. B., & Pignatiello Jr, J. J. (2010). Identifying the Time of Step Change in the Mean of Stationary Autocorrelated Processes. Journal of Applied Statistics, 26(1), 1–30. doi: 10.1002/qre.1055
Pintelon, L., & Parodi-Herz, A. (2008). Maintenance : An Evolutionary Perspective. In Complex systems maintenance handbook (pp. 21–48). Springer.
Prajapati, D. R., & Singh, S. (2012). Control charts for monitoring the autocorrelated process parameters: a literature review. International Journal of Productivity and Quality Management, 10(2), 207–249. doi: 10.1080/00401706.1998.10485479
Qiu, P. (2013). Introduction to Statistical Process Control. Taylor & Francis.
Quintana, A. E., Pisani, M. V., & Casal, R. N. (2015). Desempeño de cartas de control estadístico con límites bilaterales de probabilidad para monitorear procesos Weibull en mantenimiento. Ingeniería, Investigación y Tecnología, 16(1), 143–156. doi: 10.1016/S1405-7743(15)72115-3
Ran, Y., Zhou, X., Lin, P., Wen, Y., & Deng, R. (2019). A survey of predictive maintenance: Systems, purposes and approaches. arXiv preprint arXiv:1912.07383.
Searle, S. R. (2012). Linear models. Wiley.
Sikorska, J., Hodkiewicz, M., & Ma, L. (2011, jul). Prognostic modelling options for remaining useful life estimation by industry. Mechanical Systems and Signal Processing, 25(5), 1803–1836. doi: 10.1016/j.ymssp.2010.11.018
Son, J., Zhang, Y., Sankavaram, C., & Zhou, S. (2015). RUL prediction for individual units based on condition monitoring signals with a change point. IEEE Transactions on Reliability, 64(1), 182–196. doi: 10.1109/TR.2014.2355531
Tagaras, G. (1988). An integrated cost model for the joint optimization of process control and maintenance. Journal of the Operational Research Society, 39(8), 757–766. doi: 10.1057/palgrave.jors.0390807
Tambe, P. P., & Kulkarni, M. S. (2015). A superimposition based approach for maintenance and quality plan optimization with production schedule, availability, repair time and detection time constraints for a single machine. Journal of Manufacturing Systems, 37, 17–32. doi: 10.1016/j.jmsy.2015.09.009
Tandon, N., & Choudhury, A. (1999). A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribology international, 32(1999), 469–480.
Tobon-Mejia, D. A., Medjaher, K., & Zerhouni, N. (2012, apr). CNC machine tool’s wear diagnostic and prognostic by using dynamic Bayesian networks. Mechanical Systems and Signal Processing, 28, 167–182. doi: 10.1016/j.ymssp.2011.10.018
Wang, W. (2002). A model to predict the residual life of rolling element bearings given monitored condition information to date. IMA Journal of Management Mathematics, 13(1), 3–16. doi: 10.1093/imaman/13.1.3
Wang, W. (2012, may). A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems. European Journal of Operational Research, 218(3), 726–734. doi: 10.1016/j.ejor.2011.12.010
Wang, W., & Zhang, W. (2008). Early defect identification: application of statistical process control methods. Journal of Quality in Maintenance Engineering, 14, 225–236. doi: 10.1108/13552510810899445
Woodall, W. H., & Montgomery, D. C. (2014). Some Current Directions in the Theory and Application of Statistical Process Monitoring. Journal of Quality Technology, 46(1), 78–95.
Wu, J., & Makis, V. (2008). Economic and economicstatistical design of a chi-square chart for CBM. European Journal of Operational Research, 188(2), 516–529. doi: 10.1016/j.ejor.2007.05.002
Wu, S., & Wang, W. (2011). Optimal inspection policy for three-state systems monitored by control charts. Applied Mathematics and Computation, 217(23), 9810–9819. doi: 10.1016/j.amc.2011.04.075
Xiang, Y. (2013). Joint optimization of control chart and preventive maintenance policies: A discrete-time Markov chain approach. European Journal of Operational Research, 229(2), 382–390. doi: 10.1016/j.ejor.2013.02.041
Xie, M., Goh, T. N., & Ranjan, P. (2002). Some effective control chart procedures for reliability monitoring. Reliability Engineering and System Safety, 77(2), 143–150. doi: 10.1016/S0951-8320(02)00041-8
Yeung, T. G., Cassady, C. R., & Schneider, K. (2007). Simultaneous optimization of [Xbar] control chart and agebased preventive maintenance policies under an economic objective. IIE Transactions, 40(2), 147–159. doi: 10.1080/07408170701592515
Yin, H., Zhang, G., Zhu, H., Deng, Y., & He, F. (2015). An integrated model of statistical process control and maintenance based on the delayed monitoring. Reliability Engineering & System Safety, 133, 323–333. doi: 10.1016/j.ress.2014.09.020
Young, P. C. (2011). Recursive Estimation and Time-Series Analysis: An Introduction for the Student and Practitioner. Springer.
