1. Atributos

A measurement system by attribute classifies the piece as defective or not. One of the main objectives of measurement system analysis (MSA) by attribute is to understand and prevent classification errors.

Example:

Consider a measurement system, in which 50 pieces were selected, 3 evaluators with three measurements per piece (each evaluator), The data is presented in the Table below and in Table A 1 of Appendix A (Example given in the MSA Manual 4th Edition, page, 127). Here we consider 0 Non-Comforming and 1 Comforming, we also consider LSL=0 and USL=1.02.

Piece Operator 1 Operator 2 Operator 3 Standar Reference Value
1 1 1 1 1 0.476901
1 1 1 1 1 0.476901
1 1 1 1 1 0.476901
2 1 1 1 1 0.509015
2 1 1 1 1 0.509015
2 1 1 1 1 0.509015
3 0 0 0 0 0.576459
3 0 0 0 0 0.576459
3 0 0 0 0 0.576459
4 0 0 0 0 0.566152
4 0 0 0 0 0.566152
4 0 0 0 0 0.566152
5 0 0 0 0 0.57036
5 0 0 0 0 0.57036
5 0 0 0 0 0.57036
6 1 1 1 1 0.544951
6 1 1 0 1 0.544951
6 0 0 0 1 0.544951
7 1 1 1 1 0.465454
7 1 1 0 1 0.465454
7 1 1 1 1 0.465454
8 1 1 1 1 0.502295
8 1 1 1 1 0.502295
8 1 1 1 1 0.502295
9 0 0 0 0 0.437817
9 0 0 0 0 0.437817
9 0 0 0 0 0.437817
10 1 1 1 1 0.515573
10 1 1 1 1 0.515573
10 1 1 1 1 0.515573
11 1 1 1 1 0.488905
11 1 1 1 1 0.488905
11 1 1 1 1 0.488905
12 0 0 0 0 0.559918
12 0 0 1 0 0.559918
12 0 0 0 0 0.559918
13 1 1 1 1 0.542704
13 1 1 1 1 0.542704
13 1 1 1 1 0.542704
14 1 1 1 1 0.454518
14 1 1 0 1 0.454518
14 0 1 0 1 0.454518
15 1 1 1 1 0.517377
15 1 1 1 1 0.517377
15 1 1 1 1 0.517377
16 1 1 1 1 0.531939
16 1 1 1 1 0.531939
16 1 1 1 1 0.531939
17 1 1 1 1 0.519694
17 1 1 1 1 0.519694
17 1 1 1 1 0.519694
18 1 1 1 1 0.484167
18 1 1 1 1 0.484167
18 1 1 1 1 0.484167
19 1 1 1 1 0.520496
19 1 1 1 1 0.520496
19 1 1 1 1 0.520496
20 1 1 1 1 0.477236
20 1 1 1 1 0.477236
20 1 1 1 1 0.477236
21 1 1 0 1 0.45231
21 1 0 1 1 0.45231
21 0 1 0 1 0.45231
22 0 0 1 0 0.545604
22 0 1 1 0 0.545604
22 1 0 0 0 0.545604
23 1 1 1 1 0.529065
23 1 1 1 1 0.529065
23 1 1 1 1 0.529065
24 1 1 1 1 0.514192
24 1 1 1 1 0.514192
24 1 1 1 1 0.514192
25 0 0 0 0 0.599581
25 0 0 0 0 0.599581
25 0 0 0 0 0.599581
26 0 0 0 0 0.547204
26 1 0 0 0 0.547204
26 0 0 1 0 0.547204
27 1 1 1 1 0.502436
27 1 1 1 1 0.502436
27 1 1 1 1 0.502436
28 1 1 1 1 0.521642
28 1 1 1 1 0.521642
28 1 1 1 1 0.521642
29 1 1 1 1 0.523754
29 1 1 1 1 0.523754
29 1 1 1 1 0.523754
30 0 0 0 0 0.561457
30 0 0 0 0 0.561457
30 0 1 0 0 0.561457
31 1 1 1 1 0.503091
31 1 1 1 1 0.503091
31 1 1 1 1 0.503091
32 1 1 1 1 0.50585
32 1 1 1 1 0.50585
32 1 1 1 1 0.50585
33 1 1 1 1 0.487613
33 1 1 1 1 0.487613
33 1 1 1 1 0.487613
34 0 0 0 0 0.449696
34 0 0 1 0 0.449696
34 1 1 1 0 0.449696
35 1 1 1 1 0.498698
35 1 1 1 1 0.498698
35 1 1 1 1 0.498698
36 1 1 1 1 0.543077
36 1 1 0 1 0.543077
36 0 1 1 1 0.543077
37 0 0 0 0 0.409238
37 0 0 0 0 0.409238
37 0 0 0 0 0.409238
38 1 1 1 1 0.488184
38 1 1 1 1 0.488184
38 1 1 1 1 0.488184
39 0 0 0 0 0.427687
39 0 0 0 0 0.427687
39 0 0 0 0 0.427687
40 1 1 1 1 0.501132
40 1 1 1 1 0.501132
40 1 1 1 1 0.501132
41 1 1 1 1 0.513779
41 1 1 1 1 0.513779
41 1 1 1 1 0.513779
42 0 0 0 0 0.566575
42 0 0 0 0 0.566575
42 0 0 0 0 0.566575
43 1 1 1 1 0.46241
43 0 1 1 1 0.46241
43 1 1 0 1 0.46241
44 1 1 1 1 0.470832
44 1 1 1 1 0.470832
44 1 1 1 1 0.470832
45 0 0 0 0 0.412453
45 0 0 0 0 0.412453
45 0 0 0 0 0.412453
46 1 1 1 1 0.493441
46 1 1 1 1 0.493441
46 1 1 1 1 0.493441
47 1 1 1 1 0.486379
47 1 1 1 1 0.486379
47 1 1 1 1 0.486379
48 0 0 0 0 0.587893
48 0 0 0 0 0.587893
48 0 0 0 0 0.587893
49 1 1 1 1 0.483803
49 1 1 1 1 0.483803
49 1 1 1 1 0.483803
50 0 0 0 0 0.446697
50 0 0 0 0 0.446697
50 0 0 0 0 0.446697

