Sample Size Calculator 1

Sample Size Calculator for a Single Mean Sample size calculator for a single mean, for a given probability of error and delta Alpha Error Confidence Interval Sample Standard Deviation Beta Error Power Delta (accuracy of the estimate) D ratio (Delta/Sigma) One or two sided test (1,2)

0.05 95% 0.010 0.05 95% 0.002 0.2 2

Sample Size =

Probability of not having the population mean include Probability of the population mean being located with Baseline process standard deviation Probability of not being able to detect delta Probability of correctly detecting delta Accuracy with which the mean may be estimated (pra If D-ratio is greater than 2 the sample size will always If deviation in either direction is of interest use 2 and

328

Delta Calculator for a Single Mean and a Known Sample Size Delta is the accuracy with which the mean may be estimated for a given probability of error and sample size Alpha Error Confidence Interval Sample Standard Deviation Beta Error Power Sample Size One or two sided test (1,2) Unit of Measure

0.05 95% 0.010 0.05 95% 328 1 Mils

Probability of not having the population mean include Probability of the population mean being located with Baseline process standard deviation Probability of not being able to detect delta Probability of correctly detecting delta Specify the sample size to be evaluated If deviation in either direction is of interest use 2 and

Delta =

0.002

Mean can be accurately determined plus or minus th

Compare results to JMP 5.01 Compare results to Minitab version 13.31

Sample size equations:

www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm © TLC, 2003 Rev. 1.2 www.dr-tom.com

ng the population mean included in the confidence interval ulation mean being located within the confidence interval ndard deviation ng able to detect delta y detecting delta he mean may be estimated (practical difference of interest) an 2 the sample size will always be 5 irection is of interest use 2 and if deviation in only one direction is of interest specify 1.

and sample size

ng the population mean included in the confidence interval ulation mean being located within the confidence interval ndard deviation ng able to detect delta y detecting delta ze to be evaluated irection is of interest use 2 and if deviation in only one direction is of interest specify 1.

ely determined plus or minus the delta indicated with a known probability of detection

1.96 1.64

324.87 df n

324 325

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.65

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1.65

1.65

1.65

1.65

1.65

1.65

1.65

327.05

327.03

327.03

327.03

327.03

327.03

327.03

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327.03

327 328

327 328

327 328

327 328

327 328

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327 328

1.97

1.97

1.97

1.97

1.97

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1.97

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1.97

1.97

1.65

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1.65

1.65

1.65

1.65

1.65

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1.65

327.03

327.03

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327.03

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327 328

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1.97

1.97

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1.97

1.97

1.97

1.97

1.97

1.97

1.97

1.65

1.65

1.65

1.65

1.65

1.65

1.65

1.65

1.65

1.65

327.03

327.03

327.03

327.03

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327 328

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1.97

1.97

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1.65

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327.03

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327.03

Sample Size Calculator for a Single Sample Standard Deviation Sample size calculator for a single standard deviation, for a given probability of error and delta Alpha Error Confidence Interval Baseline Standard Deviation Beta Error Power Delta (Change in the Standard Deviation)

Sample Size =

0.05 95% 0.006 0.05 95% 0.006

46

Probability of not having the population standard Probability of the population standard deviation Baseline standard deviation for a product or pro Probability of not being able to detect delta stan Probability of correctly detecting the delta stand Accuracy with which the standard deviation may Number of units to be inspected or tested

* Warning sample sizes of >780 are not accurate due to Excel's limitation of the CHI Square Function 1.64 © TLC, 2003 Rev. 1.2 z beta www.dr-tom.com 1.64 www.itl.nist.gov/div898/handbook/prc/section2/prc232.htm Reference NIST

ng the population standard deviation included in the confidence interval ulation standard deviation located within the confidence interval viation for a product or processs ng able to detect delta standard deviation y detecting the delta standard deviation he standard deviation may be estimated (practical difference of interest) inspected or tested k 2.000

2.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

1.92 3 3.91 4.74 5.54 6.3 7.03 7.75 8.46 9.15 9.84 10.51 11.18 11.84 12.5 13.15 13.79 14.43 15.07 15.71 16.34 16.96 17.59 18.21 18.83 19.44 20.06 20.67 21.28 21.89 22.49 23.1 23.7 24.3 24.9 25.5 26.1

0.17 0.22 0.27 0.31 0.35 0.39 0.43 0.46 0.49 0.52 0.55 0.57 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.73 0.75 0.77 0.78 0.79 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.88 0.89 0.9 0.9 0.91

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

26.69 27.29 27.88 28.47 29.06 29.65 30.24 30.83 31.41 32 32.59 33.17 33.75 34.33 34.92 35.5 36.08 36.66 37.23 37.81 38.39 38.97 39.54 40.12 40.69 41.26 41.84 42.41 42.98 43.55 44.13 44.7 45.27 45.84 46.4 46.97 47.54 48.11 48.68 49.24 49.81 50.37 50.94 51.5 52.07 52.63 53.2 53.76 54.32 54.89 55.45 56.01

