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Chapter 13: G. Measurement System Analysis 127
Continued
Table 13.1
Data on an experiment involving three operators, 10 bolts, and three
measurements (in mm) on each bolt by each operator.
Bolt (part)
Operator 1 Operator 2 Operator 3
number Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3
1 26 22 26 21 23 21 24 22 26
2 28 26 28 24 29 26 24 25 24
3 28 31 28 28 27 28 32 30 27
4 35 33 31 35 31 30 34 35 31
5 37 35 38 36 38 35 35 34 35
6 40 38 40 40 38 40 36 37 38
7 39 42 41 40 39 43 43 41 43
8 42 43 46 42 46 42 43 44 45
9 50 52 50 53 52 53 49 53 49
10 28 31 28 28 27 28 32 30 27
R – 1 = 3.0 x – 1 = 35.33 R – 2 = 2.5 x – 2 = 34.67 R – 3 = 3.0 x – 3 = 34.93
Part II.G
Solution:
We first discuss GR&R using the range-based method, the approach used by IBM (1986),
Barrentine (2003), and others.
Step 1: Verify that gage calibration is current.
Step 2: Identify operators. Three operators are typically used in gage studies;
however, the more operators the better.
Step 3: Select a random sample of parts and have each operator measure all
parts. One operator measures all parts, taking several measurements on
each part, then the second operator takes measurements, then the third
operator takes measurements, and so on. All parts are measured in
random order.
Step 4: Calculate the sample mean, inter-trial range for each sample, and average
range for each operator. The sample means and average ranges are provided
in Table 13.1.
Step 4: Calculate the range of sample means (R x
– ), that is
Rx = Max( xi) Min( xi)
= 35. 33 34. 67 = 0. 66.
Continued