Generalised measures of reliability for multiple outliers

The application of the theory of reliability has become a fundamental part of measurement analysis, whether in order to optimise measurement systems so that they are resistant to the influence of outliers or in the post-analysis identification of outliers. However, the current theory of reliability is based on the assumption of a single outlier—an assumption that may not necessarily be the case. This paper extends reliability theory so that it can be applied to multiple outliers through the derivation of appropriate measures of reliability for multiple outliers. The measures of reliability covered include minimal detectable biases, reliability numbers, controllability, and external reliability.