0.92 0.92 0.93 0.93 0.94 0.94 0.94 0.95 0.95 0.95 0.96 0.96 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 1 1 1 1 1 1 1 1 1 1 1

38 39 40 41 42 43 44 45

90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141

56.57 57.13 57.69 58.26 58.82 59.38 59.94 60.49 61.05 61.61 62.17 62.73 63.29 63.84 64.4 64.96 65.52 66.07 66.63 67.18 67.74 68.3 68.85 69.41 69.96 70.51 71.07 71.62 72.18 72.73 73.28 73.84 74.39 74.94 75.49 76.05 76.6 77.15 77.7 78.25 78.8 79.36 79.91 80.46 81.01 81.56 82.11 82.66 83.21 83.76 84.31 84.86

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193

85.4 85.95 86.5 87.05 87.6 88.15 88.69 89.24 89.79 90.34 90.89 91.43 91.98 92.53 93.07 93.62 94.17 94.71 95.26 95.8 96.35 96.9 97.44 97.99 98.53 99.08 99.62 100.17 100.71 101.26 101.8 102.35 102.89 103.43 103.98 104.52 105.06 105.61 106.15 106.7 107.24 107.78 108.32 108.87 109.41 109.95 110.5 111.04 111.58 112.12 112.66 113.21

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245

113.75 114.29 114.83 115.37 115.91 116.46 117 117.54 118.08 118.62 119.16 119.7 120.24 120.78 121.32 121.86 122.4 122.94 123.48 124.02 124.56 125.1 125.64 126.18 126.72 127.26 127.8 128.34 128.88 129.42 129.96 130.5 131.03 131.57 132.11 132.65 133.19 133.73 134.27 134.8 135.34 135.88 136.42 136.96 137.49 138.03 138.57 139.11 139.64 140.18 140.72 141.26

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297

141.79 142.33 142.87 143.4 143.94 144.48 145.01 145.55 146.09 146.62 147.16 147.7 148.23 148.77 149.31 149.84 150.38 150.91 151.45 151.98 152.52 153.06 153.59 154.13 154.66 155.2 155.73 156.27 156.8 157.34 157.87 158.41 158.94 159.48 160.01 160.55 161.08 161.62 162.15 162.69 163.22 163.76 164.29 164.82 165.36 165.89 166.43 166.96 167.49 168.03 168.56 169.1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349

169.63 170.16 170.7 171.23 171.76 172.3 172.83 173.36 173.9 174.43 174.96 175.5 176.03 176.56 177.1 177.63 178.16 178.7 179.23 179.76 180.29 180.83 181.36 181.89 182.42 182.96 183.49 184.02 184.55 185.09 185.62 186.15 186.68 187.21 187.75 188.28 188.81 189.34 189.87 190.4 190.94 191.47 192 192.53 193.06 193.59 194.13 194.66 195.19 195.72 196.25 196.78

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401

197.31 197.84 198.38 198.91 199.44 199.97 200.5 201.03 201.56 202.09 202.62 203.15 203.68 204.21 204.74 205.27 205.81 206.34 206.87 207.4 207.93 208.46 208.99 209.52 210.05 210.58 211.11 211.64 212.17 212.7 213.23 213.76 214.29 214.82 215.35 215.88 216.41 216.93 217.46 217.99 218.52 219.05 219.58 220.11 220.64 221.17 221.7 222.23 222.76 223.29 223.82 224.35

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453

224.87 225.4 225.93 226.46 226.99 227.52 228.05 228.58 229.11 229.63 230.16 230.69 231.22 231.75 232.28 232.81 233.33 233.86 234.39 234.92 235.45 235.98 236.5 237.03 237.56 238.09 238.62 239.15 239.67 240.2 240.73 241.26 241.79 242.31 242.84 243.37 243.9 244.42 244.95 245.48 246.01 246.54 247.06 247.59 248.12 248.65 249.17 249.7 250.23 250.76 251.28 251.81

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505

252.34 252.86 253.39 253.92 254.45 254.97 255.5 256.03 256.56 257.08 257.61 258.14 258.66 259.19 259.72 260.24 260.77 261.3 261.82 262.35 262.88 263.4 263.93 264.46 264.98 265.51 266.04 266.56 267.09 267.62 268.14 268.67 269.2 269.72 270.25 270.78 271.3 271.83 272.35 272.88 273.41 273.93 274.46 274.99 275.51 276.04 276.56 277.09 277.62 278.14 278.67 279.19

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557

279.72 280.24 280.77 281.3 281.82 282.35 282.87 283.4 283.93 284.45 284.98 285.5 286.03 286.55 287.08 287.6 288.13 288.66 289.18 289.71 290.23 290.76 291.28 291.81 292.33 292.86 293.38 293.91 294.43 294.96 295.48 296.01 296.53 297.06 297.58 298.11 298.63 299.16 299.68 300.21 300.73 301.26 301.78 302.31 302.83 303.36 303.88 304.41 304.93 305.46 305.98 306.51

