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In many applications the function <jats:italic>g<\/jats:italic> is practically unknown, as function evaluation involves time consuming numerical simulation or some other form of experiment that is expensive to perform. The problem we address in this paper is how to optimally design experiments, in a Bayesian decision theoretic fashion, when the goal is to estimate the probability <jats:inline-formula><jats:alternatives><jats:tex-math>$$P(g(\\mathbf{X} ) \\le 0)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>P<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>g<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>X<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> using a minimal amount of resources. As opposed to existing methods that have been proposed for this purpose, we consider a general structural reliability model given in hierarchical form. We therefore introduce a general formulation of the experimental design problem, where we distinguish between the uncertainty related to the random variable <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbf{X} $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>X<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and any additional epistemic uncertainty that we want to reduce through experimentation. The effectiveness of a design strategy is evaluated through a measure of residual uncertainty, and efficient approximation of this quantity is crucial if we want to apply algorithms that search for an optimal strategy. The method we propose is based on importance sampling combined with the unscented transform for epistemic uncertainty propagation. We implement this for the myopic (one-step look ahead) alternative, and demonstrate the effectiveness through a series of numerical experiments.<\/jats:p>","DOI":"10.1007\/s11222-021-10000-2","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T12:58:49Z","timestamp":1615294729000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Sequential Bayesian optimal experimental design for structural reliability analysis"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7390-6474","authenticated-orcid":false,"given":"Christian","family":"Agrell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kristina Rognlien","family":"Dahl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,3,9]]},"reference":[{"issue":"3","key":"10000_CR1","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1007\/s11222-011-9241-4","volume":"22","author":"J Bect","year":"2012","unstructured":"Bect, J., Ginsbourger, D., Li, L., Picheny, V., Vazquez, E.: Sequential design of computer experiments for the estimation of a probability of failure. 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