Bootstrap Guided Information Criterion for Reliability Analysis Using Small Sample Size Information

Abstract

Several methods for reliability analysis have been established and applied to engineering fields bearing in mind uncertainties as a major contributing factor. Small sample size based reliability analysis can be very beneficial when rising uncertainty from statistics of interest such as mean and standard deviation are considered. Model selection and evaluation methods like Akaike Information Criteria (AIC) have demonstrated efficient output for reliability analysis. However, information criterion based on maximum likelihood can provide better model selection and evaluation in small sample size scenario by considering the well-known measure of bootstrapping for curtailing uncertainty with resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion based reliability analysis to check for uncertainty arising from statistics of interest for small sample size problems. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection frequency devised from information criterion to be combined with reliability analysis. It is also beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest under replication based approach. The proposed simulation scheme is verified using a number of small and moderate sample size focused mathematical example with AIC based reliability analysis for comparison and Monte Carlo simulation (MCS) for accuracy. The results show that the proposed simulation scheme favors the statistics of interest by reducing the spread and hence the uncertainty in small sample size based reliability analysis when compared with conventional methods whereas moderate sample size based reliability analysis did not show any considerable favor.