Zhang, N. F. (1998). A statistical control chart for stationary process data. Technometrics, 40(1), 24–38.
Zhou, W.-H., & Zhu, G.-L. (2008). Economic design of integrated model of control chart and maintenance management. Mathematical and Computer Modelling, 47(11-12), 1389–1395. doi: 10.1016/j.mcm.2007.09.008
Barraza-Barraza, D. (2015). An adaptive ARX model to Estimate an Asset Remaining Useful Life (Unpublished doctoral dissertation). Texas Tech University.
Barraza-Barraza, D., Tercero-Gómez, V. G., Beruvides, M. G., & Limón-Robles, J. (2017). An adaptive ARX model to estimate the RUL of aluminum plates based on its crack growth. Mechanical Systems and Signal Processing, 82, 519–536. doi: 10.1016/j.ymssp.2016.05.041
Barraza-Barraza, D., Tercero-Gómez, V. G., Limón-Robles, J., & Beruvides, M. G. (2016). Statistical Monitoring of Condition Degradation in Maintenance : A State-of-the- Art Review. In Proceedings of the 2016 industrial and systems engineering research conference.
Ben-Daya, M., & Rahim, M. A. (2000). Effect of maintenance on the economic design of x-control chart. European Journal of Operational Research, 120(1), 131–143. doi: 10.1016/S0377-2217(98)00379-8
Bouslah, B., Gharbi, A., & Pellerin, R. (2015). Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint. Omega, 1–17. doi: 10.1016/j.omega.2015.07.012
Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
Capizzi, G., & Masarotto, G. (2007). The EWMAST Control Charts with Estimated Limits : Properties and Recommendations. In Proceedings of the 2007 ieee ieem (pp. 1403–1407).
Cassady, R. C., Bowden, R. O., Liew, L., & Pohl, E. A. (2000). Combining preventive maintenance and statistical process control: a preliminary investigation. IIE Transactions, 32(6), 471–478. doi: 10.1080/07408170008963924
Chan, L.-Y., & Wu, S. (2009). Optimal design for inspection and maintenance policy based on the CCC chart. Computers & Industrial Engineering, 57(3), 667–676. doi: 10.1016/j.cie.2008.12.009
Chen, N., & Tsui, K. L. (2013, sep). Condition monitoring and remaining useful life prediction using degradation signals: revisited. IIE Transactions, 45(9), 939–952. doi: 10.1080/0740817X.2012.706376
Croux, C., Gelper, S., Mahieu, K., & Croux, C. (2011). Robust control charts for time series data. Expert Systems with Applications, 38(11), 13810–13815.
Escobet, T., Quevedo, J., & Puig, V. (2012). A Fault / Anomaly System Prognosis using a Data- driven Approach considering Uncertainty. In Ieee world congress on computational intelligence (pp. 10–15). Brisbane.
Gardner, E. S. (2006). Exponential smoothing: The state of the art—Part II. International journal of forecasting, 22(4), 637–666.
Ho, L. L., & Quinino, R. C. (2012). Integrating on-line process control and imperfect corrective maintenance: An economical design. European Journal of Operational Research, 222(2), 253–262. doi: 10.1016/j.ejor.2012.04.019
Ivy, J. S., & Nembhard, H. B. (2005). A modeling approach to maintenance decisions using statistical quality control and optimization. Quality and Reliability Engineering International, 21(August 2003), 355–366. doi: 10.1002/qre.616
Jammu, N. S., & Kankar, P. K. (2011). A Review on Prognosis of Rolling Element Bearings. International Journal of Engineering Science and Technology, 3(10), 7497–7503.
