Quality control using inferential statistics in Weibull-based reliability analyses

Design codes and fitness-for-service protocols have recognized the need to characterize the tensile strength of graphite as a random variable through the use of probability density functions. Characterizing probability density functions require more tests than typically needed to simply define an average value for tensile strength. ASTM and the needs of nuclear design codes should dovetail on this issue. The two-parameter Weibull distribution (an extreme-value distribution) is adopted for the tensile strength of this material. The failure data from bend tests or tensile tests are used to determine the Weibull modulus (m) and Weibull characteristic strength (o-e). To determine an estimate of the true Weibull distribution parameters, maximum likelihood estimators are used. The quality of the estimated parameters relative to the true distribution parameters depends fundamentally on the number of samples taken to failure. The statistical concepts of confidence intervals and hypothesis testing are presented pertaining to their use in assessing the goodness of the estimated distribution parameters. The inferential statistics tools enable the calculation of likelihood confidence rings. The concept of how the true distribution parameters lie within a likelihood ring with a specified confidence is presented. A material acceptance criterion is defined here, and the criterion depends on establishing an acceptable probability of failure of the component under design, as well as an acceptable level of confidence associated with the estimated distribution parameter determined using failure data from a specific type of strength test.