Evaluation of Probability Distribution Function for the Life of Pavement Structures

2000 ◽  
Vol 1730 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Stefan A. Romanoschi ◽  
John B. Metcalf
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Failure Time ◽  
Time To Failure ◽  
Closed Form Solutions ◽  
Monte Carlo Algorithms ◽  
Pavement Structures ◽  
Bootstrap Algorithm

Determination of the probability distribution function for the time to failure is essential for the development of pavement life models, because the probability distribution function reflects the variability in pavement degradation. The pavement life and failure time are associated with the number of equivalent standard axle load applications for which the degradations reach a critical level. When the critical degradation level is reached, maintenance and rehabilitation work needs to be done to improve pavement condition. Research was undertaken to identify the appropriate statistical models for determination of the probability distribution function for the time to failure of pavement structures. The study used the rutting data collected on a test lane at the first full-scale accelerated pavement test in Louisiana. The research indicated that closed-form solutions or Monte Carlo algorithms can be used when the degradation models have a known form. The bootstrap algorithm can be used to determine the confidence intervals for probability of failure at a given time. If the form of the degradation model is not known, the survival analysis method based on censored observations must be used. The methods can be used not only for rutting life models but also for other pavement life models: cracking initiation time, cracking life, roughness, and serviceability lives.

Remark on the energy determination of high-energy nucleons by means of the absorption calorimeter

1968 ◽  
Vol 46 (10) ◽  
pp. S1107-S1111 ◽  
Author(s):  
A. Somogyi ◽  
G. Válas ◽  
A. Varga
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Analytical Method ◽  
Probability Distribution Function ◽  
High Energy ◽  
Primary Energy ◽  
Numerical Calculations ◽  
Energy Determination ◽  
Ionization Calorimeter

The sources of error in energy determinations carried out by means of an ionization calorimeter are well known as are the values of the relevant corrections. Very little if anything is known, however, of the statistical uncertainties of these corrections. An analytical method has been worked out in order to determine the probability that a certain fraction of the primary energy leaves a calorimeter of a given thickness and thus escapes detection. The method makes due allowance for the fluctuation of the inelasticity coefficient. Numerical calculations have been carried out assuming various forms for the probability distribution function of the inelasticity coefficient, and the results of the calculations are given for various calorimeter thicknesses.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

DETERMINATION OF THE DISTRIBUTION FUNCTION OF THE TIME BETWEEN FAILURES OF A WEAPON MODEL WITHOUT TAKING INTO ACCOUNT THE ENEMY’S FIRE IMPACT

2019 ◽  
pp. 39-45
Author(s):  
M. Sliusarenko ◽  
O. Semenenko ◽  
T. Akinina ◽  
O. Zaritsky ◽  
V. Ivanov
Keyword(s):  
Distribution Function ◽  
Analytical Description ◽  
Time To Failure ◽  
Missile Defense ◽  
Incorrect Choice ◽  
Military Equipment ◽  
Time Between Failures ◽  
The Military ◽  
Fire Impact

In the article, based on the analysis of the requirements for the readiness of weapons and military equipment during combat use and the reliability of their operation in the course of combat operations, it was discovered that one of the reasons that causes a discrepancy between the declared failures and real ones may be the incorrect choice and justification of the time distribution function up to the refusal of military means. As a rule, during the development of these tools, the function of distribution of time to failure is chosen by analogy with similar patterns of weapons and military equipment. In the theory of reliability, special attention is given to choosing the function of time-breaking non-response (failures or failures). Therefore, the article deals with the questions of evaluating the effectiveness of functioning of complex systems and methods of modeling the processes of their functioning, taking into account the laws of the distribution of random variables. The discrepancy between the declared irregularity of the military apparatus and the fact that is actually observed in the troops can be explained by the incorrectly accepted hypothesis about the distribution of time to failure. Therefore, the article analyzes the order of the justification of such a function without taking into account the enemy's fire impact and the proposed variant of determining the function of distribution of the time of work until the refusal of the model of military equipment. The article also cites the reasons for the discrepancy between the claimed missile defense equipment and what is actually observed in the troops. The proposed mathematical model of faultlessness, which at stages of designing and design will allow to set requirements to the model of technology with the help of analytical description. The sequence of calculations of non-failure indexes based on the use of Weibull distribution is substantiated.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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