Tolerance Region: Definition

2014 ◽  
Author(s):  
Mark G. Vangel
Keyword(s):  
Tolerance Region

A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization

2005 ◽  
Vol 128 (4) ◽  
pp. 874-883 ◽  
Author(s):  
Mian Li ◽  
Shapour Azarm ◽  
Art Boyars
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Continuous Functions ◽  
Robust Design Optimization ◽  
Worst Case ◽  
New Approach ◽  
Multi Objective ◽  
Tolerance Region ◽  
Parameter Variations ◽  
Gradient Based

We present a deterministic non-gradient based approach that uses robustness measures in multi-objective optimization problems where uncontrollable parameter variations cause variation in the objective and constraint values. The approach is applicable for cases that have discontinuous objective and constraint functions with respect to uncontrollable parameters, and can be used for objective or feasibility robust optimization, or both together. In our approach, the known parameter tolerance region maps into sensitivity regions in the objective and constraint spaces. The robustness measures are indices calculated, using an optimizer, from the sizes of the acceptable objective and constraint variation regions and from worst-case estimates of the sensitivity regions’ sizes, resulting in an outer-inner structure. Two examples provide comparisons of the new approach with a similar published approach that is applicable only with continuous functions. Both approaches work well with continuous functions. For discontinuous functions the new approach gives solutions near the nominal Pareto front; the earlier approach does not.

scholarly journals Adopting Tolerance Regions in Environmental Economics

2020 ◽  
pp. 1-12
Author(s):  
Christos P. Kitsos ◽  
Thomas L. Toulias
Keyword(s):  
Confidence Interval ◽  
Environmental Economics ◽  
Optimal Level ◽  
Physical Problem ◽  
Parameters Estimation ◽  
Estimation Model ◽  
Real World Problem ◽  
Tolerance Region ◽  
Tolerance Regions ◽  
Region Approach

Uncertainty often lies when there is limited knowledge about the process one has to follow regarding the investigation of a real-world problem. In practice, uncertainty is related with the assumed estimation model of the physical problem, and mainly concerns the involved parameters. A typical examplecan be an Environmental Economics system. There are many model specifications that estimate the so-called Benefit Area of such system. For the evaluation of the optimal level of pollution, we can adopt the corresponding tolerance region, and hence we can refer to this optimal level via future observations rather than some parameters estimation. Tolerance regions can be either classical or expected tolerance regions. The associated (four) Benefit Areas can be evaluated through a proposed tolerance region procedure, and not through the usual confidence interval/region approach. Therefore, four possible optimal levels of pollution can be obtained, as well as the corresponding tolerance region for the reduction pollution point.

DETECTION AND CLASSIFICATION OF MAMMOGRAPHIC CALCIFICATIONS

1993 ◽  
Vol 07 (06) ◽  
pp. 1403-1416 ◽  
Author(s):  
LIANG SHEN ◽  
RANGARAJ M. RANGAYYAN ◽  
J.E. LEO DESAUTELS
Keyword(s):  
Region Growing ◽  
Parameter Determination ◽  
Shape Features ◽  
Detection Rates ◽  
Network Training ◽  
The Neural Network ◽  
Tolerance Region ◽  
Preliminary Study ◽  
Leave One Out

We propose a detection and classification system for the analysis of mammo-graphic calcifications. First, a new multi-tolerance region growing method is proposed for the detection of potential calcification regions and extraction of their contours. The method employs a distance metric computed on feature sets including measures of shape, centre of gravity, and size obtained for various growth tolerance values in order to determine the most suitable parameters. Then, shape features from moments, Fourier descriptors, and compactness are computed based upon the contours of the regions. Finally, a two-layer perceptron is utilized for the purpose of classification of calcifications with the shape features. A new leave-one-out algorithm-based parameter determination procedure is included in the neural network training step. In our preliminary study, detection rates were 81% and 85±3%, and correct classification rates were 94% and 87% with a test set of 58 benign calcifications and 241±10 malignant calcifications, respectively. The proposed system should provide considerable help to radiologists in the diagnosis of breast cancer.

A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibilty Robust Design Optimization

2005 ◽  
Author(s):  
Mian Li ◽  
Shapour Azarm ◽  
Art Boyars
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Continuous Functions ◽  
Robust Design Optimization ◽  
Deterministic Approach ◽  
Worst Case ◽  
New Approach ◽  
Multi Objective ◽  
Tolerance Region ◽  
Gradient Based

We present a deterministic, non-gradient based approach that uses robustness measures for robust optimization in multi-objective problems where uncontrollable parameters variations cause variation in the objective and constraint values. The approach is applicable for cases with discontinuous objective and constraint functions, and can be used for objective or feasibility robust optimization, or both together. In our approach, the parameter tolerance region maps into sensitivity regions in the objective and constraint spaces. The robustness measures are indices calculated, using an optimizer, from the sizes of the acceptable objective and constraint variation regions and from worst-case estimates of the sensitivity regions’ sizes, resulting in an outer-inner structure. Two examples provide comparisons of the new approach with a similar published approach that is applicable only with continuous functions. Both approaches work well with continuous functions. For discontinuous functions the new approach gives solutions near the nominal Pareto front; the earlier approach does not.

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