B.V. Gnedenko: The father of the Russian school of reliability theory

Gnedenko, Ekaterina; Ushakov, Igor

doi:10.3103/s0146411613020107

Cited by 8 publications

(21 citation statements)

References 3 publications

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“…By analogy with the reliability theory, which use the term probability of failure of the product in time t, we write the expression for the probability of the absence of any of the events for the time t [1] …”

Section: Mathematical Foundations Of the Analysis Of Random Events Inmentioning

confidence: 99%

“…Similar term, but with another semantic content (failure intensity), is used in the reliability theory and is determined as follows [1] ) (…”

Section: Mathematical Foundations Of the Analysis Of Random Events Inmentioning

confidence: 99%

“…The situation mathematically defined is reduced to the theorem by B.V. Gnedenko for limit distribution of the maximum and minimum value [1].…”

mentioning

confidence: 99%

“…Let us find the distribution function, which is subject to the given value when n → ∞ (in practice at sufficiently large n). According to the B.V. Gnedenko theorem [1], the limit distribution of the third type of the minimum value is the Weibull-Gnedenko distribution. Thus, and it is especially necessary to emphasize, the WeibullGnedenko distribution is the distribution of the random variable that is a minimum of a large number of independently operating variables.…”

mentioning

confidence: 99%

“…In the probability theory, for approximation of distributions of selected data, different laws are applied, including the WeibullGnedenko law, normal, log-normal ones etc. For the mathematical analysis of the above random events, we use the Weibull-Gnedenko distribution [1]. Let's give a mathematical and physical basis of the applicability of this distribution, the function of which has the form:…”

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confidence: 99%

See 4 more Smart Citations

Analysis of random events in physical and chemical processes flowing in materials of semiconductor products under external influences and thermal aging

Milenin¹

2015

Semicond. Phys. Quantum Electron. Optoelectron.

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Section: Mathematical Foundations Of the Analysis Of Random Events Inmentioning

confidence: 99%

“…Similar term, but with another semantic content (failure intensity), is used in the reliability theory and is determined as follows [1] ) (…”

Section: Mathematical Foundations Of the Analysis Of Random Events Inmentioning

confidence: 99%

“…The situation mathematically defined is reduced to the theorem by B.V. Gnedenko for limit distribution of the maximum and minimum value [1].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Analysis of random events in physical and chemical processes flowing in materials of semiconductor products under external influences and thermal aging

Milenin¹

2015

Semicond. Phys. Quantum Electron. Optoelectron.

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Improved Priority Scheme for Unreliable Queueing System

Dudin

Dudina

Dudin

2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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A novel flexible discipline for providing priority in a singleserver queue is applied to the system where the service can be unreliable what results in the loss of a customer or repetition of its service. According to this discipline, arriving customers are stored in the finite buffers dedicated to the customers of the corresponding type if the buffer is not full. After the staying in the corresponding buffer during the exponentially distributed time, the customers try to enter the main buffer of a finite capacity which is common for both types of customers. If this main buffer is full, the customer returns to the dedicated buffer and repeats the attempts to enter the main buffer later. Customers staying in the dedicated buffers are impatient and can go away from the system after a certain patience period duration of which has an exponential distribution. Customers of both types, which succeed to enter the main buffer, are picked up for the service in the order of their admission to this buffer. Providing the preference to priority customers is managed via the corresponding choice of capacities of the dedicated buffers and the rate of trials to transfer to the main buffer. Performance measures of this system are obtained under the assumption that the arrival flows of two types of customers are defined by the Markov arrival processes and the service time has the distribution of phase-type with failures type. Some aspects relating to an optimal choice of the parameters of the system are discussed via numerical experiments.

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Correlation characteristics assessment of construction products reliability parameters

Chiganova

2021

E3S Web Conf.

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Since the reliability of construction products, by definition, is a probability of failure-free operation, then to assess the correlation characteristics between the parameters of the reliability of construction products that are not observed at the same time, we will use the designations and terms used in the theory of probability and mathematical statistics. Existing statistical methods for assessing the conditional mathematical expectation applied to the construction product reliability are based on the possibility of simultaneous measurement of the value of random variables. Because of this, they get a set of extreme points in the plane of those variables, and then build a regression line estimates based on those parameters. Such methods are obviously unacceptable for the case when the quantities the mentioned random variables are cumulatively unobserved. The solution to this problem will allow us to find estimates (not statistical) of the regression line and a number of other characteristics associated with it for simultaneously unobservable random variables. The algorithm described in the current work illustrates an example of interest in the theory of reliability for finding the extrema of the averaged function over the given initial parameters of the construction product.

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B.V. Gnedenko: The father of the Russian school of reliability theory

Cited by 8 publications

References 3 publications

Analysis of random events in physical and chemical processes flowing in materials of semiconductor products under external influences and thermal aging

Analysis of random events in physical and chemical processes flowing in materials of semiconductor products under external influences and thermal aging

Improved Priority Scheme for Unreliable Queueing System

Correlation characteristics assessment of construction products reliability parameters

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