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Geometric and Geometric-Like Processes and Their Applications in Warranty Analysis
Published in Mangey Ram, S. B. Singh, Mathematics Applied to Engineering and Management, 2020
Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall
Stochastic processes, such as renewal processes, are often used to model the occurrence of recurrent events over time. Under the assumption of a renewal process, the time between events are modeled to be independent and identically distributed random variables. In many scenarios, this assumption is justifiable and reflects the modeled situation well. However, if trends over time are observed, this assumption does not hold. These types of trends can be observed in many practical problems in a variety of fields (e.g., engineering—a system’s lifetime is stochastically decreasing because of aging or imperfect repairs, and at the same time the maintenance/repair time required to keep an aging system operational is stochastically increasing; in epidemiology—the number of infected cases is increasing at the start of an infectious disease outbreak and shows a decreasing trend at the later stages of the outbreak; in economics—the trends in the economic development of a country or a region show a periodic cycle in its gross national product, increasing at the early stage of the cycle and decreasing at the end of the cycle. All these examples have one common feature, their characterization involves a specific monotone trend over a substantial time interval).
Analysis of Stochastic Models in Manufacturing Systems Pertaining to Repair Machine Failure
Published in Cornelius Leondes, Optimization Methods for Manufacturing, 2019
Using regenerative point technique in the Markov renewal process, the following reliability characteristics of interest to system designers and operation managers have been obtained for models A, B and C. reliability of the system and mean time to system failure (MTSF);pointwise and steady state availabilities of the system;the probability that the repairman is busy at an epoch and in steady state;expected number of repairs by the repairman in (0, t) and in steady state; andexpected profit incurred by the system in (0, t) and in steady state.
Precast segmental bridge construction in seismic zones
Published in Fabio Biondini, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Resilience and Sustainability, 2012
Fabio Biondini, Dan M. Frangopol
If the deterioration process is assumed to be a state transition Biondini & Garavaglia (2005) have shown that the Markov Renewal Process (Howard, 1971, Limnios & Oprisan, 2001) seems to be suitable to describe such a dynamic process. The MRP can represent the development of the system’s life among different service states with different waiting times; it is also able to take in account the age t0 of the system, i.e. the time already spent by the system into the current service state before the prevision is carried out. This is one of the main aspects in reliability analysis when maintenance must be planned.
A Novel Approach for the Assessment of the Nocturnal Image of the Cultural Landscape
Published in LEUKOS, 2023
Lodovica Valetti, Franco Pellerey, Anna Pellegrino
The renewal process is constantly evolving, and technology is moving toward smart city concept, transforming the current lighting systems in smart grid, able to transmit information about users, weather, traffic, security, and diagnosis operation data, and embedding data analytics procedures and new technology solutions from Industry 4.0 Manufacturing Systems (Jin et al. 2016). Within this frame, it can be assumed that in the future, smart and adaptive lighting system could be designed with an actual holistic approach, which includes functional, environmental, but also expressive requirements.
A risk-aware maintenance model based on a constrained Markov decision process
Published in IISE Transactions, 2022
Jianyu Xu, Xiujie Zhao, Bin Liu
The renewal process theorem and the Markov Decision Process (MDP) are the most commonly used approaches to model CBM processes. The renewal process approach tends to describe the maintenance process by a series of renewal cycles, which occur whenever the system is restored to the as-good-as-new state upon maintenance. Compared with the renewal process method, the MDP is more flexible in CBM modeling, in the sense that it can easily characterize multiple maintenance actions that do not constitute a renewal cycle. In addition, MDP is able to model the maintenance process for a finite horizon, whereas the renewal cycle theorem finds that to be tedious. In the literature, a large body of studies have appeared on CBM modeling using MDP and its variants (Zhu and Xiang, 2021). Papakonstantinou and Shinozuka (2014) conducted a survey on the application of MDP models in structural inspection and maintenance policies. Zhang and Revie (2017) developed a Partially Observable Markov Decision Process (POMDP) to model the decision-making process in maintenancee actions, with application to rapid gravity filters of a water utility. Chen et al. (2015) developed a monotone control-limit CBM policy considering the updating of degradation parameters. Elwany et al. (2011) formulated the maintenance problem for systems subject to continuous monitoring into a MDP model. A monotone control-limit policy was devised considering measurement noise. Liu, Wu, et al. (2017) developed a MDP model for CBM considering age-state-dependent operating cost. Junca and Sanchez-Silva (2013) presented a maintenance model for systems deteriorating as a result of shocks and the optimal decision was obtained based on MDP. Byon et al. (2010) examined the optimal maintenance strategy for wind turbines considering stochastic weather conditions. A POMDP model was established to describe the maintenance process. Havinga and de Jonge (2020) formulated a MDP model for the cyclic patrolling repairman problem considering condition-based preventive maintenance. Lagos et al. (2020) developed a MDP model for airline maintenance operations. Flory et al. (2015) addressed the maintenance problem for a continuously degrading system that operates in a partially observable environment and formulated the problem as a POMDP.