{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:40:37Z","timestamp":1682502037895},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We consider an <jats:italic>r<\/jats:italic> component system having an arbitrary binary monotone structure function. We suppose that shocks occur according to a point process and that, independent of what has already occurred, each new shock is one of <jats:italic>r<\/jats:italic> different types, with respective probabilities <jats:italic>p<\/jats:italic>\n               <jats:sub>1<\/jats:sub>, \u2026, p<jats:sub>\n                  <jats:italic>r<\/jats:italic>\n               <\/jats:sub>. We further suppose that there are given integers <jats:italic>n<\/jats:italic>\n               <jats:sub>1<\/jats:sub>, \u2026, n<jats:sub>\n                  <jats:italic>r<\/jats:italic>\n               <\/jats:sub> such that component <jats:italic>i<\/jats:italic> fails (and remains failed) when there have been a total of <jats:italic>n<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>i<\/jats:italic>\n               <\/jats:sub> type-<jats:italic>i<\/jats:italic> shocks. Letting <jats:italic>L<\/jats:italic> be the time at which the system fails, we are interested in using simulation to estimate <jats:bold>E<\/jats:bold>[<jats:italic>L<\/jats:italic>], <jats:bold>E<\/jats:bold>[<jats:italic>L<\/jats:italic>\n               <jats:sup>2<\/jats:sup>], and <jats:bold>P<\/jats:bold>(<jats:italic>L<\/jats:italic> &amp;gt; <jats:italic>t<\/jats:italic>). We show how to efficiently accomplish this when the point process is (i) a Poisson, (ii) a renewal, and (iii) a Hawkes process.<\/jats:p>","DOI":"10.1017\/s002190020001130x","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:11Z","timestamp":1459263071000},"page":"377-386","source":"Crossref","is-referenced-by-count":0,"title":["Simulation Analysis of System Life when Component Lives are Determined by a Marked Point Process"],"prefix":"10.1017","volume":"51","author":[{"given":"Sheldon M.","family":"Ross","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S002190020001130X_ref9","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1354716666"},{"key":"S002190020001130X_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(92)90063-X"},{"key":"S002190020001130X_ref7","volume-title":"Simulation","year":"2013"},{"key":"S002190020001130X_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/1403255"},{"key":"S002190020001130X_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760568"},{"key":"S002190020001130X_ref4","volume":"1","year":"2003","journal-title":"An Introduction to the Theory of Point Processes"},{"key":"S002190020001130X_ref3","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1151337084"},{"key":"S002190020001130X_ref2","volume-title":"Probability Approximations via the Poisson Clumping Heuristic","year":"1989"},{"key":"S002190020001130X_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996891"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190020001130X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:05:26Z","timestamp":1682499926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190020001130X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":9,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S002190020001130X"],"URL":"https:\/\/doi.org\/10.1017\/s002190020001130x","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}