Determination of the best distribution and effective interval using statistical characterization of uncertain variables

Abstract

Abstract In this paper, an algorithm for estimating the best distribution about data containing uncertainties is proposed. The proposed algorithm combines sequence statistical modeling (SSM) and a method for determining the minimum experimental data. SSM is a method for selecting the best distribution about data using a goodness of fit (GoF) test and a comparison of the likelihood. The method used to determine the minimum experimental data determines the minimum data needed to an estimate the best distribution. The SSM presented herein is a method for selecting a suitable data distribution when considering only a parametric distribution. Thus, in this paper, the SSM was improved in order to select the correct distribution of both parametric and non-parametric distributions simultaneously. In addition, with the existing method for determining the minimum data, the data should be added based on actual experiments when the results data show an insufficient number, and there is a limitation in that the designers cannot broadly identify the data required. To overcome this limitation, SSM and random sampling are applied to the method to determine the minimum data, and thereby, ensure that the designer knows the approximate minimum data needed. To verify the validity of the proposed algorithm, it was applied to a real world case study on determining multiple statistical parameters in the bolt fastening problem. The sequence of verification methods used is as follows: First, the best distribution of the bearing surface and thread friction coefficient estimated by the proposed algorithm and based on a normal distribution are selected as comparison targets. Second, the bearing surface and thread friction coefficient data are sampled within the 95% confidence interval of the two distributions. Third, the reliability of the sampled friction coefficient data are compared using a Monte-Carlo simulation and an equation to calculate the bolt fastening force. In this study, the effectiveness of the proposed algorithm is validated. Highlights The algorithm to determine appropriate probability distribution of data is proposed. The sequential statistical modeling is improved to consider both parametric and non-parametric distribution. The method to determine minimum data is improved to verify sufficiency of data without actual experiments. The effectiveness and validation of the proposed algorithm is verified using the bolt-fastening data.