Quality Controk

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Step 1

t X ACF rk X(t-1) Regress X(t) on X(t-1) for Step 2
1 547 0.6583 X(t): X(2) to X(75) B3:B76
2 524 0.3732 547 X(t-1): X(1) to X(74) D3:D76
3 516 0.2205 524
4 494 0.0726 516
5 482 -0.0396 494
6 442 -0.0121 482
7 439 0.0465 442
8 446 -0.0248 439
9 471 -0.1523 446
10 482 -0.1668 471
11 434 -0.0581 482
12 447 -0.1134 434
13 465 -0.1119 447
14 453 -0.0169 465
15 469 -0.0010 453
16 538 -0.0822 469
17 514 -0.0649 538
18 520 0.0092 514
19 509 -0.0120 520
20 511 509
21 502 511
22 478 502
23 505 478
24 541 505
25 499 541
26 501 499
27 509 501
28 474 509
29 482 474
30 520 482
31 550 520
32 555 550
33 517 555
34 529 517
35 522 529
36 535 522
37 518 535
38 499 518
39 485 499
40 451 485
41 487 451
42 515 487
43 501 515
44 503 501
45 517 503
46 501 517
47 466 501
48 493 466
49 500 493
50 512 500
51 515 512
52 518 515
53 535 518
54 514 535
55 531 514
56 515 531
57 499 515
58 487 499
59 509 487
60 514 509
61 528 514
62 518 528
63 515 518
64 509 515
65 499 509
66 508 499
67 489 508
68 485 489
69 446 485
70 457 446
71 482 457
72 509 482
73 499 509
74 514 499
75 531 514
&L&F&R&A

