Improved Methods for Distribution Identification and Regression Parameter Estimation in a Satellite Reliability Application

Abstract

This article expands the methods for analyzing satellite reliability by presenting a framework of measures to determine the best statistical distribution to use in data parameterization, and applying robust regression to improve the fit of the Weibull distribution in the regression parameterization method when data outliers are present. The distribution identification framework is defined by four statistical goodness-of-fit measures, while the robust regression methodology is developed through comparing how least-squares and iteratively reweighted least squares robust linear regression can parameterize satellite reliability data. Both of these methodologies are then applied to deep space satellite reliability data to evaluate their performance. All four measures comprising the distributional assessment framework show agreement by selecting the Weibull distribution. These results serve as a proof of concept for the framework and warrant its inclusion in future satellite reliability studies. Robust regression's use in the regression parameterization method in the presence of outliers yielded positive results. Specifically, improvement is indicated through visual inspection of the resulting Weibull distribution, and by closer agreement of the robust regression Weibull parameters to the MLE parameters than the least-squares regression parameters. Ultimately, the improved fit produced by the use of robust regression in the regression parameterization method justifies its increased computational complexity as compared to traditional least-squares regression. Incorporation of these methods and framework provides quantitative enhancements to distribution fitting and parameter estimation in satellite reliability studies.