Determination of Optimal Warranty Period with Preventive Maintenance Actions for Items from Heterogeneous Populations

<div>Optimal set of parameters and the corresponding minimum ECR for different settings of <svg height="14.6529pt" id="M148" style="vertical-align:-5.36457pt" version="1.1" viewbox="-0.0498162 -9.28833 56.9088 14.6529" width="56.9088pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.671,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 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transform="matrix(.013,0,0,-0.013,33.439,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.403,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg> and <svg height="11.5303pt" id="M151" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -8.34882 45.832 11.5303" width="45.832pt" 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="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.358,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.936,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.199,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.439,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.403,0)"><path d="M244 635C114 635 38 519 38 422C38 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Mathematical Problems in Engineering

tab1

Table 1

Table 1: Determination of Optimal Warranty Period with Preventive Maintenance Actions for Items from Heterogeneous Populations 