Step 2 (REG)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.6770278834
R Square 0.4583667549
Adjusted R Square 0.4508440709
Standard Error 20.3252206417
Observations 74
ANOVA
df SS MS F Significance F
Regression 1 25171.6005737809 25171.6005737809 60.9312789509 0
Residual 72 29744.2507775705 413.1145941329
Total 73 54915.8513513514
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 164.9509888272 42.899638903 3.845043759 0.000257715 79.4321228359 250.4698548185 79.4321228359 250.4698548185
X Variable 1 0.6693528155 0.0857501617 7.8058490218 0 0.4984129948 0.8402926363 0.4984129948 0.8402926363
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted Y Residuals Standard Residuals Percentile Y
1 531.0869789328 -7.0869789328 -0.3510920979 0.6756756757 434
2 515.6918641751 0.3081358249 0.0152651862 2.027027027 439
3 510.3370416507 -16.3370416507 -0.8093443314 3.3783783784 442
4 495.6112797087 -13.6112797087 -0.6743088688 4.7297297297 446
5 487.5790459221 -45.5790459221 -2.2580062681 6.0810810811 446
6 460.8049333001 -21.8049333001 -1.080226123 7.4324324324 447
7 458.7968748534 -12.7968748534 -0.633962889 8.7837837838 451
8 463.4823445623 7.5176554377 0.3724280041 10.1351351351 453
9 480.216164951 1.783835049 0.0883719841 11.4864864865 457
10 487.5790459221 -53.5790459221 -2.6543298369 12.8378378378 465
11 455.4501107757 -8.4501107757 -0.4186222575 14.1891891892 466
12 464.1516973778 0.8483026222 0.0420252903 15.5405405405 469
13 476.2000480577 -23.2000480577 -1.1493407305 16.8918918919 471
14 468.1678142711 0.8321857289 0.0412268523 18.2432432432 474
15 478.8774593199 59.1225406801 2.9289570402 19.5945945946 478
16 525.0628035928 -11.0628035928 -0.5480562252 20.9459459459 482
17 508.9983360196 11.0016639804 0.5450273415 22.2972972973 482
18 513.0144529129 -4.0144529129 -0.1988777882 23.6486486486 482
19 505.6515719419 5.3484280581 0.264963512 25 482
20 506.990277573 -4.990277573 -0.2472205772 26.3513513514 485
21 500.966102233 -22.966102233 -1.13775095 27.7027027027 485
22 484.9016346599 20.0983653401 0.995681985 29.0540540541 487
23 502.9741606797 38.0258393203 1.8838170435 30.4054054054 487
24 527.0708620395 -28.0708620395 -1.390643028 31.7567567568 489
25 498.9580437864 2.0419562136 0.1011594218 33.1081081081 493
26 500.2967494175 8.7032505825 0.4311629164 34.4594594595 494
27 505.6515719419 -31.6515719419 -1.568032994 35.8108108108 499
28 482.2242233977 -0.2242233977 -0.0111081271 37.1621621622 499
29 487.5790459221 32.4209540779 1.6061485282 38.5135135135 499
30 513.0144529129 36.9855470871 1.8322805022 39.8648648649 499
31 533.0950373794 21.9049626206 1.0851816202 41.2162162162 499
32 536.4418014572 -19.4418014572 -0.9631555173 42.5675675676 500
33 511.0063944663 17.9936055337 0.8914112452 43.9189189189 501
34 519.0386282529 2.9613717471 0.1467076774 45.2702702703 501
35 514.353158544 20.646841456 1.0228537364 46.6216216216 501
36 523.0547451462 -5.0547451462 -0.2504143295 47.972972973 502
37 511.6757472818 -12.6757472818 -0.6279621751 49.3243243243 503
38 498.9580437864 -13.9580437864 -0.691487716 50.6756756757 505
39 489.5871043687 -38.5871043687 -1.9116223644 52.027027027 508
40 466.82910864 20.17089136 0.9992749563 53.3783783784 509
41 490.9258099998 24.0741900002 1.1926461123 54.7297297297 509
42 509.6676888352 -8.6676888352 -0.4294011716 56.0810810811 509
43 500.2967494175 2.7032505825 0.1339202398 57.4324324324 509
44 501.6354550486 15.3645449514 0.7611664111 58.7837837838 509
45 511.0063944663 -10.0063944663 -0.4957212458 60.1351351351 511
46 500.2967494175 -34.2967494175 -1.6990762661 61.4864864865 512
47 476.8694008733 16.1305991267 0.7991170767 62.8378378378 514
48 494.9419268931 5.0580731069 0.2505791982 64.1891891892 514
49 499.6273966019 12.3726033981 0.6129442918 65.5405405405 514
50 507.6596303885 7.3403696115 0.3636451851 66.8918918919 514
51 509.6676888352 8.3323111648 0.4127864122 68.2432432432 515
52 511.6757472818 23.3242527182 1.1554938848 69.5945945946 515
53 523.0547451462 -9.0547451462 -0.4485761139 70.9459459459 515
54 508.9983360196 22.0016639804 1.0899722487 72.2972972973 515
55 520.377333884 -5.377333884 -0.2663955195 73.6486486486 516
56 509.6676888352 -10.6676888352 -0.5284820638 75 517
57 498.9580437864 -11.9580437864 -0.5924068237 76.3513513514 517
58 490.9258099998 18.0741900002 0.8954034356 77.7027027027 518
59 505.6515719419 8.3484280581 0.4135848503 79.0540540541 518
60 508.9983360196 19.0016639804 0.9413509104 80.4054054054 518
61 518.3692754373 -0.3692754373 -0.0182940699 81.7567567568 520
62 511.6757472818 3.3242527182 0.1646849626 83.1081081081 520
63 509.6676888352 -0.6676888352 -0.0330776028 84.4594594595 522
64 505.6515719419 -6.6515719419 -0.3295218413 85.8108108108 524
65 498.9580437864 9.0419562136 0.4479425445 87.1621621622 528
66 504.9822191263 -15.9822191263 -0.7917662653 88.5135135135 529
67 492.2645156309 -7.2645156309 -0.3598873451 89.8648648649 531
68 489.5871043687 -43.5871043687 -2.1593245949 91.2162162162 531
69 463.4823445623 -6.4823445623 -0.3211382414 92.5675675676 535
70 470.8452255333 11.1547744667 0.5526125033 93.9189189189 535
71 487.5790459221 21.4209540779 1.061203621 95.2702702703 538
72 505.6515719419 -6.6515719419 -0.3295218413 96.6216216216 541
73 498.9580437864 15.0419562136 0.7451852211 97.972972973 550
74 508.9983360196 22.0016639804 1.0899722487 99.3243243243 555
&L&F&R&A

