Reliability analysis using bootstrap information criterion for small sample size response functions
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RESEARCH PAPER
Reliability analysis using bootstrap information criterion for small sample size response functions Eshan Amalnerkar 1 & Tae Hee Lee 1
&
Woochul Lim 2
Received: 30 January 2020 / Revised: 11 August 2020 / Accepted: 13 August 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Statistical model selection and evaluation methods like Akaike information criteria (AIC) and Monte Carlo simulation (MCS) have often established efficient output for reliability analysis with large sample size. Information criterion can provide better model selection and evaluation in small sample sizes setup by considering the well-known measure of bootstrap resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion to check for uncertainty arising from model selection as well as statistics of interest for small sample size using reliability analysis. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection devised from efficient bootstrap simulation or variance reduced bootstrap information criterion to be combined with reliability analysis. It is beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest for uncertainty analysis. The proposed simulation scheme is verified using a number of sample size focused response functions under repetitions-centred approach with AIC-based reliability analysis for comparison and MCS for accuracy. The results show that the proposed simulation scheme aids the statistics of interest by reducing the spread and hence the uncertainty in sample size-based reliability analysis when compared with conventional methods. Keywords Efficient bootstrap simulation . Reliability analysis . Small sample size . Uncertainty analysis . Akaike information criteria
1 Introduction Highlights • Simulation scheme proposed for using ordinary bootstrap resampling in variance reduced bootstrap information criterion (EIC) for reliability analysis. • Simulation scheme compared with Akaike information criteria and Monte Carlo simulation-based reliability analysis for various response functions. • Small sample-based analysis with repetitions to show the robustness of method. • Uncertainty reduction by considering spread of reliability values and not a single fixed value. • Using model occurrence number, mean, absolute percent error and standard deviation as statistics of interest for comparisons. Responsible Editor: Nam Ho Kim Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02724-y) contains supplementary material, which is available to authorized users. * Tae Hee Lee [email protected] 1
Hanyang University, Seoul, South Korea
2
Mando Corporation, Seongnam, Gyeonggi-do, South Korea
A wide classification of statistical models can be found in mathematical statistics. Statistical modelling includes data generation from the true model and obtaining approximati
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