Replacement policy for heterogeneous items subject to gamma degradation processes. (English) Zbl 1491.62273
Summary: A hybrid preventive maintenance policy for heterogeneous degrading items is discussed. It combines the classical age-replacement strategy, when a system is replaced either on failure or at the predetermined age, with replacement of the system when degradation reaches the predetermined level at some intermediate time. Items come from two subpopulations with different reliability characteristics. Non-homogeneous gamma processes model degradation of an item from each subpopulation. We justify probabilistically the superiority of the proposed policy over that for homogeneous populations and over the policy without possibility of additional replacement. The corresponding long-run cost rate is derived for the suggested cost structure. Some detailed numerical illustrations are presented and relevant sensitivity analysis for the main parameters of the model is performed.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
Keywords:
heterogeneous degradation process; mixed gamma process; dependent increments; hybrid preventive maintenance policy; probabilistic analysisReferences:
| [1] | Alaswad, S.; Xiang, Y., A review on condition-based maintenance optimization models for stochastically deteriorating system, Reliab Eng Syst Saf, 157, 54-63 (2017) · doi:10.1016/j.ress.2016.08.009 |
| [2] | Barlow, RE; Hunter, L., Optimum preventive maintenance policies, Oper Res, 8, 90-100 (1960) · Zbl 0095.34304 · doi:10.1287/opre.8.1.90 |
| [3] | Castanier, B.; Berenguer, C.; Grall, A., A sequential condition-based repair/replacement policy with non-periodic inspections for a system subject to continuous wear, Appl Stoch Model Bus Ind, 19, 327-347 (2003) · Zbl 1076.90018 · doi:10.1002/asmb.493 |
| [4] | Cha, JH; Finkelstein, M., On preventive maintenance under different assumptions on the failure/repair processes, Qual Reliab Eng Int, 34, 66-77 (2018) · doi:10.1002/qre.2237 |
| [5] | Cha, JH; Finkelstein, M.; Levitin, G., On preventive maintenance of systems with lifetimes dependent on a random shock process, Reliab Eng Syst Saf, 168, 90-97 (2017) · doi:10.1016/j.ress.2017.03.023 |
| [6] | Cha, JH; Finkelstein, M.; Levitin, G., Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process, Eur J Oper Res, 266, 122-134 (2018) · Zbl 1403.90261 · doi:10.1016/j.ejor.2017.09.021 |
| [7] | Cha, JH; Finkelstein, M.; Levitin, G., On optimal replacement of systems with failure rates described by a random jump process, Qual Reliab Eng Int, 34, 1590-1604 (2018) · doi:10.1002/qre.2343 |
| [8] | Çinlar, E., On a generalization of gamma process, J Appl Probab, 17, 467-480 (1980) · Zbl 0434.60043 · doi:10.2307/3213036 |
| [9] | Finkelstein, M.; Cha, JH, Stochastic Modelling for reliability (shocks, burn-in and heterogeneous populations) (2013), London: Springer, London · Zbl 1271.90002 · doi:10.1007/978-1-4471-5028-2 |
| [10] | Finkelstein, M.; Gertsbakh, I., On ‘time-free’ preventive maintenance of systems with structures described by signatures, Appl Stoch Model Bus Ind, 31, 836-845 (2015) · doi:10.1002/asmb.2111 |
| [11] | Finkelstein, M.; Cha, JH; Levitin, G., On a new age-replacement policy for items with observed stochastic degradation, Qual Reliab Eng Int, 36, 1132-1143 (2020) · doi:10.1002/qre.2619 |
| [12] | Gertsbakh, I., Reliability theory with applications to preventive maintenance (2005), Berlin: Springer, Berlin · Zbl 0959.62088 |
| [13] | Grall, A.; Dieulle, D.; Berenguer, C.; Roussignol, M., Continuous-time predictive maintenance scheduling for a deteriorating system, IEEE Trans Reliab, 51, 141-150 (2002) · doi:10.1109/TR.2002.1011518 |
| [14] | Hamidi, M.; Szidarovsky, F.; Szidarovszky, M., New one cycle criteria for optimizing preventive replacement policies, Reliab Eng Syst Saf, 154, 42-48 (2016) · doi:10.1016/j.ress.2016.04.010 |
| [15] | Jardine, AKS; Lin, D.; Banjevic, D., A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mech Syst Signal Process, 20, 1483-1510 (2006) · doi:10.1016/j.ymssp.2005.09.012 |
| [16] | Lehmann, EL, Some concepts of dependence, Ann Math Stat, 37, 1137-1153 (1966) · Zbl 0146.40601 · doi:10.1214/aoms/1177699260 |
| [17] | Liao, H.; Elsayed, EA; Chan, LY, Maintenance of continuously monitored degrading systems, Eur J Oper Res, 175, 821-835 (2006) · Zbl 1142.90375 · doi:10.1016/j.ejor.2005.05.017 |
| [18] | Nakagawa, T., Maintenance theory of reliability (2005), London: Springer, London |
| [19] | Pan, Z.; Balakrishnan, N., Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes, Reliab Eng Syst Saf, 96, 949-957 (2011) · doi:10.1016/j.ress.2011.03.014 |
| [20] | Rausand M, Høyland A (2003) System reliability theory: models, statistical methods, and applications, 2nd edn. Wiley · Zbl 1052.93001 |
| [21] | Shaked, M.; Shanthikumar, JG, Stochastic orders (2007), New York: Springer, New York · Zbl 1111.62016 · doi:10.1007/978-0-387-34675-5 |
| [22] | Tsai, CC; Tseng, ST; Balakrishnan, N., Optimal design for degradation tests based on gamma processes with random effects, IEEE Trans Reliab, 61, 604-613 (2012) · doi:10.1109/TR.2012.2194351 |
| [23] | Tseng, ST; Balakrishnan, N.; Tsai, CC, Optimal step-stress accelerated degradation test plan for gamma degradation processes, IEEE Trans Reliab, 58, 611-618 (2009) · doi:10.1109/TR.2009.2033734 |
| [24] | van Noortwijk, JM, A survey of the application of gamma processes in maintenance, Reliab Eng Syst Saf, 4, 2-21 (2009) · doi:10.1016/j.ress.2007.03.019 |
| [25] | Wang, H., A survey of maintenance policies of deteriorating systems, Eur J Oper Res, 226, 469-489 (2002) · Zbl 0995.90020 · doi:10.1016/S0377-2217(01)00197-7 |
| [26] | Wang, H.; Pham, H., Reliability and optimal maintenance (2006), London: Springer, London · Zbl 1128.90021 |
| [27] | Wu Y, Xie L, Wu N, Li J. (2011) Time-dependent reliability model of components with strength degradation based-on gamma process, proceedings of 9th international conference on reliability, maintainability and safety (ICRMS), 363-368 |
| [28] | Xu W, Wang W (2012) An adaptive gamma process based model for residual useful life prediction. In Proceedings of IEEE conference on prognostics and system health management (PHM) 2012 (pp.1-4) |
| [29] | Zhang, M.; Gaudoin, O.; Xie, M., Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance, Eur J Oper Res, 245, 531-541 (2015) · Zbl 1346.90293 · doi:10.1016/j.ejor.2015.02.050 |
| [30] | Zhao, X.; Gaudoin, O.; Doyen, L.; Xie, M., Optimal inspection and replacement policy based on experimental degradation data with covariates, IISE Transactions, 51, 322-336 (2019) · doi:10.1080/24725854.2018.1488308 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
