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A Transient Analysis-Based Approach
Published in Mohamed Ibnkahla, Adaptation and Cross Layer Design in Wireless Networks, 2018
A continuous-time Markov chain (CTMC) is generally used to model and analyze the behavior of a system that possesses the Markov property. This Markov property states that the future state of the system depends only on the current state, not on any past state. The evolution of a CTMC is defined as () X={H(t),t≥0},
Population growth I: birth and death processes
Published in Henry C. Tuckwell, Elementary Applications of Probability Theory, 2018
are called the transition probabilities of the continuous time Markov chain. If the transition probabilities depend only on time differences they are said to be stationary and the corresponding process is called temporally homogeneous.
Simulation based model for component replenishment in multi-product ATO systems with shared resources
Published in International Journal of Modelling and Simulation, 2022
Azeem Shami, Ashesh Kumar Sinha
To analyze the dynamics of the system we can model it as a continuous-time Markov chain problem. Let , denote a subsystem which represents the manufacturing process of components ,, …,. The subcontracting units are ,, …,, while the in-house manufacturing facility is .
Stochastic modelling and analysis of a deteriorating serial production–inventory network
Published in International Journal of Production Research, 2023
Spyros I. Vlastos, A. S. Xanthopoulos, D. E. Koulouriotis
The continuous-time Markov chain of the presented model can be completely described by the associated transition rate matrix Q that has dimensions equal to that of the state space. The elements of the Q matrix assume non-negative values and correspond to the rate that the system transits from state to state . The elements on the diagonal of the transition rate matrix are selected so that the sum of the entries in each row equals to 0.
Joint optimization of production lot-sizing and condition-based maintenance in an imperfect production process with dependent indicators
Published in Quality Technology & Quantitative Management, 2023
Nan Zhang, Sen Tian, Bin Liu, Jun Zhang
With respect to the maintenance planning (Qiu et al., 2019; Scarf, 2007; Wang et al., 2020), condition-based maintenance (CBM) has received increasing attention in recent years. It allows to make maintenance decisions based on the sensor information with respect to the health condition of the system, especially when failure data are rare in highly reliable mechanical systems nowadays. In this framework, various models have been proposed to investigate the maintenance strategy, where the maintenance cost and the system availability are the most commonly used assessment criteria. Various system configurations, deterioration characteristics, inspection policies and maintenance criteria have been studied (Hu & Chen, 2020; Zhang et al., 2020, Zhang et al., 2020). The influence of the CBM on product scheduling and the integrated optimization of the EMQ and CBM have been investigated by several researchers. Boukas and Liu (2001) addressed the production and maintenance problem of a failure-prone manufacturing system which had three states following a continuous-time Markov chain. The optimal production and maintenance rates were discussed. Jafari and Makis (2019) also utilized a continuous-time Markov chain with three states to model a production system. By assuming that the non-failure states were partially observable, they derived the optimal Bayesian control policy in the semi-Markov decision process (SMDP) framework. Sloan and Shanthikumar (2000) developed a Markov decision process model to determine the maintenance and production schedules of a multiple-product, single-machine system. The impact of the machine condition on the yield of each type of the products was examined. Peng and van Houtum (2016) modelled the deterioration of the machine by a Gamma process and took the preventive maintenance (PM) threshold and the lot-sizing as the decision parameters in the evaluation of the joint optimization problem. Cheng et al. (2018) combined the health condition of the machine and the quality information in determining the optimal maintenance policy.