Step 2 (REG)

547
524
516
494
482
442
439
446
471
482
434
447
465
453
469
538
514
520
509
511
502
478
505
541
499
501
509
474
482
520
550
555
517
529
522
535
518
499
485
451
487
515
501
503
517
501
466
493
500
512
515
518
535
514
531
515
499
487
509
514
528
518
515
509
499
508
489
485
446
457
482
509
499
514
X Variable 1
Residuals
X Variable 1 Residual Plot

Step 3

Point #15 is #16 in original data
&L&F&R&A

Step 4

t X X(t-1) X(16) is deleted
1 547 Regress X(t) on X(t-1) for Step 5
2 524 547 X(t): X(2) to X(74) B3:B75
3 516 524 X(t-1): X(1) to X(73) C3:C75
4 494 516
5 482 494
6 442 482
7 439 442
8 446 439
9 471 446
10 482 471
11 434 482
12 447 434
13 465 447
14 453 465
15 469 453
16 514 469
17 520 514
18 509 520
19 511 509
20 502 511
21 478 502
22 505 478
23 541 505
24 499 541
25 501 499
26 509 501
27 474 509
28 482 474
29 520 482
30 550 520
31 555 550
32 517 555
33 529 517
34 522 529
35 535 522
36 518 535
37 499 518
38 485 499
39 451 485
40 487 451
41 515 487
42 501 515
43 503 501
44 517 503
45 501 517
46 466 501
47 493 466
48 500 493
49 512 500
50 515 512
51 518 515
52 535 518
53 514 535
54 531 514
55 515 531
56 499 515
57 487 499
58 509 487
59 514 509
60 528 514
61 518 528
62 515 518
63 509 515
64 499 509
65 508 499
66 489 508
67 485 489
68 446 485
69 457 446
70 482 457
71 509 482
72 499 509
73 514 499
74 531 514
&L&F&R&A

