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Cost Estimating Relationships
Published in Howard Eisner, Cost-Effectiveness Analysis, 2021
The regression methods for generating the CER itself include [6]:Ordinary least squaresGeneralized least squaresTransformational linear and log-linear modelGeneralized linear modelNon-linear least squaresRidge regressionMinimum unbiased percentage errorAdvanced regression methods
Project Integration
Published in Adedeji B. Badiru, Project Management Essentials, 2021
Several alternate models of learning curves have been presented in the literature. Some of the most notable models are the log-linear model, the S-curve, the Stanford-B model, DeJong’s learning formula, Levy’s adaptation function, Glover’s learning formula, Pegels’ exponential function, Knecht’s upturn model, and Yelle’s product model. The univariate learning curve expresses a dependent variable (e.g., production cost) in terms of some independent variable (e.g., cumulative production). The log-linear model is by far the most popular and most used of all the learning curve models. The log-linear model states that the improvement in productivity is constant (i.e., it has a constant slope) as output increases. There are two basic forms of the log-linear model: the average cost model and the unit cost model. The average cost model is used more than the unit cost model. It specifies the relationship between the cumulative average cost per unit and cumulative production. The relationship indicates that cumulative cost per unit will decrease by a constant percentage as the cumulative production volume doubles. The model is expressed as Ax=C1xb
Design of Multi-Stress Accelerated Life Testing Plans Based on D-Optimal Experimental Design
Published in Lirong Cui, Ilia Frenkel, Anatoly Lisnianski, Stochastic Models in Reliability Engineering, 2020
Xiangxiang Zhang, Jun Yang, Xuefeng Kong
As assumed in Subsection 27.2.1, the acceleration model is described as a log-linear model. Then let Y = ln T be the log transformation of lifetime T, it can be obtained that Y follows a smallest-extreme value distribution. And the log-linear model can be transformed to a more generalized linear model by defining μ(x) = ln α(x) as: μ(x)=β0+β1x1+β2x2+⋯+βkxk,
A nonparametric EWMA control chart for monitoring mixed continuous and count data
Published in Quality Technology & Quantitative Management, 2023
Li Xue, Qiuyu Wang, Zhen He, Peihua Qiu
Model (2) is a saturated log-linear model and is capable of systematically evaluating the relationships and interactions between variables. The three-way log-linear model can be divided into different kinds, such as the second-order interaction effect model, the conditional independent model, and the joint independent model. When some items are deleted from Model (2), the resultant models can describe a variety of associations among and . First, to facilitate representation, the highest-order term of variables is used to represent each log-linear model that we are addressing. For example, the model with three-way interaction terms is expressed as , whereas the model means that every pair of variables interacts except the three-way interaction term, and the correlation between any two variables is the same at two levels of the other variables. Based on the specifics of the variables and how they are related to each other, the specific log-linear model will be determined. To choose the appropriate log-linear model, it is usually necessary to use the likelihood ratio test statistic as well as the hierarchy principle. That is, if there are high-order interaction items in the model, all low-order items should be included in the model. In response to this situation, the method of model selection is based on the backward elimination method, in which each step involves removing only one item at a time. For example, the likelihood ratio test statistic(cf. He et al., 2022) would be calculated as follows.
Improving Efficiency and Accuracy in English Translation Learning: Investigating a Semantic Analysis Correction Algorithm
Published in Applied Artificial Intelligence, 2023
The log-linear model is a statistical model used to estimate the probability distribution of a target variable based on a set of input features. In translation, the log-linear model estimates the likelihood of a particular translation given a source sentence or phrase. Feature Extraction: Relevant features are extracted from the input data. In translation, these features can include various linguistic and contextual information such as word alignments, language models, part-of-speech tags, and syntactic structures. The implementation of a log-linear model involves the following steps:Model Parameterization: The log-linear model assigns weight parameters to each feature. These parameters capture the importance or contribution of each feature to the overall translation probability. The parameterization could be mastered from training data utilizing maximum likelihood estimation or gradient-based optimization methods.Scoring and Translation Selection: Given an input sentence or phrase, the log-linear model calculates a score for each possible translation option based on the weighted sum of the extracted features. The translation option with the highest score is selected as the output translation.Training and Model Refinement: The log-linear model is trained using a labeled dataset of source sentences and their corresponding translations. The model parameters are optimized to maximize the likelihood of generating the correct translation given the input data. Training typically involves iterative optimization algorithms that adjust the parameter values to minimize a loss function, such as cross-entropy loss.