Defect Initiation, Growth, and Failure – A General Statistical Model and Data Analyses

2009 ◽  
pp. 27-37 ◽  
Author(s):  
Wayne B. Nelson
Keyword(s):  
Statistical Model ◽  
Data Analyses ◽  
General Statistical

Formulating a general statistical model forBetulaspp. invasion of lowland heath ecosystems

2005 ◽  
Vol 42 (6) ◽  
pp. 1031-1041 ◽  
Author(s):  
P. MANNING ◽  
P. D. PUTWAIN ◽  
N. R. WEBB
Keyword(s):  
Statistical Model ◽  
General Statistical

A General Statistical Model for Random Fatigue

1974 ◽  
Vol 96 (1) ◽  
pp. 34-40 ◽  
Author(s):  
P. H. Wirsching ◽  
E. B. Haugen
Keyword(s):  
Statistical Model ◽  
Narrow Band ◽  
Wide Band ◽  
Fatigue Tests ◽  
Material Strength ◽  
Probabilistic Design ◽  
Mean Values ◽  
Design Procedures ◽  
General Statistical ◽  
Random Fatigue

A general statistical model for fatigue under stationary random gaussian stress is presented. This phenomenological model requires only a limited amount of data from fatigue tests in which specimens are subjected to stationary narrow band, gaussian stresses. A theoretical extension is made to predict fatigue under wide band stresses and arbitrary mean values. Statistical variability in material strength is included in the model. Moreover, the model has the property of adaptability in that it is easily modified to reflect new data as it becomes available. Furthermore, it is easily incorporated into probabilistic design procedures where reliability requirements are specified.

scholarly journals GND-PCA-Based Statistical Modeling of Diaphragm Motion Extracted from 4D MRI

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Windra Swastika ◽  
Yoshitada Masuda ◽  
Rui Xu ◽  
Shoji Kido ◽  
Yen-Wei Chen ◽  
...  
Keyword(s):  
Statistical Model ◽  
Principal Component ◽  
Motion Model ◽  
4D Mri ◽  
Left Diaphragm ◽  
Margin Of Error ◽  
Spatial Domains ◽  
General Statistical ◽  
Leave One Out ◽  
Diaphragm Motion

We analyzed a statistical model of diaphragm motion using regular principal component analysis (PCA) and generalized N-dimensional PCA (GND-PCA). First, we generate 4D MRI of respiratory motion from 2D MRI using an intersection profile method. We then extract semiautomatically the diaphragm boundary from the 4D-MRI to get subject-specific diaphragm motion. In order to build a general statistical model of diaphragm motion, we normalize the diaphragm motion in time and spatial domains and evaluate the diaphragm motion model of 10 healthy subjects by applying regular PCA and GND-PCA. We also validate the results using the leave-one-out method. The results show that the first three principal components of regular PCA contain more than 98% of the total variation of diaphragm motion. However, validation using leave-one-out method gives up to 5.0 mm mean of error for right diaphragm motion and 3.8 mm mean of error for left diaphragm motion. Model analysis using GND-PCA provides about 1 mm margin of error and is able to reconstruct the diaphragm model by fewer samples.

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