Step 5 (REG after del #16)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.698658218
R Square 0.4881233056
Adjusted R Square 0.4809137747
Standard Error 19.6208584608
Observations 73
ANOVA
df SS MS F Significance F
Regression 1 26065.0489923558 26065.0489923558 67.7052795739 0
Residual 71 27333.4441583291 384.978086737
Total 72 53398.4931506849
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 154.2662284501 41.9322935683 3.6789360973 0.0004523602 70.655610913 237.8768459872 70.655610913 237.8768459872
X Variable 1 0.6904100069 0.0839065394 8.2283217957 0 0.5231051214 0.8577148925 0.5231051214 0.8577148925
RESIDUAL OUTPUT PROBABILITY OUTPUT
Observation Predicted Y Residuals Standard Residuals Percentile Y
1 531.9205022514 -7.9205022514 -0.4065105215 0.6849315068 434
2 516.0410720915 -0.0410720915 -0.0021079771 2.0547945205 439
3 510.5177920359 -16.5177920359 -0.8477563722 3.4246575342 442
4 495.3287718831 -13.3287718831 -0.6840836398 4.7945205479 446
5 487.0438517997 -45.0438517997 -2.3118230517 6.1643835616 446
6 459.4274515217 -20.4274515217 -1.0484150762 7.5342465753 447
7 457.3562215009 -11.3562215009 -0.5828447967 8.904109589 451
8 462.1890915495 8.8109084505 0.4522095791 10.2739726027 453
9 479.4493417232 2.5506582768 0.1309095551 11.6438356164 457
10 487.0438517997 -53.0438517997 -2.7224137022 13.0136986301 465
11 453.9041714661 -6.9041714661 -0.3543485317 14.3835616438 466
12 462.8795015564 2.1204984436 0.1088321044 15.7534246575 469
13 475.3068816815 -22.3068816815 -1.1448746327 17.1232876712 471
14 467.0219615981 1.9780384019 0.1015205093 18.4931506849 474
15 478.0685217093 35.9314782907 1.8441411308 19.8630136986 478
16 509.136972022 10.863027978 0.5575322155 21.2328767123 482
17 513.2794320637 -4.2794320637 -0.2196368494 22.602739726 482
18 505.6849219873 5.3150780127 0.2727901674 23.9726027397 482
19 507.0657420012 -5.0657420012 -0.259993288 25.3424657534 482
20 500.8520519387 -22.8520519387 -1.172854859 26.7123287671 485
21 484.2822117719 20.7177882281 1.0633162683 28.0821917808 485
22 502.9232819595 38.0767180405 1.9542430539 29.4520547945 487
23 527.7780422097 -28.7780422097 -1.476999384 30.8219178082 487
24 498.7808219178 2.2191780822 0.1138967216 32.1917808219 489
25 500.1616419317 8.8383580683 0.4536183986 33.5616438356 493
26 505.6849219873 -31.6849219873 -1.6261915914 34.9315068493 494
27 481.5205717441 0.4794282559 0.0246060949 36.301369863 499
28 487.0438517997 32.9561482003 1.6914357911 37.6712328767 499
29 513.2794320637 36.7205679363 1.8846402347 39.0410958904 499
30 533.9917322722 21.0082677278 1.0782247891 40.4109589041 499
31 537.443782307 -20.443782307 -1.0492532346 41.7808219178 499
32 511.2082020429 17.7917979571 0.9131432372 43.1506849315 500
33 519.4931221263 2.5068778737 0.1286625771 44.5205479452 501
34 514.6602520776 20.3397479224 1.0439137914 45.8904109589 501
35 523.635582168 -5.635582168 -0.2892396686 47.2602739726 501
36 511.8986120498 -12.8986120498 -0.6620061891 48.6301369863 502
37 498.7808219178 -13.7808219178 -0.7072845795 50 503
38 489.1150818205 -38.1150818205 -1.95621203 51.3698630137 505
39 465.6411415842 21.3588584158 1.0962184465 52.7397260274 508
40 490.4959018344 24.5040981656 1.2576442009 54.1095890411 509
41 509.827382029 -8.827382029 -0.4530550662 55.4794520548 509
42 500.1616419317 2.8383580683 0.1456754107 56.8493150685 509
43 501.5424619456 15.4575380544 0.7933400757 58.2191780822 509
44 511.2082020429 -10.2082020429 -0.5239240397 59.5890410959 509
45 500.1616419317 -34.1616419317 -1.7533063481 60.9589041096 511
46 475.9972916885 17.0027083115 0.8726441333 62.3287671233 512
47 494.6383618761 5.3616381239 0.2751798107 63.698630137 514
48 499.4712319248 12.5287680752 0.6430243793 65.0684931507 514
49 507.7561520081 7.2438479919 0.3717820324 66.4383561644 514
50 509.827382029 8.172617971 0.4194500662 67.8082191781 514
51 511.8986120498 23.1013879502 1.1856517384 69.1780821918 515
52 523.635582168 -9.635582168 -0.4945349938 70.5479452055 515
53 509.136972022 21.863027978 1.12209436 71.9178082192 515
54 520.8739421402 -5.8739421402 -0.3014732156 73.2876712329 515
55 509.827382029 -10.827382029 -0.5557027289 74.6575342466 516
56 498.7808219178 -11.7808219178 -0.6046369169 76.0273972603 517
57 490.4959018344 18.5040981656 0.9497012129 77.397260274 517
58 505.6849219873 8.3150780127 0.4267616613 78.7671232877 518
59 509.136972022 18.863027978 0.9681228661 80.1369863014 518
60 518.8027121193 -0.8027121193 -0.0411982614 81.5068493151 518
61 511.8986120498 3.1013879502 0.159175112 82.8767123288 520
62 509.827382029 -0.827382029 -0.0424644157 84.2465753425 520
63 505.6849219873 -6.6849219873 -0.3430958085 85.6164383562 522
64 498.7808219178 9.2191780822 0.4731635408 86.9863013699 524
65 504.9945119804 -15.9945119804 -0.8208996349 88.3561643836 528
66 491.8767218483 -6.8767218483 -0.3529397122 89.7260273973 529
67 489.1150818205 -43.1150818205 -2.2128311866 91.095890411 531
68 462.1890915495 -5.1890915495 -0.2663240594 92.4657534247 531
69 469.7836016259 12.2163983741 0.6269923695 93.8356164384 535
70 487.0438517997 21.9561482003 1.1268736466 95.2054794521 535
71 505.6849219873 -6.6849219873 -0.3430958085 96.5753424658 541
72 498.7808219178 15.2191780822 0.7811065287 97.9452054795 550
73 509.136972022 21.863027978 1.12209436 99.3150684932 555
&L&F&R&A