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609

307.03 307.56 308.08 308.6 309.13 309.65 310.18 310.7 311.23 311.75 312.28 312.8 313.33 313.85 314.37 314.9 315.42 315.95 316.47 317 317.52 318.04 318.57 319.09 319.62 320.14 320.66 321.19 321.71 322.24 322.76 323.28 323.81 324.33 324.86 325.38 325.9 326.43 326.95 327.48 328 328.52 329.05 329.57 330.09 330.62 331.14 331.67 332.19 332.71 333.24 333.76

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661

334.28 334.81 335.33 335.85 336.38 336.9 337.42 337.95 338.47 338.99 339.52 340.04 340.56 341.09 341.61 342.13 342.66 343.18 343.7 344.23 344.75 345.27 345.8 346.32 346.84 347.37 347.89 348.41 348.94 349.46 349.98 350.5 351.03 351.55 352.07 352.6 353.12 353.64 354.16 354.69 355.21 355.73 356.26 356.78 357.3 357.82 358.35 358.87 359.39 359.92 360.44 360.96

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713

361.48 362.01 362.53 363.05 363.57 364.1 364.62 365.14 365.66 366.19 366.71 367.23 367.75 368.28 368.8 369.32 369.84 370.37 370.89 371.41 371.93 372.45 372.98 373.5 374.02 374.54 375.07 375.59 376.11 376.63 377.15 377.68 378.2 378.72 379.24 379.76 380.29 380.81 381.33 381.85 382.37 382.9 383.42 383.94 384.46 384.98 385.51 386.03 386.55 387.07 387.59 388.11

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765

388.64 389.16 389.68 390.2 390.72 391.25 391.77 392.29 392.81 393.33 393.85 394.38 394.9 395.42 395.94 396.46 396.98 397.5 398.03 398.55 399.07 399.59 400.11 400.63 401.15 401.68 402.2 402.72 403.24 403.76 404.28 404.8 405.33 405.85 406.37 406.89 407.41 407.93 408.45 408.97 409.5 410.02 410.54 411.06 411.58 412.1 412.62 413.14 413.66 414.19 414.71 415.23

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

766 767 768 769 770 771 772 773 774 775 776 777 778 779

415.75 416.27 416.79 417.31 417.83 418.35 418.87 419.4 419.92 420.44 420.96 421.48 422 422.52

1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Size Calculator for Proportion Defective Sample size calculator the proportion defective, for a given probability of error and delta Alpha Error Confidence Interval Baseline Proportion Defective Beta Error Power Delta (change in proportion defective) One or two sided (1,2)

Sample Size =

0.05 95% 0.20 0.10 90% 0.10 2

Probability of not having the population proportion def Probability of the population proportion defective bein Baseline population proportion defective, if unknown u Probability of not being able to detect delta Probability of correctly detecting delta Accuracy with which the proportion defective may be If deviation in either direction is of interest use 2 and i Sample size for the test

168

Sample size equations 1.96 1.64 1.28 137 One sided 168 Two sided

Two sided

One sided Reference NIST www.itl.nist.gov/div898/handbook/prc/section2/prc242.htm Compare results to Minitab version 13.31

Upper Confidence Interval for Sample Size assuming Zero Defective 5 10 15 20 30 40 50 60 70 80 90 100 125 150 175 200 300 400 500

45.05% 25.89% 18.10% 13.91% 9.50% 7.22% 5.82% 4.87% 4.19% 3.68% 3.27% 2.95% 2.37% 1.98% 1.70% 1.49% 0.99% 0.75% 0.60%

Observed Failure Rate=0 Upper 95% CI for Proportion Defective

Sample Size Upper 95% CI

50.00% 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% 0

50

100

150

Upper 95

10.00% 5.00% 0.00% 0

© TLC, 2003 Rev. 1.2 www.dr-tom.com

50

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ng the population proportion defective included in the confidence interval ulation proportion defective being located within the confidence interval roportion defective, if unknown use .5 or best estimate g able to detect delta y detecting delta he proportion defective may be estimated (practical difference of interest) irection is of interest use 2 and if deviation in only one direction is of interest specify 1.

ero Defective

ed Failure Rate=0

0

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Sample Size Calculator for Defects per Unit (DPU) Sample size calculator for estimating the defect density, for a given probability of error and delta Alpha Error Confidence Interval Baseline Defects per Unit (DPU) Beta Error Power Delta (Change in the DPU)

Sample Size =

0.05 95% 0.010 0.05 95% 0.050

129

Reference NIST © TLC, 2003 Rev. 1.2 www.dr-tom.com http://www.itl.nist.gov/div898/handbook/prc/section2/prc25.htm

Probability of not having the population DPU inclu Probability of the population DPU located within th Baseline defect per unit for a product or processs Probability of not being able to detect delta DPU Probability of correctly detecting delta DPU Accuracy with which the DPU may be estimated (p Number of units to be inspected or tested z alpha 1.64 z beta 1.64

ng the population DPU included in the confidence interval ulation DPU located within the confidence interval nit for a product or processs ng able to detect delta DPU y detecting delta DPU he DPU may be estimated (practical difference of interest) inspected or tested k 6.000