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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 251
Virginia Giorno ◽  
Amelia G. Nobile

We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state j (operating, F, R). Due to a failure, a transition from an operating state to F occurs after which a repair is required, so that a transition leads to the state R. Subsequently, there is a restore phase, after which the system restarts from one of the operating states. In particular, we assume that the intensity functions of failures, repairs and restores are proportional and that the birth-death process that models the system is a time-inhomogeneous Prendiville process.

2021 ◽  
Khaled Yassin ◽  
Arne Helms ◽  
Daniela Moreno ◽  
Hassan Kassem ◽  
Leo Höning ◽  

Abstract. A new approach to derive a synthetic wind field model which combines spatial correlations from the Mann model and intermittency is introduced. The term intermittency describes the transition from Gaussian to non-Gaussian velocity increment statistics at small scales, where non-Gaussian velocity increment statistics imply a higher probability for extreme values than a Gaussian distribution. The presented new model is named the Time-mapped Mann model. The intermittency is introduced by applying a special random time-mapping procedure to the regular Mann model. The Time-mapping procedure is based on the so-called Continuous-time random walk model. As will be shown, the new Time-mapped Mann field reflects spatial correlations from the Mann model in the plane perpendicular to flow direction and temporal intermittency. In a first wind turbine study, the new Time-mapped Mann field and a regular Mann field are used as inflow to a wind turbine in a Blade Element Momentum simulation. It is shown that the wind field intermittency carries over to the loads of the wind turbine, and, thus, shows the importance of carefully modeling synthetic wind fields.

2021 ◽  
Vol 5 (4) ◽  
pp. 254
Yuri G. Kondratiev ◽  
José Luís da Silva

We consider random time changes in Markov processes with killing potentials. We study how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence their time behavior. As applications, we study the parabolic Anderson problem, the non-local Schrödinger operators as well as the generalized Anderson problem.

Arnab Pal ◽  
Sarah Kostinski ◽  
Shlomi Reuveni

Abstract The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun will end before those which have just started. Yet, the inspection paradox teaches us that the converse can also happen when randomness is at play. The paradox comes from probability theory, where it is often illustrated by measuring how long passengers wait upon arriving at a bus stop at a random time. Interestingly, such passengers may on average wait longer than the mean time between bus arrivals – a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this viewpoint, we review the inspection paradox and its origins. The insight gained is then used to explain why, in some situations, stochastic resetting expedites the completion of random processes. Importantly, this is done with elementary mathematical tools which help develop a probabilistic intuition for stochastic resetting and how it works. This viewpoint can thus be used as an accessible introduction to the subject.

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 20-27
Manoharan M ◽  
Rajarathinam A ◽  

In any organization a number of factors are required to generate production activities and the manpower is the most vital factor. The manpower requirements may increase in course of time due to increase in production activities or due to depletion of manpower at random time points. Hence recruitment is to be made whenever the total demands for manpower crosses the so called threshold level. In this paper an estimate of the expected time to recruitment is derived under the assumption that the threshold level is a random variable which follows the Generalized Exponentiated Gamma distribution. The variances also found out. The results are substantiated with numerical examples

Sheema Dwivedi

Abstract: The term Performance evaluation alludes to the customary audit of a representative's work execution and in general commitment to an organization. Otherwise called a yearly audit, execution survey or assessment, or worker examination, a presentation examination assesses a representative's abilities, accomplishments, and development, or deficiency in that department. Organizations use execution evaluations to give representatives higher perspective criticism on their work and to legitimize pay increments and rewards, just as end choices. They can be directed at some random time yet will in general be yearly, semi-yearly, or quarterly. Keyword: Appraisal, effectiveness, job analysis’s, accomplishment

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2695
Jiří Tomčala

Accurate prediction methods are generally very computationally intensive, so they take a long time. Quick prediction methods, on the other hand, are not very accurate. Is it possible to design a prediction method that is both accurate and fast? In this paper, a new prediction method is proposed, based on the so-called random time-delay patterns, named the RTDP method. Using these random time-delay patterns, this method looks for the most important parts of the time series’ previous evolution, and uses them to predict its future development. When comparing the supercomputer infrastructure power consumption prediction with other commonly used prediction methods, this newly proposed RTDP method proved to be the most accurate and the second fastest.

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