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

Then click Calculate to get the results. You can also generate the analyses and download them in Word format.

Analysis result
APPRAISERS vs APPRAISERS

Analysis result
Operator 1 (row) vs Operator 2 (column)

Frequency Table

1 0 Total
1 97 3 100
0 6 44 50
Total 103 47 150

Observed Proportions

1 0 Total
1 0.647 0.020 0.667
0 0.040 0.293 0.333
Total 0.687 0.313 1.000

Expected Proportions

1 0 Total
1 0.458 0.209 0.667
0 0.229 0.104 0.333
Total 0.687 0.313 1.000

Analysis result
Kappa: 0.86

Analysis result
Operator 1 (row) vs Operator 3 (column)

Frequency Table

1 0 Total
1 92 8 100
0 7 43 50
Total 99 51 150

Observed proportions

1 0 Total
1 0.613 0.053 0.667
0 0.047 0.287 0.333
Total 0.660 0.340 1.000

Expected Proportions

1 0 Total
1 0.44 0.227 0.667
0 0.22 0.113 0.333
Total 0.66 0.340 1.000

Analysis result
Kappa: 0.78

Analysis result
Operator 2 (row) vs Operator 3 (column)

Frequency Table

1 0 Total
1 94 9 103
0 5 42 47
Total 99 51 150

Observed Proportions

1 0 Total
1 0.627 0.06 0.687
0 0.033 0.28 0.313
Total 0.660 0.34 1.000

Expected Proportions

1 0 Total
1 0.453 0.233 0.687
0 0.207 0.107 0.313
Total 0.660 0.340 1.000

Analysis result
Kappa: 0.79

Analysis result
AGREEMENTS

Agreement Table

Agreement(abs) Agreement(%) Lower confidence interval Upper confidence interval
Operator 1 42 84 70.89 92.83
Operator 2 45 90 78.19 96.67
Operator 3 40 80 66.28 89.97
Todos 39 78 64.04 88.47

Analysis result
APPRAISERS vs STANDARD

Analysis result
Operator 1 (row) vs Standard (column)

Frequency Table

1 0 Total
1 97 3 100
0 5 45 50
Total 102 48 150

Observed Proportions

1 0 Total
1 0.647 0.02 0.667
0 0.033 0.30 0.333
Total 0.680 0.32 1.000

Expected proportions

1 0 Total
1 0.453 0.213 0.667
0 0.227 0.107 0.333
Total 0.680 0.320 1.000

Analysis result
Kappa: 0.88

Analysis result
Operator 2 (row) vs Standard (column)

Frequency Table

1 0 Total
1 100 3 103
0 2 45 47
Total 102 48 150

Observed Proportions

1 0 Total
1 0.667 0.02 0.687
0 0.013 0.30 0.313
Total 0.680 0.32 1.000

Expected Proportions

1 0 Total
1 0.467 0.22 0.687
0 0.213 0.10 0.313
Total 0.680 0.32 1.000

Analysis result
Kappa: 0.92

Analysis result
Operator 3 (row) vs Standard (column)

Frequency Table

1 0 Total
1 93 6 99
0 9 42 51
Total 102 48 150

Observed Proportions

1 0 Total
1 0.62 0.04 0.66
0 0.06 0.28 0.34
Total 0.68 0.32 1.00

Expected Proportions

1 0 Total
1 0.449 0.211 0.66
0 0.231 0.109 0.34
Total 0.680 0.320 1.00

Analysis result
Kappa: 0.77

Analysis result
AGREEMENTS

Agreement Table

Agreement(abs) Agreement(%) Lower confidence interval Upper confidence interval Error Rate False alarm rate
Operator 1 vs Standard 42 84 70.89 92.83 6.25 4.902
Operator 2 vs Standard 45 90 78.19 96.67 6.25 1.961
Operator 3 vs Standard 40 80 66.28 89.97 12.5 8.824
All 39 78 64.04 88.47

