By Gennadij V Arkadov, Alexander F Getman, Andrei N Rodionov

This ebook presents an summary of probablistic tools for calculating the energy and working lifetime of apparatus and pipelines of nuclear energy vegetation (NPPs), together with utilizing the factors of resistance to complete or partial destruction with the formation of breaks, leaks or defects within the steel, taking into consideration the getting older of apparatus and pipelines in service.  The authors pay specific consciousness to the sensible program of the result of calculations of the energy and working lifetime of apparatus and pipelines, the optimization of inservice inspection and maintainance and service. The goals of this booklet are: -To describe the most equipment utilized in nuclear energy engineering for the choice of quantitative features of the reliability of apparatus and piping of NPP -To make clear the mechanisms of getting older of kit and piping in carrier and talk about the impression of these mechanisms on reliability -To review the opportunity of broad sensible program of the equipment for deciding upon the reliability features and using those tools for fixing the present difficulties in operation it is a revised and translated model of an unique Russian language paintings released in 2010 by way of Energoatomizdat, Russia.

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T t t dP(t ) =ln P (t ) | =ln P (t ) =− ∫ l (t )dt , 0 P(t ) 0 0 ∫ from the basic equation of the relationship of the main reliability indicators is as follows:  t  P(= t ) exp − ∫ l(t )dt  . 35]  0  The value of λ(t) dt is the likelihood that the element worked flawlessly in the operating time range [0, t] and fails in the interval [t, t + dt]. 35] shows that all the reliability indicators P(t), Q(t), f(t) and λ(t) are equal in the sense that knowing one of them, we can define others.

The formula of total probability. 13] where P(H i) is the probability of hypothesis H i; P(A|H i) is the conditional probability of event A under hypothesis Hi. Since event A can occur with one of the hypotheses H 1, H 2, ... H n, then A = AH 1 ∨ AH 2 ∨ ... H n are incompatible, so P( A)= P( A ∧ H i ) + ... + P( A ∧ H n )= n ∑ P( AH ). 13]. The Bayes formula (the formula of probability of hypotheses). If the probabilities of hypotheses H 1 , H 2 , ... , P(H n), and event A took place as a result of the experiment, then the new (conditional) probabilities of the hypotheses are evaluated: = P( A | H i ) P( H i ) P( A | H i ) P( H i ) P( A | H i ) = .

F.. 29] Q(t )= P {0 < T < t}= P {T ∈ (0, t )}= t ∫ f (t )dt. 30] The extension of the interval to the left to zero is due to the fact that T cannot be negative. Because P(t) = P{T ≥ t}, then 0 P(= t ) P {t ≤ T < ∞ = } ∞ ∫ f (t )dt.  Since all values of the operating time obtained by testing lie under the curve f(t), then t ∞ ∫ t ∞ 0 t f (t )dt =∫ f (t )dt + ∫ f (t )dt =Q(t ) + P (t ) = 1. 32] Statistical estimation of failure rate (FR), expressed in units of inverse operating time, is defined by the ratio of the number of objects ∆n(t, t + 0 16 Probabilistic safety assessment for optimum nuclear PLiM ∆t), failed in the operating time period [t, t + ∆t], to the product of the number N of efficiently working object at time t by the duration of the operating time period ∆t: Dn(t , t + Dt ) lˆ (t ) = .

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