Application of HMC-SS Method in Pipeline Reliability Analysis and Residual Life Assessment

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Simulation method</td><td class="align_center">Sample number</td><td class="align_center">Elapsed time (s)</td><td class="align_center">Probability of failure (<span class="nowrap"><svg height="12.7178pt" id="M171" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 14.7794 12.7178" width="14.7794pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.275,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g></svg>)</span></td><td class="align_center">Running time (<i>T</i>) (years)</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">MCS</td><td class="align_center"><span style="width: 17.5728ptpx;"><svg height="11.7978pt" id="M172" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 17.5728 11.7978" width="17.5728pt" xmlns="http://www.w3.org/2000/svg" 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<div>Comparison of results between HMC-SS, SS, and MC methods.</div>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: Application of HMC-SS Method in Pipeline Reliability Analysis and Residual Life Assessment 