Statistical Modeling of the Effectiveness of Preventive Maintenance for Repairable Systems

References

• Badr, M. M. (2019), “Goodness-of-Fit Tests for the Compound Rayleigh Distribution with Application to Real Data,” Heliyon, 5, e02225. DOI: 10.1016/j.heliyon.2019.e02225.
   PubMed Web of Science ®Google Scholar
• Block, H. W., Borges, W. S., and Savits, T. H. (1985), “Age-Dependent Minimal Repair,” Journal of Applied Probability, 22, 370–385. DOI: 10.2307/3213780.
   Web of Science ®Google Scholar
• Cai, J., Cigsar, C., and Ye, Z.-S. (2020), “Assessing the Effect of Repair Delays on a Repairable System,” Journal of Quality Technology, 52, 293–303. DOI: 10.1080/00224065.2019.1611347.
   Web of Science ®Google Scholar
• Chan, J.-K., and Shaw, L. (1993), “Modeling Repairable Systems with Failure Rates that Depend on Age and Maintenance,” IEEE Transactions on Reliability, 42, 566–571. DOI: 10.1109/24.273583.
   Web of Science ®Google Scholar
• Cheng, J., and Druzdzel, M. J. (2013), “Computational Investigation of Low-Discrepancy Sequences in Simulation Algorithms for Bayesian Networks,” arXiv preprint arXiv:1301.3841.
   Google Scholar
• Cook, R. J., and Lawless, J. F. (2007), The Statistical Analysis of Recurrent Events, New York: Springer.
   Google Scholar
• Coull, B. A., Hobert, J. P., Ryan, L. M., and Holmes, L. B. (2001), “Crossed Random Effect Models for Multiple Outcomes in a Study of Teratogenesis,” Journal of the American Statistical Association, 96, 1194–1204. DOI: 10.1198/016214501753381841.
   Web of Science ®Google Scholar
• Dhillon, B. S. (2009), Human Reliability, Error, and Human Factors in Engineering Maintenance: With Reference to Aviation and Power Generation, Boca Raton, FL: CRC Press.
   Google Scholar
• Dijoux, Y., and Gaudoin, O. (2009), “The Alert-Delay Competing Risks Model for Maintenance Analysis,” Journal of Statistical Planning and Inference, 139, 1587–1603. DOI: 10.1016/j.jspi.2008.05.021.
   Web of Science ®Google Scholar
• Doyen, L. (2011), “On the Brown–Proschan Model When Repair Effects are Unknown,” Applied Stochastic Models in Business and Industry, 27, 600–618. DOI: 10.1002/asmb.869.
   Web of Science ®Google Scholar
• Doyen, L., Drouilhet, R., and Brenière, L. (2019), “A Generic Framework for Generalized Virtual Age Models,” IEEE Transactions on Reliability, 69, 816–832. DOI: 10.1109/TR.2019.2906732.
   Web of Science ®Google Scholar
• Doyen, L., and Gaudoin, O. (2004), “Classes of Imperfect Repair Models based on Reduction of Failure Intensity or Virtual Age,” Reliability Engineering & System Safety, 84, 45–56. DOI: 10.1016/S0951-8320(03)00173-X.
   Web of Science ®Google Scholar
• Duan, C., Deng, C., Gharaei, A., Wu, J., and Wang, B. (2018), “Selective Maintenance Scheduling Under Stochastic Maintenance Quality with Multiple Maintenance Actions,” International Journal of Production Research, 56, 7160–7178. DOI: 10.1080/00207543.2018.1436789.
   Web of Science ®Google Scholar
• Durbin, J. (1973), “Weak Convergence of the Sample Distribution Function When Parameters are Estimated,” The Annals of Statistics, 1, 279–290. DOI: 10.1214/aos/1176342365.
   Web of Science ®Google Scholar
• Efron, B., and Tibshirani, R. J. (1994), An Introduction to the Bootstrap, Boca Raton, FL: CRC Press.
   Google Scholar
• Fang, K.-T., Lin, D. K., Winker, P., and Zhang, Y. (2000), “Uniform Design: Theory and Application,” Technometrics, 42, 237–248. DOI: 10.1080/00401706.2000.10486045.
   Web of Science ®Google Scholar
• Giorgio, M., Guida, M., and Pulcini, G. (2014), “Repairable System Analysis in Presence of Covariates and Random Effects,” Reliability Engineering & System Safety, 131, 271–281. DOI: 10.1016/j.ress.2014.04.009.
