Abstract
Many real-world critical systems, e.g., aircrafts, manned space flight systems and submarines, complex technological processes utilize mission aborts to enhance their survivability. Specifically, a mission can be aborted when a certain malfunction condition is met and a rescue or recovery procedure is then initiated. In this paper, we consider systems with observed degradation when a decision to abort a mission or to continue operation is executed at inspection. If this degradation is larger than the optimally predetermined level, then a mission is aborted, whereas if it is smaller, a system continues its operation either under the initial (full load) regime or under the lighter regime with the decreased load. The latter option also depends on the observed value of degradation at inspection. An optimal problem minimizing the expected costs with respect to the relevant levels of deterioration and inspection time is formulated and analytical relationships for the probabilities of interest and expected cost rates are derived. A new virtual age-based approach to age recalculation after the switching of regimes is proposed. A detailed illustrative example is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alaswad S, Xiang Y (2017) A review on condition-based maintenance optimization models for stochastically deteriorating system. Reliab Eng Syst Saf 157:54–63
Badía FG, Berrade MD (2009) Optimum maintenance policy of a periodically inspected system under imperfect repair. Adv Oper Res. https://doi.org/10.1155/2009/691203
Badıa FG, Berrade MD, Campos CA (2002) Optimal inspection and preventive maintenance of units with revealed and unrevealed failures. Reliab Eng Syst Saf 78:157–163
Castro IT (2013) An age-based maintenance strategy for a degradation-threshold shock-model for a system subjected to multiple defects. Asia Pac J Oper Res 30:1350016–1350029
Castro IT, Caballe NC, Perez CJ (2015) A condition-based maintenance for a system subject to multiple degradation processes and external shocks. Int J Syst Sci 46:1692–1704
Cha JH, Mi J, Yun WY (2008) Modelling a general standby system and evaluation of its performance. Appl Stoch Models Bus Ind 24:159–169
Çinlar E (1980) On a generalization of gamma process. J Appl Probab 17:467–480
Dai MDM, Chen KH (2014) Cost evaluation of airline maintenance investigation-triggering methods. Top 22:950–975
Finkelstein M (2008) Failure rate modelling for reliability and risk. Springer, London
Finkelstein M, Hazra NK (2017) On stochastic comparisons for load sharing series and parallel systems. Probab Eng Inf Sci 31:311–329
Finkelstein M, Levitin G (2018) Optimal mission duration for partially repairable systems operating in a random environment. Methodol Comput Appl Probab 20:505–516
Finkelstein M, Cha JH, Levitin G (2020) On a new age-replacement policy for items with observed stochastic degradation. Qual Reliab Eng Int 36:1132–1144
Gertsbakh I (2005) Reliability theory with applications to preventive maintenance. Springer, Berlin
Grall A, Dieulle D, Berenguer C, Roussignol M (2002) Continuous-time predictive maintenance scheduling for a deteriorating system. IEEE Trans Reliab 51:141–150
Kahle W (2019) Imperfect repair in degradation processes: a Kijima-type approach. Appl Stoch Model Bus 35:211–220
Kijima M (1989) Some results for repairable systems with general repair. J Appl Probab 26:89–102
Levitin G, Finkelstein M (2018a) Optimal mission abort policy for systems operating in a random environment. Risk Anal 38:795–803
Levitin G, Finkelstein M (2018b) Optimal mission abort policy for systems in a random environment with variable shock rate. Reliab Eng Syst Saf 169:11–17
Levitin G, Xing L, Dai Y (2018) Mission abort policy in heterogeneous non-repairable 1-out-of-N warm standby systems. IEEE Trans Reliab 67:342–354
Levitin G, Finkelstein M, Xiang Y (2020a) Optimal aborting rule in multi-attempt missions performed by multicomponent systems. Eur J Oper Res 283:244–252
Levitin G, Finkelstein M, Huang Y (2020b) Optimal mission abort policies for multistate systems. Reliab Eng Syst Saf 193:106671
Liao H, Elsayed EA, Chan LY (2006) Maintenance of continuously monitored degrading systems. Eur J Oper Res 175:821–835
Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York
Montoro-Cazorla D, Pérez-Ocón R (2011) Two shock and wear systems under repair standing a finite number of shocks. Eur J Oper Res 214:298–307
Montoro-Cazorla D, Pérez-Ocón R (2012) A shock and wear system under environmental conditions subject to internal failures, repair, and replacement. Reliab Eng Syst Saf 99:55–61
Montoro-Cazorla D, Pérez-Ocón R (2015) A reliability system under cumulative shocks governed by a BMAP. Appl Math Model 39:7620–7629
Montoro-Cazorla D, Pérez-Ocón R, Segovia MC (2009) Shock and wear models under policy n using phase-type distributions. Appl Math Model 33:543–554
Myers A (2009) Probability of loss assessment of critical k-out-of-n: G systems having a mission abort policy. IEEE Trans Reliab 58:694–701
Nakagawa T (2005) Maintenance theory of reliability. Springer, London
Nelson W (1990) Accelerated testing, statistical models, test plans and data analysis. Wiley, New York
Pan Z, Balakrishnan N (2011) Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes. Reliab Eng Syst Saf 96:949–957
Qiu Q, Cui L (2019a) Optimal mission abort policy for systems subject to random shocks based on virtual age process. Reliab Eng Syst Saf 189:11–20
Qiu Q, Cui L (2019b) Gamma process based optimal mission abort policy. Reliab Eng Syst Saf 190:106496
Qiu Q, Cui L, Wu B (2020) Dynamic mission abort policy for systems operating in a controllable environment with self-healing mechanism. Reliab Eng Syst Saf 203:107069
Rausand M, Høyland A (2003) System reliability theory: models, statistical methods, and applications, 2nd edn. Wiley, New York
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York
Sun Q, Ye ZS, Peng W (2018) Scheduling preventive maintenance considering the saturation effect. IEEE Trans Reliab 68(2):741–752
Tseng ST, Balakrishnan N, Tsai CC (2009) Optimal step-stress accelerated degradation test plan for gamma degradation processes. IEEE Trans Reliab 58:611–618
van Noortwijk JM (2009) A survey of the application of gamma processes in maintenance. Reliab Eng Syst Saf 94:2–21
Yang L, Sun Q, Ye ZS (2019) Designing mission abort strategies based on early-warning information: application to UAV. IEEE Trans Ind Inf 16(1):277–287
Yu M, Tang Y (2017) Optimal replacement policy based on maximum repair time for a random shock and wear model. Top 25:80–94
Acknowledgements
The authors would like to thank the referees for helpful comments and advices, which have improved the presentation of this paper. The work of the second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1A2B5B02069500). The work of the second author was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant number: 2019R1A6A1A11051177).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Finkelstein, M., Cha, J.H. & Ghosh, S. Optimal inspection for missions with a possibility of abortion or switching to a lighter regime. TOP 29, 722–740 (2021). https://doi.org/10.1007/s11750-020-00591-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-020-00591-w