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discrete probability distribution sampling

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Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
..., and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009212
EISBN: 978-1-62708-176-4
... density function. There are many well-known theoretically established probability density functions that display a wide variety of shapes for both discrete and continuous random variables. Statistical distributions that may be used to describe samples and populations of data are derived mathematically...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009213
EISBN: 978-1-62708-176-4
... is the proportion of defective items in the entire lot. Probability Mass Function The binomial probability distribution is a discrete probability distribution with two parameters: the sample size, n , and the proportion defective, p . The binomial probability mass function is: (Eq 37) f ( x...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003712
EISBN: 978-1-62708-182-5
... is known or can readily be assumed about random events. One can then use that prediction to make a judgement about a specific outcome of an investigation, that is, whether or not the outcome occurred by chance. Probability, Sampling Distributions, and the Normal Curve Imagine a coin-tossing exercise...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002431
EISBN: 978-1-62708-194-8
..., such as Weibull probability paper. Although not statistically rigorous, plotting of CDFs on different types of probability paper can be very helpful in evaluating whether or not it is reasonable to assume a particular statistical distribution. Sample versus Population Parameters When performing...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... Probability Plot An experiment was performed to measure fracture toughness, K , of a brittle material. A random sample of n = 5 was obtained. It is assumed that the observations in this random sample are independent and from the same distribution. The tilde, ˜, indicates a random sample...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
... is active. The reader is strongly encouraged to integrate mechanical failure data and fractographic analysis. Fig. 3 Sample with multiple failure populations As was just noted, discrete fracture origins are quite often grouped by flaw distributions. The data for each flaw distribution can also...
Book Chapter

Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003088
EISBN: 978-1-62708-199-3
.... In the probabilistic approach, each design parameter is accorded a statistical distribution of values. From these distributions and from an allowable limit on probability of failure, minimum acceptable dimensions in critical areas (or minimum strength levels for critical components) can be calculated. Compared...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... a Potts model simulation of a two-component system in which the initial distribution of components is equal and R A = R B = 0.5. The A and B components are differentiated by the gray scale. The simulation was performed using a square (1,2) lattice, Glauber dynamics, metropolis transition probability...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002432
EISBN: 978-1-62708-194-8
... distribution is limited to samples of known size ( n is known) with a count of the number of times a certain event is observed. If the sample size is indefinite, that is, n is not known, the Poisson distribution can be used. In this case, the probability of exactly k failures occurring in time t...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006368
EISBN: 978-1-62708-192-4
.... Mode The mode is the data that have the highest amount of occurrences. For example, consider the dataset [1,5,9,4,2,5,6]. The mode of this sample is 5, which has the highest occurrence among the data, that is, two. Median The median of a distribution is a value such that the number of data...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005432
EISBN: 978-1-62708-196-2
.... Texture can be incorporated by statistical sampling of data and subsequent mapping on the CA ( Ref 17 ), by direct import of data from electron backscattered diffraction (EBSD) in the scanning electron microscope ( Ref 18 ), or by coupling the CA simulation with a spatially discrete deformation simulation...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005505
EISBN: 978-1-62708-197-9
... with known variation. They are described through probability distributions and associated properties. By sampling from these distributions following their prescribed properties, the effects of this input variation on performance can be assessed. Through this sampling, stochastic analysis is used to measure...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001759
EISBN: 978-1-62708-178-8
... of preferred orientations, but this method is qualitative and sometimes misleading. The orientation distribution function (ODF) is a function defined over the range of Euler angles φ, θ, and ϕ. It provides the probability that a grain has a particular orientation given by the three Euler angles. If a range...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003515
EISBN: 978-1-62708-180-1
... distributions for two NDE techniques Inspection Intervals A key aspect of a damage tolerant fracture control program is the interval between inspections. This depends on the specific values of the level of damage that will cause fracture, the rate of evolution of damage, and the probability...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009219
EISBN: 978-1-62708-176-4
... shows the trend toward increasing variability with increasing mean life, as evidenced by the gradual flattening of the cumulative probability curves. Fig. 5 Schematic S / N diagram showing log normal distribution of lives at various stress levels Fig. 6 Probability plot of percent...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001727
EISBN: 978-1-62708-178-8
... samples to be examined may reduce the uncertainty in the average value. Types of Samples Random Samples Sampling is occasionally directed at obtaining an extreme value, such as the best or worst case. However, a sample usually is collected to determine the distribution of some characteristic...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006462
EISBN: 978-1-62708-190-0
... threshold level ( D I ). Formally, this metric is known as the probability of detection (POD). As depicted in Fig. 7 , the POD is based on the concept that, for a given flaw size, there will be a distribution of flaw signals. However, it must be recognized that, in the absence of any meaningful flaw...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005534
EISBN: 978-1-62708-197-9
... in a physical sample, this is generally both expensive and time-consuming. Accordingly, a subset of possible measurements is evaluated or sampled, and a distribution of values for that property is computed. The basic approach is to construct approximations of the analysis codes that are efficient to run...
Series: ASM Handbook
Volume: 9
Publisher: ASM International
Published: 01 December 2004
DOI: 10.31399/asm.hb.v09.a0003759
EISBN: 978-1-62708-177-1
... states that there is 95% probability that the true volume fraction of the phase of interest is within the interval given by this equation. Note that the sampling error E n strongly depends on the sample size n , and therefore it can be kept as small as desired by increasing the sample size n...