A measurement systems study involving 25 parts, three measuring units, and two r
ID: 3263691 • Letter: A
Question
A measurement systems study involving 25 parts, three measuring units, and two replicatemeasurementsperpartisshowninthefollowingtable. Theproduct specification is 122.50 7.50. Perform a crossed gauge R&R study in Minitab. Statistical tests are to be at = 0.05 significance level. (a) What are the estimates of the variance components due to repeatability, reproducibility, and total gauge R&R? What are the corresponding percent contributions to total measurement variation? (b) What are the estimates of the variance components due to part, measuring unit total R&R, and part*unit interaction. What are the corresponding percent contributions to total measurement variation? (c) What is the estimated P/T ratio and number of distinct categories? Given that it is ideal for the % Study Variation and P/T ratio to be less than 0.10, acceptable up to 0.30, and it is ideal that the distinct number of categories be 5, will the joint measurement system of the three measuring units be acceptable? (d) Do the measuring units make reproducible measurements? Identify any sources of variation that contribute to any observed variability. Justify your reasoning from the gauge R&R output. (e) If any of the measuring units are statistically different, repeat the crossed gauge R&R study comparing only the two measuring units that are not statistically different. Provide corresponding answers to parts (a) – (d) above. Given that it is ideal for the % Study Variation and P/T ratio to be less than 0.10, acceptable up to 0.30, and it is ideal that the distinct number of categories be 5, will the joint measurement system of the later two measuring units be acceptable?
Measurement data.
Sample Meas1 Meas2
1 126.3 126.1
2 123.0 123.1
3 123.2 123.3
4 120.0 119.9
5 121.5 121.9
6 121.5 121.0
7 122.7 122.3
8 119.4 119.8
9 122.1 121.5
10 121.3 121.0
11 124.8 124.6
12 122.1 121.9
13 120.9 121.3
14 127.4 127.6
15 123.7 123.1
16 120.1 119.9
17 120.7 120.6
18 124.2 124.6
19 126.9 126.4
20 125.7 125.4
21 123.4 124.0
22 122.8 122.2
23 120.1 119.6
24 124.6 124.3
25 120.1 120.3
unit 2 Meas1 Meas2
125.5 126.0
126.0 122.3
122.3 122.8
122.8 123.6
123.6 123.1
123.1 121.1
121.1 121.2
121.2 122.4
122.4 122.0
122.0 121.9
121.9 122.6
122.6 123.5
123.5 122.8
122.8 119.8
119.8 119.4
119.4 122.1
122.1 122.4
122.4 120.3
120.3 120.9
120.9 124.8
124.8 124.8
124.8 122.3
122.3 123.1
123.1 121.4
121.4 122.1
Unit3 Meas1 Meas2
126.1 125.6
122.7 123.0
123.4 123.2
120.4 120.6
122.0 122.7
121.8 121.7
123.5 122.9
119.7 119.6
121.6 122.4
120.6 120.3
124.9 124.7
123.0 122.3
121.0 121.8
127.0 127.6
122.9 122.7
120.5 120.8
120.9 120.2
125.0 124.3
127.4 126.7
125.9 125.1
124.3 123.5
122.0 121.4
119.8 120.4
124.5 124.4
120.2 119.4
Explanation / Answer
a) & b)
Gage R&R
Variance Components
Process tolerance = 7.5
Gage Evaluation
Number of Distinct Categories = 1
c) The measurement system is not acceptable because % Study Var and % P/T is greater than 30% and Number of Distinct Categories is less than 5.
d)Reproducibility is the problem i.e. the measuring unit are not measuring consistently between the measurement.Measuring unit 2 is the problem.
e)After removing measuring unit 2.---
Gage R&R Study - ANOVA Method
Two-Way ANOVA Table With Interaction
to remove interaction term = 0.05
Two-Way ANOVA Table Without Interaction
Gage R&R
Variance Components
Process tolerance = 7.5
Gage Evaluation
Number of Distinct Categories = 8
Now the measurement system is accepatable after removing measuring unit 2
Source VarComp %Contribution(of VarComp) Total Gage R&R 2.49745 59.10 Repeatability 0.53747 12.72 Reproducibility 1.95998 46.38 Unit 0.00000 0.00 Unit*Sample 1.95998 46.38 Part-To-Part 1.72846 40.90 Total Variation 4.22591 100.00
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