   Web of Science ®Google Scholar
• Green, P. J., and Mira, A. (2001), “Delayed Rejection in Reversible Jump Metropolis–Hastings,” Biometrika, 88, 1035–1053. DOI: 10.1093/biomet/88.4.1035.
   Web of Science ®Google Scholar
• Haario, H., Saksman, E., and Tamminen, J. (1999), “Adaptive Proposal Distribution for Random Walk Metropolis Algorithm,” Computational Statistics, 14, 375–395. DOI: 10.1007/s001800050022.
   Web of Science ®Google Scholar
• Haario, H., Saksman, E., and Tamminen, J. (2001), “An Adaptive Metropolis Algorithm,” Bernoulli, 7, 223–242.
   Web of Science ®Google Scholar
• Hu, J., Sun, Q., and Ye, Z.-S. (2020), “Condition-based Maintenance Planning for Systems Subject to Dependent Soft and Hard Failures,” IEEE Transactions on Reliability, 70, 1468–1480. DOI: 10.1109/TR.2020.2981136.
   Web of Science ®Google Scholar
• Jank, W. (2005), “Quasi-Monte Carlo Sampling to Improve the Efficiency of Monte Carlo EM,” Computational Statistics & Data Analysis, 48, 685–701. DOI: 10.1016/j.csda.2004.03.019.
   Web of Science ®Google Scholar
• Khatab, A., and Aghezzaf, E.-H. (2016), “Selective Maintenance Optimization When Quality of Imperfect Maintenance Actions are Stochastic,” Reliability Engineering & System Safety, 150, 182–189. DOI: 10.1016/j.ress.2016.01.026.
   Web of Science ®Google Scholar
• Khatab, A., Ait-Kadi, D., and Rezg, N. (2014), “Availability Optimisation for Stochastic Degrading Systems under Imperfect Preventive Maintenance,” International Journal of Production Research, 52, 4132–4141. DOI: 10.1080/00207543.2013.835499.
   Web of Science ®Google Scholar
• Kijima, M. (1989), “Some Results for Repairable Systems with General Repair,” Journal of Applied Probability, 26, 89–102. DOI: 10.2307/3214319.
   Web of Science ®Google Scholar
• Kijima, M., Morimura, H., and Suzuki, Y. (1988), “Periodical Replacement Problem Without Assuming Minimal Repair,” European Journal of Operational Research, 37, 194–203. DOI: 10.1016/0377-2217(88)90329-3.
   Web of Science ®Google Scholar
• Kocis, L., and Whiten, W. J. (1997), “Computational Investigations of Low-Discrepancy Sequences,” ACM Transactions on Mathematical Software (TOMS), 23, 266–294. DOI: 10.1145/264029.264064.
   Web of Science ®Google Scholar
• Lawless, J. (1995), “The Analysis of Recurrent Events for Multiple Subjects,” Journal of the Royal Statistical Society, Series C, 44, 487–498. DOI: 10.2307/2986140.
   Web of Science ®Google Scholar
• Lawless, J. F. (1987), “Regression Methods for Poisson Process Data,” Journal of the American Statistical Association, 82, 808–815. DOI: 10.1080/01621459.1987.10478502.
   Web of Science ®Google Scholar
• Liao, G.-L., Chen, Y. H., and Sheu, S.-H. (2009), “Optimal Economic Production Quantity Policy for Imperfect Process with Imperfect Repair and Maintenance,” European Journal of Operational Research, 195, 348–357. DOI: 10.1016/j.ejor.2008.01.004.
   Web of Science ®Google Scholar
• Lim, T. (1998), “Estimating System Reliability with Fully Masked Data under Brown-Proschan Imperfect Repair Model,” Reliability Engineering & System Safety, 59, 277–289. DOI: 10.1016/S0951-8320(97)00085-9.
   Web of Science ®Google Scholar
• Lin, D., Zuo, M. J., and Yam, R. C. (2000), “General Sequential Imperfect Preventive Maintenance Models,” International Journal of Reliability, Quality and Safety Engineering, 7, 253–266. DOI: 10.1142/S0218539300000213.
   Google Scholar
• Lindqvist, B. H. (2006), “On the Statistical Modeling and Analysis of Repairable Systems,” Statistical Science, 21, 532–551. DOI: 10.1214/088342306000000448.
   Web of Science ®Google Scholar
• Liu, Y., Huang, H.-Z., and Zhang, X. (2011a), “A Data-Driven Approach to Selecting Imperfect Maintenance Models,” IEEE Transactions on Reliability, 61, 101–112. DOI: 10.1109/TR.2011.2170252.
