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# Equivalence of Instruments

This procedure is used to determine if measurement instruments are equivalent in terms of bias and measurement error. One operator measures the same part multiple times on each instrument. This procedure requires that the part is run the same number of times on each instrument. The output includes a worksheet containing the consistency chart for each instrument, the ANOM chart for instrument bias and the Analysis of Mean Moving Ranges chart for measurement error. The data used below can be downloaded at this link.

This procedure is based on two articles written by Dr. Donald Wheeler and Dr. James Beagle III, When are Instruments Equivalent, Part 1 and Part 2, published at www.qualitydigest.com.

Sample A B C
1 215 213 220
2 217 210 211
3 216 220 217
4 214 211 210
5 213 217 213
6 218 216 217
7 214 216 212
8 217 212 214
9 222 215 212
10 216 215 214
11 219 219 209
12 210 209 214
13 218 212 218
14 214 217 213
15 211 216 212
16 214 223 210
17 218 219 211
18 216 214 212
19 218 212 216
20 216 214 213
21 211 216 219
22 222 217 210
23 214 215 210
24 211 221 213
25 211 220 210
26 217 220 208
27 222 220 218
28 219 211 212
29 216 212 210
30 208 214 212

#### Output – Consistency Charts

It is recommended you run the three options above one at-a-time. You would start with only “Check Consistency of Each Instrument” checked. This generates a consistency chart for each instrument as well as a summary of the results. If an instrument’s consistency chart is not in statistical control, you should not use that instrument in the rest of the analysis. The summary and consistency chart for instrument A is shown below.

The summary gives each instrument’s average moving range, standard deviation, probable error and if it is consistent are not.

#### Output – Comparing Instrument Measurement Error

Using only the instruments that are consistent, run the second option above: Check for Differences in Measurement Error. This tells you if any instruments have a measurement error that is significantly different from the others. The analysis uses the ANOMmR technique described in the reference above.

The output provides an interpretation of the results. Only use the instruments whose measurement error is in control for the bias analysis. The calculations used are also given.

#### Output – Comparing Instrument Bias

Using only the instruments whose measurement system is in control, run the third option below: Check for Instrument Bias, This tells you if any instruments have a bias that is significantly different from the others. The analysis uses the ANOM technique described in the reference above.

If there is an instrument beyond the detection limits (like instrument C above), the software will combine the instruments in control and adjust the average using just those points. The ANOM chart is then redrawn. If a known standard is included, the value of the standard will be used as the center line and the ANOM redrawn.

The software will also check to see if the bias is of practical importance. This occurs is the bias is greater than 1.128SD(E) where SD(E) is the measurement error.

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