Step 5 (REG after del #16)

547
524
516
494
482
442
439
446
471
482
434
447
465
453
469
514
520
509
511
502
478
505
541
499
501
509
474
482
520
550
555
517
529
522
535
518
499
485
451
487
515
501
503
517
501
466
493
500
512
515
518
535
514
531
515
499
487
509
514
528
518
515
509
499
508
489
485
446
457
482
509
499
514
X Variable 1
Residuals
X Variable 1 Residual Plot

Step 6 (I-MR after del #16)

The process is in control.
From Step 5,
a ^ = 154.2662284501
φ ^ = 0.6904100069
What are the estimated model and parameters?
&L&F&R&A

Step 6 (I-MR after del #16)

547
X Variable 1
Residuals
X Variable 1 Residual Plot
1
547 547
524 524
516 516
494 494
482 482
442 442
439 439
446 446
471 471
482 482
434 434
447 447
465 465
453 453
469 469
514 514
520 520
509 509
511 511
502 502
478 478
505 505
541 541
499 499
501 501
509 509
474 474
482 482
520 520
550 550
555 555
517 517
529 529
522 522
535 535
518 518
499 499
485 485
451 451
487 487
515 515
501 501
503 503
517 517
501 501
466 466
493 493
500 500
512 512
515 515
518 518
535 535
514 514
531 531
515 515
499 499
487 487
509 509
514 514
528 528
518 518
515 515
509 509
499 499
508 508
489 489
485 485
446 446
457 457
482 482
509 509
499 499
Y
Predicted Y
X Variable 1
Y
X Variable 1 Line Fit Plot
524
1
516
494
482
442
439
446
471
482
434
447
465
453
469
514
520
509
511
502
478
505
541
499
501
509
474
482
520
550
555
517
529
522
535
518
499
485
451
487
515
501
503
517
501
466
493
500
512
515
518
535
514
531
515
499
487
509
514
528
518
515
509
499
508
489
485
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457
482
509
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514
1
Sample Percentile
Y
Normal Probability Plot
1

Observation

I

n

d

i

v

i

d

u

a

l

V

a

l

u

e

71645750433629221581

50

25

0

-25

-50

_

X=0.0

UCL=55.6

LCL=-55.6

Observation

M

o

v

i

n

g

R

a

n

g

e

71645750433629221581

60

45

30

15

0

__

MR=20.89

UCL=68.25

LCL=0

I-MR charts for Residuals after deleting #16

Res_1

P

e

r

c

e

n

t

50250-25-50-75

99.9

99

95

90

80

70

60

50

40

30

20

10

5

1

0.1

Mean

>0.100

-2.70269E-11

StDev20.19

N74

RJ0.991

P-Value

Probability Plot of Res_1

Normal

Observation

I

n

d

i

v

i

d

u

a

l

V

a

l

u

e

71645750433629221581

550

525

500

475

450

_

X=499.9

UCL=547.7

LCL=452.1

Observation

M

o

v

i

n

g

R

a

n

g

e

71645750433629221581

60

45

30

15

0

__

MR=17.97

UCL=58.72

LCL=0

1

1

1

1

1

1

1

1

1

1

I-MR charts for X

Observation

I

n

d

i

v

i

d

u

a

l

V

a

l

u

e

71645750433629221581

50

25

0

-25

-50

_

X=-0.0

UCL=57.7

LCL=-57.7

Observation

M

o

v

i

n

g

R

a

n

g

e

71645750433629221581

80

60

40

20

0

__

MR=21.71

UCL=70.92

LCL=0

1

I-MR charts for residuals

Res_2

P

e

r

c

e

n

t

7550250-25-50

99.9

99

95

90

80

70

60

50

40

30

20

10

5

1

0.1

Mean

>0.100

2.602740E-10

StDev19.48

N73

RJ0.991

P-Value

Probability Plot of Res_2

Normal

MBD0001DE10.unknown

MBD0004A2AA.unknown

MBD0004AD82.unknown

MBD000290E1.unknown

MBD0002192F.unknown