Kirchg¨assner, G., Wolters, J., & Hassler, U. (2012). Introduction to Modern Time Series Analysis. Springer.
Landau, I. D., & Zito, G. (2006). Digital Control Systems. Design, Identification and Implementation. London: Springer.
Lee, J., Qiu, G., Yu, G., & Lin, J. (2007). IMS Bearing Data Set. Retrieved from https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-epository/
Lei, Y., Li, N., Guo, L., Li, N., Yan, T., & Lin, J. (2018). Machinery health prognostics: A systematic review from data acquisition to rul prediction. Mechanical Systems and Signal Processing, 104, 799–834.
Lim, C. K. R., & Mba, D. (2014). Switching Kalman filter for failure prognostic. Mechanical Systems and Signal Processing, 52-53, 426–435. doi: 10.1016/j.ymssp.2014.08.006
Linderman, K., McKone-Sweet, K. E., & Anderson, J. C. (2005). An integrated systems approach to process control and maintenance. European Journal of Operational Research, 164(2), 324–340. doi: 10.1016/j.ejor.2003.11.026
Liu, L., Yu, M., Ma, Y., & Tu, Y. (2013). Economic and economic-statistical designs of an X control chart for twounit series systems with condition-based maintenance. European Journal of Operational Research, 226(3), 491–499. doi: 10.1016/j.ejor.2012.11.031
Ljung, L., & S¨oderstr¨om, T. (1983). Theory and practice of recursive identification.
Mehrafrooz, Z., & Noorossana, R. (2011). An integrated model based on statistical process control and maintenance. Computers & Industrial Engineering, 61(4), 1245–1255. doi: 10.1016/j.cie.2011.07.017
Montgomery, D. C. (2009). Introduction to Statistical Quality Control. Wiley.
Moubray, J. (1992). RCM II: Reliability-Centered Maintenance (1st ed.). New York: Industrial Press Inc.
NASA. (2008). NASA Reliability-Centered Maintenance Guide for Facilities and Collateral Equipment (Tech. Rep. No. September).
Nectoux, P., Gouriveau, R., Medjaher, K., Ramasso, E., Chebel-Morello, B., Zerhouni, N., & Varnier, C. (2012). PRONOSTIA: An experimental platform for bearings accelerated degradation tests. In Conference on prognostics and health management. (pp. 1–8).
Panagiotidou, S., & Nenes, G. (2009). An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart. Reliability Engineering and System Safety, 94, 732–741. doi: 10.1016/j.ress.2008.07.003
Panagiotidou, S., & Tagaras, G. (2010). Statistical process control and condition-based maintenance: a meaningful relationship through data sharing. Production and Operations Management, 19(2), 156–171. doi: 10.1111/j.1937-5956.2009.01073.x
Panagiotidou, S., & Tagaras, G. (2012). Optimal integrated process control and maintenance under general deterioration. Reliability Engineering and System Safety, 104, 58–70. doi: 10.1016/j.ress.2012.03.019
Pen˜abaena Niebles, R., Oviedo-Trespalacios, O´ ., Va´zques Cabeza, J. G., & Fernández Cantillo, L. M. (2013). Diseño estadístico de cartas de control para datos autocorrelacionados. Ingeniería y Desarrollo, 31(2), 1–50.
Perry, M. B., & Pignatiello Jr, J. J. (2010). Identifying the Time of Step Change in the Mean of Stationary Autocorrelated Processes. Journal of Applied Statistics, 26(1), 1–30. doi: 10.1002/qre.1055
Pintelon, L., & Parodi-Herz, A. (2008). Maintenance : An Evolutionary Perspective. In Complex systems maintenance handbook (pp. 21–48). Springer.
Prajapati, D. R., & Singh, S. (2012). Control charts for monitoring the autocorrelated process parameters: a literature review. International Journal of Productivity and Quality Management, 10(2), 207–249. doi: 10.1080/00401706.1998.10485479
Qiu, P. (2013). Introduction to Statistical Process Control. Taylor & Francis.
Quintana, A. E., Pisani, M. V., & Casal, R. N. (2015). Desempeño de cartas de control estadístico con límites bilaterales de probabilidad para monitorear procesos Weibull en mantenimiento. Ingeniería, Investigación y Tecnología, 16(1), 143–156. doi: 10.1016/S1405-7743(15)72115-3
Ran, Y., Zhou, X., Lin, P., Wen, Y., & Deng, R. (2019). A survey of predictive maintenance: Systems, purposes and approaches. arXiv preprint arXiv:1912.07383.
