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Communication failure analysis for a fleet formation flight of drones based on absorbing Markov chain
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
R. Abdallah, C. Sarraf, R. Kouta, J. Gaber, M. Wack
An Absorbing Markov Chain (AMC), where there is at least one absorbing state, is considered. An absorbing state is characterized by the fact of once it is entered, it cannot be left. Each state in the transition diagram can be taken as an absorbing state. The transition between states can have multiple steps in order to attain the absorbing state. Two important variables should be calculated: the mean time tmean in addition to the length of the path until the state is absorbed. We aim to evaluate the probability of being in each transient state leading to the absorbing state. Transitions between states are based on the probabilities that are function of the failure rates, of internal components as well as the occurrences of related events within the surrounding environments.
Systems of Linear Equations
Published in James R. Kirkwood, Bessie H. Kirkwood, Elementary Linear Algebra, 2017
James R. Kirkwood, Bessie H. Kirkwood
For a finite state absorbing Markov chain with k nonabsorbing states, the expected number of transitions that the nonabsorbing state i undergoes before absorption is Ni1+Ni2+⋯+Nik, where N = (I − Q)−1.
Monitoring processes with multiple dependent production lines using time between events control charts
Published in Quality Engineering, 2023
Hussam Ahmad, Adel Ahmadi Nadi, Mohammad Amini, Bahram Sadeghpour Gildeh
The ATS of the EWMA-TBE chart can not be calculated straightforwardly as the Shewhart-type chart. In what follows, we follow a discrete Markov Chain approach proposed by Brook and Evans (1972) to evaluate the ATS of the proposed EWMA-TBE control chart. In this approach, the IC and OC zones in a control chart are considered as the transient and absorbing states of an absorbing Markov Chain. An absorbing Markov Chain is a Markov Chain with at least one absorbing state so that it is possible to go from any transient state to at least one absorbing state in a finite number of steps. To this end, the IC zone is divided into subintervals where ((see Figure 3)). Each subinterval represents a transient state of the Markov Chain. If the Markov Chain is in the transient state at inspection i. If the Markov chain is in the absorbing state We assume that Hj is the representative value of state Let be the submatrix of probabilities corresponding to the transient states defined above, i.e.,
Personalized financing decision support with health evolution model for elder care
Published in IISE Transactions on Healthcare Systems Engineering, 2019
As Fig. 3 shows, the stage space {} represents aging in place, ILC, ALF, SNH, and HC. The absorbing stage indicates death or discharge from the system. This type of Markov chain is called an absorbing Markov chain. We define as consisting of the set of transient stages and a single absorbing stage