   Web of Science ®Google Scholar
• Liu, Y., Li, Y., Huang, H.-Z., and Kuang, Y. (2011b), “An Optimal Sequential Preventive Maintenance Policy Under Stochastic Maintenance Quality,” Structure and Infrastructure Engineering, 7, 315–322. DOI: 10.1080/15732470802658920.
   Web of Science ®Google Scholar
• Louis, T. A. (1982), “Finding the Observed Information Matrix When Using the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 44, 226–233. DOI: 10.1111/j.2517-6161.1982.tb01203.x.
   Web of Science ®Google Scholar
• Mendenhall, W., Beaver, R. J., and Beaver, B. M. (2012), Introduction to Probability and Statistics, Boston, MA: Cengage Learning.
   Google Scholar
• Mitra, A. (2016), Fundamentals of Quality Control and Improvement, Hoboken: Wiley.
   Google Scholar
• Morokoff, W. J., and Caflisch, R. E. (1995), “Quasi-Monte Carlo Integration,” Journal of Computational Physics, 122, 218–230. DOI: 10.1006/jcph.1995.1209.
   Web of Science ®Google Scholar
• Nakagawa, T. (1979), “Optimum Policies When Preventive Maintenance is Imperfect,” IEEE Transactions on Reliability, 28, 331–332. DOI: 10.1109/TR.1979.5220624.
   Web of Science ®Google Scholar
• Nakagawa, T. (1986), “Periodic and Sequential Preventive Maintenance Policies,” Journal of Applied Probability, 23, 536–542.
   Web of Science ®Google Scholar
• Nakagawa, T. (1988), “Sequential Imperfect Preventive Maintenance Policies,” IEEE Transactions on Reliability, 37, 295–298.
   Web of Science ®Google Scholar
• Park, J., Chang, W., and Lie, C. (2012), “Stress-Reducing Preventive Maintenance Model for a Unit Under Stressful Environment,” Reliability Engineering & System Safety, 108, 42–48. DOI: 10.1016/j.ress.2012.06.021.
   Web of Science ®Google Scholar
• Peng, W., Shen, L., Shen, Y., and Sun, Q. (2018), “Reliability Analysis of Repairable Systems with Recurrent Misuse-Induced Failures and Normal-Operation Failures,” Reliability Engineering & System Safety, 171, 87–98. DOI: 10.1016/j.ress.2017.11.016.
   Web of Science ®Google Scholar
• Pham, H., and Zhang, X. (2003), “NHPP Software Reliability and Cost Models with Testing Coverage,” European Journal of Operational Research, 145, 443–454. DOI: 10.1016/S0377-2217(02)00181-9.
   Web of Science ®Google Scholar
• R Core Team. (2020), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Ramírez, P. A. P., and Utne, I. B. (2015), “Use of Dynamic Bayesian Networks for Life Extension Assessment of Ageing Systems,” Reliability Engineering & System Safety, 133, 119–136. DOI: 10.1016/j.ress.2014.09.002.
   Web of Science ®Google Scholar
• Reason, J., and Hobbs, A. (2017), Managing Maintenance Error: A Practical Guide, Boca Raton, FL: CRC Press.
   Google Scholar
• Remy, E., Corset, F., Despréaux, S., Doyen, L., and Gaudoin, O. (2013), “An Example of Integrated Approach to Technical and Economic Optimization of Maintenance,” Reliability Engineering & System Safety, 116, 8–19. DOI: 10.1016/j.ress.2013.02.001.
   Web of Science ®Google Scholar
• Rigdon, S. E., Ma, X., and Bodden, K. M. (1998), “Statistical Inference for Repairable Systems Using the Power Law Pocess,” Journal of Quality Technology, 30, 395–400. DOI: 10.1080/00224065.1998.11979875.
   Web of Science ®Google Scholar
• Said, U., and Taghipour, S. (2017), “Modeling Failure Process and Quantifying the Effects of Multiple Types of Preventive Maintenance for a Repairable System,” Quality and Reliability Engineering International, 33, 1149–1161. DOI: 10.1002/qre.2088.
   Web of Science ®Google Scholar
• Shan, Q., Hong, Y., and Meeker, W. Q. (2020), “Seasonal Warranty Pprediction based on Recurrent Event Data,” The Annals of Applied Statistics, 14, 929–955. DOI: 10.1214/20-AOAS1333.
   Web of Science ®Google Scholar
• Si, W., and Yang, Q. (2016), “A Generalized Mixed Effect kijima Model and Application in Optimal Maintenance Planning,” IEEE Transactions on Reliability, 65, 1551–1561. DOI: 10.1109/TR.2016.2570566.
