Uncertainty in importance measures: Developing the epistemic Risk Achievement Worth

Risk or Reliability Achievement Worth (RAW) is one of the most widely employed importance measures. RAW is defined as the ratio of the reliability (or risk metric) value attained when a component is failed over the base case value of the reliability. Both the numerator and denominator are typically point estimates. In this work, we extend RAW to the case in which epistemic uncertainty is taken into consideration (epistemic RAW; ERAW). ERAW considers the effect of the component being down not only on the reliability point estimate but on its entire epistemic distribution. We discuss the properties of the new measure for series and parallel systems. In particular, for series systems, we show that aleatory uncertainty makes the value of ERAW independent of epistemic uncertainty.