Searle, S. R. (2012). Linear models. Wiley.
Sikorska, J., Hodkiewicz, M., & Ma, L. (2011, jul). Prognostic modelling options for remaining useful life estimation by industry. Mechanical Systems and Signal Processing, 25(5), 1803–1836. doi: 10.1016/j.ymssp.2010.11.018
Son, J., Zhang, Y., Sankavaram, C., & Zhou, S. (2015). RUL prediction for individual units based on condition monitoring signals with a change point. IEEE Transactions on Reliability, 64(1), 182–196. doi: 10.1109/TR.2014.2355531
Tagaras, G. (1988). An integrated cost model for the joint optimization of process control and maintenance. Journal of the Operational Research Society, 39(8), 757–766. doi: 10.1057/palgrave.jors.0390807
Tambe, P. P., & Kulkarni, M. S. (2015). A superimposition based approach for maintenance and quality plan optimization with production schedule, availability, repair time and detection time constraints for a single machine. Journal of Manufacturing Systems, 37, 17–32. doi: 10.1016/j.jmsy.2015.09.009
Tandon, N., & Choudhury, A. (1999). A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribology international, 32(1999), 469–480.
Tobon-Mejia, D. A., Medjaher, K., & Zerhouni, N. (2012, apr). CNC machine tool’s wear diagnostic and prognostic by using dynamic Bayesian networks. Mechanical Systems and Signal Processing, 28, 167–182. doi: 10.1016/j.ymssp.2011.10.018
Wang, W. (2002). A model to predict the residual life of rolling element bearings given monitored condition information to date. IMA Journal of Management Mathematics, 13(1), 3–16. doi: 10.1093/imaman/13.1.3
Wang, W. (2012, may). A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems. European Journal of Operational Research, 218(3), 726–734. doi: 10.1016/j.ejor.2011.12.010
Wang, W., & Zhang, W. (2008). Early defect identification: application of statistical process control methods. Journal of Quality in Maintenance Engineering, 14, 225–236. doi: 10.1108/13552510810899445
Woodall, W. H., & Montgomery, D. C. (2014). Some Current Directions in the Theory and Application of Statistical Process Monitoring. Journal of Quality Technology, 46(1), 78–95.
Wu, J., & Makis, V. (2008). Economic and economicstatistical design of a chi-square chart for CBM. European Journal of Operational Research, 188(2), 516–529. doi: 10.1016/j.ejor.2007.05.002
Wu, S., & Wang, W. (2011). Optimal inspection policy for three-state systems monitored by control charts. Applied Mathematics and Computation, 217(23), 9810–9819. doi: 10.1016/j.amc.2011.04.075
Xiang, Y. (2013). Joint optimization of control chart and preventive maintenance policies: A discrete-time Markov chain approach. European Journal of Operational Research, 229(2), 382–390. doi: 10.1016/j.ejor.2013.02.041
Xie, M., Goh, T. N., & Ranjan, P. (2002). Some effective control chart procedures for reliability monitoring. Reliability Engineering and System Safety, 77(2), 143–150. doi: 10.1016/S0951-8320(02)00041-8
Yeung, T. G., Cassady, C. R., & Schneider, K. (2007). Simultaneous optimization of [Xbar] control chart and agebased preventive maintenance policies under an economic objective. IIE Transactions, 40(2), 147–159. doi: 10.1080/07408170701592515
Yin, H., Zhang, G., Zhu, H., Deng, Y., & He, F. (2015). An integrated model of statistical process control and maintenance based on the delayed monitoring. Reliability Engineering & System Safety, 133, 323–333. doi: 10.1016/j.ress.2014.09.020
Young, P. C. (2011). Recursive Estimation and Time-Series Analysis: An Introduction for the Student and Practitioner. Springer.
Zhang, N. F. (1998). A statistical control chart for stationary process data. Technometrics, 40(1), 24–38.
Zhou, W.-H., & Zhu, G.-L. (2008). Economic design of integrated model of control chart and maintenance management. Mathematical and Computer Modelling, 47(11-12), 1389–1395. doi: 10.1016/j.mcm.2007.09.008
Section
Technical Papers