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Introduction and Background
Published in Hamed Fazlollahtabar, Seyed Taghi Akhavan Niaki, Reliability Models of Complex Systems for Robots and Automation, 2017
Hamed Fazlollahtabar, Seyed Taghi Akhavan Niaki
In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements, and those systems or objects are, therefore, brought back to an as-good-as-new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption cannot be made. The quintessential problem with imperfect maintenance is how to model it. In many cases, it is very difficult to assess by how much a partial repair will improve the condition of a system or object, and it is equally difficult to assess how such a repair influences the rate of deterioration. Kallen (2011) proposed a superposition of the renewal process that is used to model the effect of imperfect maintenance. It constituted a different modeling approach than the more common use of a virtual age process.
Modeling the time-varying performance of electrical infrastructure during post disaster recovery using tensors
Published in Paolo Gardoni, Routledge Handbook of Sustainable and Resilient Infrastructure, 2018
Jia et al. (2017) developed an integration of the deterioration and recovery processes, which can be used to model the whole life cycle of infrastructure components based on renewal theory (Kumar & Gardoni 2014b). Sharma and Gardoni (2018b) provided a spatial extension of the recovery modeling by modeling network recovery for interdependent infrastructure. Sharma et al. (2018b) proposed a framework to maximize infrastructure resilience by optimizing the recovery planning and execution strategies. Sharma et al. (2018a) also provided metrics to measure the resilience associated with various recovery curves. Sharma et al. (2018c) provides a brief review of the above listed works, so we refrain from repeating it here.
Renewal-theory-based Life-cycle Risk Assessment of Bridge Deck Unseating under Hurricanes
Published in Nigel Powers, Dan M. Frangopol, Riadh Al-Mahaidi, Colin Caprani, Maintenance, Safety, Risk, Management and Life-Cycle Performance of Bridges, 2018
David Y. Yang, Dan M. Frangopol
In this paper, a new method is proposed for life-cycle risk assessment of bridge deck unseating under hurricanes. The uncertainties from both demand and capacity sides are taken into account. The proposed method considers both hurricane reoccurrence as a stochastic process and capacity deterioration due to pitting corrosion. Life-cycle risk is formulated for (non)deteriorating but repairable systems based on renewal theory. A number of conclusions are drawn: Unseating-resistant systems are important for risk mitigation of coastal bridges under hurricanes. The benefit of such systems can well outweigh the associated cost.For unseating-resistant systems, capacity deterioration should be considered in the risk assessment. The use of non-deteriorating systems shows better cost-effectiveness in risk mitigation despite the higher initial cost.Occurrence of unseating failures and the associated consequences can be modeled as a renewal-reward process. As a result, life-cycle risk of repairable systems can be assessed using renewal theory. In the most general sense, sampling-based methods are needed for risk assessment.Future work based on the proposed method should consider climate change effects. This can be achieved by hazard analysis pivoting on general climate models and by extending the current risk formulation to nonstationary processes.
Stochastic life-cycle analysis: renewal-theory life-cycle analysis with state-dependent deterioration stochastic models
Published in Structure and Infrastructure Engineering, 2019
This paper proposes a renewal-theory life-cycle analysis (RTLCA) with SDSMs for deterioration. The renewal theory allows us to efficiently evaluate different life-cycle performance quantities such as age, instantaneous probability of being in service, availability, costs of operation and failure of the system, and benefits. The general formulation of SDSMs proposed in Jia and Gardoni (2018a) is used to model the deterioration due to multiple deterioration processes including their interactions. The paper by Jia and Gardoni (2018a) focuses on the general formulation of SDSMs, and Bayesian calibration of SDSMs using deterioration data, as well as illustrating the impact of interaction between different deterioration processes on the variation of the system state variables. The novel contribution of the current paper is the integration of SDSMs into the RTLCA for more realistic modelling of the deterioration processes and accurate estimation of the various life-cycle performance quantities. The adoption of SDSMs in the RTLCA introduces additional computational challenges in estimating the time-variant performance indicators (required informing interventions such as repair or replacement) and in establishing the probability density functions (PDFs) in the RTLCA for intervention and renewal intervals (required to estimate the life-cycle performance quantities).
Joint optimization of condition-based maintenance and spare part inventory for two-component system
Published in Journal of Industrial and Production Engineering, 2018
Xiao-Hong Zhang, Jian-Chao Zeng, Jie Gan
To minimize the total maintenance cost of the system, the optimization of the proposed policy can be defined as a constrained optimization problem. Considering that it is only assumed that all the maintenance activities are perfectly executed, it can be easily seen that, in reality, after a certain period, complete renewal of the system would be performed. When that is done, the future evolution of the system would not depend on the past state. This indicates that the evolution of the state of the system is regenerative. Renewal theory is often used to model single-component maintenance optimization by considering the period between two successive renewals as a renewal cycle. Owing to the uncertainties involved at the complete regeneration points in a multi-component system, it would be rather tedious to describe the renewal cycle. At each maintenance decision point, only the components in a subset of all the components are simultaneously maintained. However, it would be interesting to explore the semi-regenerative properties of the process [14, L. 41]. The asymptotic behavior of such a semi-regenerative process can be restricted to a semi-regenerative cycle defined by two successive intervention points. At the beginning of each inspection period, the system operation may be interrupted by maintenance activities based on the system state. After an intervention, the evolutions of all the component and the global system only depend on the determined deterioration levels. Hence, an inspection cycle can be considered as a semi-regeneration point in the process of the system maintenance. The long-run criterion for cost rate can be expressed as follows based on the semi-regenerative properties of the deterioration process of the maintained system:
Total productive maintenance of make-to-stock production-inventory systems via artificial-intelligence-based iSMART
Published in International Journal of Systems Science: Operations & Logistics, 2021
Angelo Encapera, Abhijit Gosavi, Susan L. Murray
The literature offers two models for determining the maintenance-interval: renewal theory (Ross, 2014) and MDPs/SMDPs (Bertsekas, 2014). Determining the optimal maintenance interval in the MTS production-inventory (PI) system requires using the age of the machine as well as the inventory level in the warehouse. Renewal-theoretic models can account for the age but disregard the inventory level; the latter is critical when one considers PI systems, as shutting down the machine for maintenance is not appropriate when the inventory is running low. MDP/SMDP models, on the other hand, are more detailed and can capture the state of the system in terms of its age as well as the finished product inventory in the warehouse, thereby developing a model that can adjust its maintenance policy according to not only the age, but also the level of the inventory. One of the earliest applications of the MDP to solve the preventive maintenance problem can be found in Marcellus and Dada (1991). Van der Duyn Schouten and Vanneste (1995) and Das and Sarkar (1999) study TPM in the context of production-inventory systems. The model in Das and Sarkar (1999) is more versatile in the sense that it employs the very flexible gamma distribution for production, repair, and inter-failure times. The gamma distribution carries the critical property of increasing failure rates for their time between failures which is typical of most systems as equipment ages. Finally, their model uses the exponential distribution for inter-arrival times of demand. This leads to a Poisson rate of arrival, which can be well-approximated by the normal distribution demand patterns that are known to exist widely in production systems (Askin & Goldberg, 2001). As such, we employ the generally applicable model of Das and Sarkar (1999) for testing our new algorithm. However, our algorithm will be simulation-based and will hence be capable of using any given distribution for the input parameters. In other words, our algorithm is flexible enough for usage with other MDP/SMDP models for studying TPM in PI systems.