Analysis result
GRAY BAND

Gray band chart

Gray Band Pieces Operator 1 A Operator1 B Operator1 C Operator 2 A Operator 2 B Operator 2 C Operator 3 A Operator 3 B Operator 3 C Standard Signal Standard Value
No 25 0 0 0 0 0 0 0 0 0 0 - 0.6
No 48 0 0 0 0 0 0 0 0 0 0 - 0.588
No 3 0 0 0 0 0 0 0 0 0 0 - 0.576
No 5 0 0 0 0 0 0 0 0 0 0 - 0.57
No 42 0 0 0 0 0 0 0 0 0 0 - 0.567
Yes 4 0 0 0 0 0 0 0 0 0 0 - 0.566
Yes 30 0 0 0 0 0 0 0 1 0 0 X 0.562
Yes 12 0 0 0 0 0 1 0 0 0 0 X 0.56
Yes 26 0 0 0 1 0 0 0 0 1 0 X 0.547
Yes 22 0 0 1 0 1 1 1 0 0 0 X 0.546
Yes 6 1 1 1 1 1 0 0 0 0 1 X 0.545
Yes 36 1 1 1 1 1 0 0 1 1 1 X 0.543
Yes 13 1 1 1 1 1 1 1 1 1 1 + 0.543
No 16 1 1 1 1 1 1 1 1 1 1 + 0.532
No 23 1 1 1 1 1 1 1 1 1 1 + 0.529
No 29 1 1 1 1 1 1 1 1 1 1 + 0.524
No 28 1 1 1 1 1 1 1 1 1 1 + 0.522
No 19 1 1 1 1 1 1 1 1 1 1 + 0.52
No 17 1 1 1 1 1 1 1 1 1 1 + 0.52
No 15 1 1 1 1 1 1 1 1 1 1 + 0.517
No 10 1 1 1 1 1 1 1 1 1 1 + 0.516
No 24 1 1 1 1 1 1 1 1 1 1 + 0.514
No 41 1 1 1 1 1 1 1 1 1 1 + 0.514
No 2 1 1 1 1 1 1 1 1 1 1 + 0.509
No 32 1 1 1 1 1 1 1 1 1 1 + 0.506
No 31 1 1 1 1 1 1 1 1 1 1 + 0.503
No 27 1 1 1 1 1 1 1 1 1 1 + 0.502
No 8 1 1 1 1 1 1 1 1 1 1 + 0.502
No 40 1 1 1 1 1 1 1 1 1 1 + 0.501
No 35 1 1 1 1 1 1 1 1 1 1 + 0.499
No 46 1 1 1 1 1 1 1 1 1 1 + 0.493
No 11 1 1 1 1 1 1 1 1 1 1 + 0.489
No 38 1 1 1 1 1 1 1 1 1 1 + 0.488
No 33 1 1 1 1 1 1 1 1 1 1 + 0.488
No 47 1 1 1 1 1 1 1 1 1 1 + 0.486
No 18 1 1 1 1 1 1 1 1 1 1 + 0.484
No 49 1 1 1 1 1 1 1 1 1 1 + 0.484
No 20 1 1 1 1 1 1 1 1 1 1 + 0.477
No 1 1 1 1 1 1 1 1 1 1 1 + 0.477
Yes 44 1 1 1 1 1 1 1 1 1 1 + 0.471
Yes 7 1 1 1 1 1 0 1 1 1 1 X 0.466
Yes 43 1 1 1 0 1 1 1 1 0 1 X 0.462
Yes 14 1 1 1 1 1 0 0 1 0 1 X 0.454
Yes 21 1 1 0 1 0 1 0 1 0 1 X 0.452
Yes 34 0 0 0 0 0 1 1 1 1 0 X 0.45
Yes 50 0 0 0 0 0 0 0 0 0 0 - 0.447
No 9 0 0 0 0 0 0 0 0 0 0 - 0.438
No 39 0 0 0 0 0 0 0 0 0 0 - 0.428
No 45 0 0 0 0 0 0 0 0 0 0 - 0.412
No 37 0 0 0 0 0 0 0 0 0 0 - 0.409

Limit table

Specification limits Upper gray band boundaries Lower gray band boundaries
Upper Limit: 1.02 0.5662 0.4708
Lower Limit: 0.00 0.5427 0.4467
d: 0.0234 0.0241

Analysis result
d: 0.0238

Analysis result
%RR: 2.3325
Last modified 19.11.2025: Atualizar Manual (288ad71)