Question

Suppose the thickness of a certain part is important to a major customer. You want to know how “good” the micrometer you use is, i.e., is the measurement system acceptable? You decide to run a Gage R&R by having 3 operators measure 5 parts 2 times each. You perform the Gage R&R using operators A, B and C. The data from the study are given in Table 1 below. Perform the Gage R&R study and interpret the results.

Table 1: Gage R&R Data

Operator Part Trial 1 Trial 2

A 1 170 158

A 2 212   208

A 3 190 178

A 4 192 193

A 5 159 145

B 1 158 153

B 2 209 194

B 3 187 175

B 4 187 175

B 5 147 138

C 1 155   151

C 2 208 200

C 3 182 178

C 4 185 179

C 5 150 149

Answer 1

There are a total of 3 operators 5 parts and 2 readings for each part.

The operator skill is an important factor that has a huge impact on the final output.

so, lets first analyze the operators.

When comparing the data from 3 operators, each had a different reading value for each part. Since the actual real value of the part is almost a constant it varies in the Gage R&R due to 2 factors

• Operator error ( depending on the skill of the operator)
• Accuracy and precision of the micrometer

The value of reading by any device can vary vastly if it's incorrectly used. The accuracy and precision of the micrometer are the same for the 3 operators and hence the major contributor of value difference between the 3 operators for the same material is the operator error.

Form the data table, the values of operator 'B' and 'C' are much more relatable and the difference is mostly in a smaller range of 2mm-4mm. But for the operator 'A' the values for each item varies in a range of 8mm-10mm with the other 2 operators. Hence it is clear that operator 'A' projects an operator error which is responsible for the large change in values.

Thus operator 'A' can be eliminated for further analysis. By analyzing the readings from operators 'B' and 'C', even though there is a chance of human error, a constant quantity of error can be found in all the reading. This constant difference between the operators are mostly in a range of 2mm-3mm, excluding some abrupt changes which can be happened due to other factors.

Thus from the data, it can be concluded that the particular micrometer has an error in the range of 2mm-3mm when all other factors are excluded and depending on the requirement of the customer it can be determined as good or not for the pariticular requirment.