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Microsoft Excel: The Universal Tool of Analysis
Published in Natalie M. Scala, James P. Howard, Handbook of Military and Defense Operations Research, 2020
Joseph M. Lindquist, Charles A. Sulewski
This functionality also enables the generation of data referred to as random variates. A random variate is, quite simply, an instance of a randomly generated number from a given probability distribution. As an example, to calculate a normally distributed random variate with a mean of 20 and standard deviation of 6, we type the following command into the formula bar: =NORM.INV(RAND(),20,6).
Use of Simulation for Decision Models
Published in Gerald W. Evans, Multiple Criteria Decision Analysis for Industrial Engineering, 2016
The key to a Monte Carlo simulation is the generation of random variates. A random variate value is an independent sample from a prescribed probability distribution, such as a normal distribution or a binomial distribution. These values are required in order to execute a simulation model with random aspects, such as a Monte Carlo simulation. For example, in the influence diagram for the lead poison testing decision example presented in Chapter 6, random variates are needed to represent the number of children with lead poisoning in the sample tested; these random variates should correspond to the hypergeometric distribution, as noted in the example.
Error and uncertainty
Published in W. Schofield, M. Breach, Engineering Surveying, 2007
Random variates are assumed to have a continuous frequency distribution called normal distribution and obey the law of probability. A random variate, x, which is normally distributed with a mean and standard deviation, is written in symbol form as N(μ, σ2). Random errors alone are treated by statistical processes.
Radiation-Induced Damage–Based System and Method for Indirectly Monitoring High-Dose Ionizing Radiation
Published in Nuclear Technology, 2018
Karen Colins, Yu Liu, Liqian Li, Kiranpreet Birdee
Importantly, the relation given by Eq. (2) is independent of the probability density function of the underlying distribution of the random variate. For a sample of size , solution of Eq. (2) yields a confidence of only that at least a fraction of the population will be included between the least value and the greatest value of the sample. That solution supports the observed high frequency of poor agreements in reliability test comparisons, illustrated by the plot of Fig. 7b.
Integrated parameter and tolerance optimization of a centrifugal compressor based on a complex simulator
Published in Journal of Quality Technology, 2020
Mei Han, Xuejun Liu, Min Huang, Matthias H. Y. Tan
The quality loss function measures the quality cost of each compressor that has been accepted for delivery to the customer. The quality loss function we use is motivated by the engineers’ emphasis on achieving a small failure probability on all three PMs. Note that each of the PMs and is a larger-the-better PM and each has been normalized by its threshold design requirement. As the customer and engineers view a probability of failure less than (probability that a standard normal random variate is less than −2) to be desirable and a probability of failure more than 0.0228 to be undesirable, a suitable quality loss function is where is an indicator function, which equals 1 if the event is true and equals 0 otherwise. This is because the expectation of the loss function with respect to the distribution of is which gives a positive contribution to the expected loss for any failure probability larger than and a negative contribution representing a reward due to exceeding the customer’s expectation on the failure probability otherwise. Note that while can be fixed in the computer simulation, it is a random variable in the manufacturing process. By abuse of notation, we do not distinguish between a random and a fixed since it should be clear from the context.
Construction, Properties, and Analysis of Group-Orthogonal Supersaturated Designs
Published in Technometrics, 2020
Bradley Jones, Ryan Lekivetz, Dibyen Majumdar, Christopher J. Nachtsheim, Jonathan W. Stallrich
The simulation proceeds as follows. For the ith treatment combination we: Designate of the ng groups to be active. The results do not depend on which groups of the are selected to be active, and for this reason we always select the first groups without loss of generality.For each active group, we select factors to be active. If , it does not matter which factor is chosen to be active. If , it does matter, and in this case we select the first two columns, which maximizes the group power.For each active factor, we generate a random variate from an exponential distribution with mean μ = 1 and add it to to obtain the absolute value of the factor effect.With now determined, calculate E(.Compute random response vectors , for .Apply each of the three model selection approaches to each of the nsim response vectors and record the power and Type I error rates.