   Web of Science ®Google Scholar
• Sun, Q., Ye, Z.-S., and Peng, W. (2018), “Scheduling Preventive Maintenance Considering the Saturation Effect,” IEEE Transactions on Reliability, 68, 741–752. DOI: 10.1109/TR.2018.2874265.
   Web of Science ®Google Scholar
• Tanwar, M., Rai, R. N., and Bolia, N. (2014), “Imperfect Repair Modeling Using Kijima Type Generalized Renewal Process,” Reliability Engineering & System Safety, 124, 24–31. DOI: 10.1016/j.ress.2013.10.007.
   Web of Science ®Google Scholar
• Tierney, L., and Mira, A. (1999), “Some Adaptive Monte Carlo Methods for Bayesian Inference,” Statistics in Medicine, 18, 2507–2515. DOI: 10.1002/(SICI)1097-0258(19990915/30)18:17/18<2507::AID-SIM272>3.0.CO;2-J.
   PubMed Web of Science ®Google Scholar
• Toledo, M. L. G. d., Freitas, M. A., Colosimo, E. A., and Gilardoni, G. L. (2016), “Optimal Periodic Maintenance Policy Under Imperfect Repair: A Case Study on the Engines of Off-Road Vehicles,” IIE Transactions, 48, 747–758. DOI: 10.1080/0740817X.2016.1147663.
   Web of Science ®Google Scholar
• Wu, S., and Clements-Croome, D. (2005), “Preventive Maintenance Models with Random Maintenance Quality,” Reliability Engineering & System Safety, 90, 99–105. DOI: 10.1016/j.ress.2005.03.012.
   Web of Science ®Google Scholar
• Wu, S., and Zuo, M. J. (2010), “Linear and Nonlinear Preventive Maintenance Models,” IEEE Transactions on Reliability, 59, 242–249. DOI: 10.1109/TR.2010.2041972.
   Web of Science ®Google Scholar
• Xu, Z., Hong, Y., Meeker, W. Q., Osborn, B. E., and Illouz, K. (2017), “A Multi-Level Trend-Renewal Process for Modeling Systems with Recurrence Data,” Technometrics, 59, 225–236. DOI: 10.1080/00401706.2016.1164758.
   Web of Science ®Google Scholar
• Ye, Z.-S., and Chen, N. (2014), “The Inverse Gaussian Process as a Degradation Model,” Technometrics, 56, 302–311. DOI: 10.1080/00401706.2013.830074.
   Web of Science ®Google Scholar
• Ye, Z.-S., and Tang, L.-C. (2016), “Augmenting the Unreturned for Field Data with Information on Returned Failures Only,” Technometrics, 58, 513–523. DOI: 10.1080/00401706.2015.1093033.
   Web of Science ®Google Scholar
• Ye, Z.-S., Xie, M., and Tang, L.-C. (2013), “Reliability Evaluation of Hard Disk Drive Failures based on Counting Processes,” Reliability Engineering & System Safety, 109, 110–118. DOI: 10.1016/j.ress.2012.07.003.
   Web of Science ®Google Scholar
• Ye, Z.-S., Xie, M., Tang, L.-C., and Chen, N. (2014), “Semiparametric Estimation of Gamma Processes for Deteriorating Products,” Technometrics, 56, 504–513. DOI: 10.1080/00401706.2013.869261.
   Web of Science ®Google Scholar
• Zeng, D., Mao, L., and Lin, D. (2016), “Maximum Likelihood Estimation for Semiparametric Transformation Models with Interval-Censored Data,” Biometrika, 103, 253–271. DOI: 10.1093/biomet/asw013.
   PubMed Web of Science ®Google Scholar
• Zhang, M., Gaudoin, O., and Xie, M. (2015), “Degradation-based Maintenance Decision Using Stochastic Filtering for Systems under Imperfect Maintenance,” European Journal of Operational Research, 245, 531–541. DOI: 10.1016/j.ejor.2015.02.050.
   Web of Science ®Google Scholar
• Zhang, M., and Xie, M. (2017), “An Ameliorated Improvement Factor Model for Imperfect Maintenance and its Goodness of Fit,” Technometrics, 59, 237–246. DOI: 10.1080/00401706.2016.1164757.
   Web of Science ®Google Scholar
• Zhang, Z., and Sun, J. (2010), “Interval Censoring,” Statistical Methods in Medical Research, 19, 53–70.
   PubMed Web of Science ®Google Scholar