A two-stage Monte Carlo approach to the expression of uncertainty with non-linear measurement equation and small sample size

Metrologia ◽  
2005 ◽  
Vol 43 (1) ◽  
pp. 34-41 ◽  
Author(s):  
Stephen V Crowder ◽  
Robert D Moyer
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Small Sample Size ◽  
Linear Measurement ◽  
Small Sample ◽  
Two Stage ◽  
Measurement Equation ◽  
Monte Carlo Approach ◽  
Non Linear ◽  
Expression Of Uncertainty

Design Curve Construction Based on Monte Carlo Simulation

2013 ◽  
Author(s):  
Zhigang Wei ◽  
Limin Luo ◽  
Burt Lin ◽  
Dmitri Konson ◽  
Kamran Nikbin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Sample Size ◽  
Test Data ◽  
Confidence Level ◽  
Small Sample Size ◽  
Test Sample ◽  
Small Sample ◽  
Tolerance Limit ◽  
Design Curve

Good durability/reliability performance of products can be achieved by properly constructing and implementing design curves, which are usually obtained by analyzing test data, such as fatigue S-N data. A good design curve construction approach should consider sample size, failure probability and confidence level, and these features are especially critical when test sample size is small. The authors have developed a design S-N curve construction method based on the tolerance limit concept. However, recent studies have shown that the analytical solutions based on the tolerance limit approach may not be accurate for very small sample size because of the assumptions and approximations introduced to the analytical approach. In this paper a Monte Carlo simulation approach is used to construct design curves for test data with an assumed underlining normal (or lognormal) distribution. The difference of factor K, which measures the confidence level of the test data, between the analytical solution and the Monte Carlo simulation solutions is compared. Finally, the design curves constructed based on these methods are demonstrated and compared using fatigue S-N data with small sample size.

Error-rate estimation in discriminant analysis of non-linear longitudinal data: A comparison of resampling methods

2016 ◽  
Vol 27 (4) ◽  
pp. 1153-1167 ◽  
Author(s):  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Cristian Meza ◽  
Vicente Núñez-Antón
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Cross Validation ◽  
Numerical Study ◽  
Small Sample Size ◽  
Parametric Bootstrap ◽  
Small Sample ◽  
Misclassification Error ◽  
Non Linear ◽  
Misclassification Error Rate

Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.

Uncertainty Evaluation Study of CMM Dynamic Measurement Based on Quasi Monte Carlo Method

2011 ◽  
Vol 103 ◽  
pp. 366-371 ◽  
Author(s):  
Wei Hong Zhong ◽  
Xiu Shui Ma ◽  
Ying Dao Li ◽  
Yuan Li
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Small Sample Size ◽  
Dynamic Measurement ◽  
Small Sample ◽  
Uncertainty Evaluation ◽  
Effective Diameter ◽  
Large Sample Size ◽  
Quasi Monte Carlo ◽  
Measuring Machine

In a contact measurement process, the coordinate measuring machine（CMM）probe will bring dynamic measurement error, therefore, dynamic calibration of the probe tip effective diameter should to be done at different probing speeds, and calibration uncertainty should to be given. There are some problems, slow convergence and unstable, using Monte Carlo (MC) method in uncertainty. In this paper, Quasi Monte Carlo (QMC) method is presented in the probe tip effective diameter uncertainty evaluation. At a certain positioning speed and distance approximation, probe tip effective diameter experimental tests are done with changing probing speeds. MC and QMC methods are used on uncertainty evaluation respectively, and the results are compared and analyzed. The simulation shows that QMC can be used on dynamic uncertainty evaluation of CMM probe tip. Compared with MC, QMC obtains a better stability and precision in small sample size and gains higher computing speed in large sample size.显示对应的拉丁字符的拼音 字典名词 assessment动词 assessevaluatepass judgment

A Novel Quota Sampling Algorithm for Generating Representative Random Samples given Small Sample Size

2013 ◽  
Vol 2 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Ahmed M. Fouad ◽  
Mohamed Saleh ◽  
Amir F. Atiya
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Sampling Method ◽  
Optimization Problems ◽  
Small Sample Size ◽  
Probability Distributions ◽  
Small Sample ◽  
Sampling Algorithm ◽  
Quasi Monte Carlo ◽  
Quota Sampling

In this paper, a novel algorithm is proposed for sampling from discrete probability distributions using the probability proportional to size sampling method, which is a special case of Quota sampling method. The motivation for this study is to devise an efficient sampling algorithm that can be used in stochastic optimization problems -- when there is a need to minimize the sample size. Several experiments have been conducted to compare the proposed algorithm with two widely used sample generation methods, the Monte Carlo using inverse transform, and quasi-Monte Carlo algorithms. The proposed algorithm gave better accuracy than these methods, and in terms of time complexity it is nearly of the same order.

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