Response to the discussion of "The effect of parameter uncertainty on achieved safety integrity of safety system"

This letter is in response to the discussion of our recent paper entitled " The effect of parameter uncertainty on achieved safety integrity of safety system " [1]. We are grateful to the discussants for their constructive comments and suggestions, and in particular their insight into our proposed methods to measure safety-related (SR) uncertainty. The detailed response is given below. We agree that the second index, i M1 , is always zero for any input parameter. Thus, this index is indeed incapable of assessing the parameters' importance. In all four examples in the original paper [1], was empirically observed subject to numerical errors. In this regard, we thank the discussants for providing a theoretical proof of this fact. Combining the idea of the original paper [1] and Borgonovo's moment-independent importance measure index i  [2], the discussants suggested the following index for measuring the mean effect of parameter uncertainty on SR uncertainty: (1) which, unfortunately, is not suitable for measuring the SR uncertainty as defined in [1]. Fig. 1 illustrates an example where parameter X i is considered. Assume X i takes two values, x 1 and x 2 , with probabilities p and 1-p (0≤p≤1), respectively. Eq. (1) calculates the expected