A New Sine-Based Probabilistic Approach: Theory and Monte Carlo Simulation with Reliability Application

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Models</td><td class="align_center"><span style="width: 25.924ptpx;"><svg height="12.4307pt" id="M2813" style="vertical-align:-3.18149pt" version="1.1" viewbox="-0.0498162 -9.24921 25.924 12.4307" width="25.924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.227,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 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668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.228,3.132)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.336,3.132)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.232,3.132)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">NWS-Weibull</td><td class="align_center">2.835674</td><td class="align_center">0.011050</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">Weibull</td><td class="align_center">2.796292</td><td class="align_center">0.048666</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">WS-Weibull</td><td class="align_center">2.997012</td><td class="align_center">0.013830</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">E-Weibull</td><td class="align_center">1.889375</td><td class="align_center">0.217175</td><td class="align_center">2.1298119</td><td class="align_center">—</td></tr><tr><td class="align_left">FW-Extension</td><td class="align_center">—</td><td class="align_center">0.437756</td><td class="align_center">—</td><td class="align_center">3.680363</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The values of the MLEs of all the fitted models.</div>

Journal of Mathematics

tab8

Table 8

Table 8: A New Sine-Based Probabilistic Approach: Theory and Monte Carlo Simulation with Reliability Application 