Cost Optimization of Two-Dimensional Warranty Products under Preventive Maintenance

<div>Minimum warranty cost under the same <svg height="12.235pt" id="M231" style="vertical-align:-3.27288pt" version="1.1" viewbox="-0.0498162 -8.96212 12.3038 12.235" width="12.3038pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.176,3.132)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z"></path></g></svg> and different <span class="nowrap"><svg height="11.9087pt" id="M232" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 13.7391 11.9087" width="13.7391pt" 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="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.606,3.132)"><path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Cost Optimization of Two-Dimensional Warranty Products under Preventive Maintenance 