Parameter Estimation of the Weibull Distribution in Modeling the Reliability of Technical Objects

Abstract

The article discusses one of the most widely used distribution laws for reliability analysis – Weibull distribution. It describes a wide range of processes for all stages of the life cycle of technical objects, including yield stress of steel distribution and failures in the reliability theory regarding the wide range of technical objects (e.g., metal cutting tools, bearings, compressors, and wheels). A significant number of works are devoted to evaluating distribution law parameters based on empirical data in search of the most precise one, ignoring the probabilistic character of the parameters themselves. Parameters may have a relatively wide confidence range, which can be considered the parameter estimation error compared to biases of parameters estimated by different methods. Moreover, many approaches should be used for certain selection volumes, including comprehensive calculating procedures. Instead, this paper suggested and statistically confirmed a universal simplified approach. It demands a minimal set of data and connects the shape and scale parameters of the Weibull distribution with the variation coefficient as one of the leading statistical characteristics. This approach does not demand variational sequence arrangement. Nevertheless, it is supposed to be quite efficient for the engineering practice of reliability analysis. The adequacy of the results was confirmed using generated selections analysis and experimental data on cutting tool reliability. Within the achieved results, it was also demonstrated that the variation coefficient reflects not only selection stability and variable volatility degree, which are its main aim, but the cause of failure as well.

Keywords

• cutting tool life
• least squared estimation
• maximum likelihood estimation
• confidence interval
• variation coefficient
• bias
• empirical data