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For a typical measurement system analysis, the sources of measurement variability are broken into three categories: part-to-part, repeatability and reproducibility.
Repeatability is the variability due to the gage itself. Reproducibility is the variability due to different operators using the gage differently. Repeatability and reproducibility together are called gage repeatability and reproducibility (GR&R).
When you have a gage that simply determines whether a part is in specification (pass) or out of specification (fail), the sources of measurement error are broken down differently. There are still three categories to look at: percent effectiveness, percent miss rate and percent false alarm rate.
The first, percent effectiveness, measures how well a measurement system can identify parts correctly as in or out of specification. The remaining two, percent miss rate and percent false alarm rate, identify how often specific errors are likely to be made. Percent miss rate measures how often an operator can “miss” an out of specification part, sending it out to customers. Percent false alarm rate measures how often an operator can raise a false alarm, or misidentify good product as out of specification.
A pass-fail gage is called an attribute gage. As in a typical GR&R study, attribute gage studies use multiple operators who repeat measurements on the same part several times. Unlike a typical study, however, the measurements are either “pass” or “fail.” All of the precautions of a typical study such as randomization and blinding should be observed.
ExampleLet’s take a look at an example to understand an attributes GR&R study. The background to understand the data is as follows:
Acme Gasket produces gaskets for the chemical industry. These gaskets must be at least 0.450 millimeter thick, but cannot be thicker than 0.545 millimeter. Thus, any gasket with a thickness between 0.450 millimeter and 0.545 millimeter will pass, while gaskets with thicknesses outside this range will fail.
The test is performed by first passing the 25-millimeter wide gasket through a slit 0.545 millimeter high and 200 millimeter wide in an aluminum plate. If the part passes through, it is not too thick. Next the operator attempts to pass the gasket through a slit 0.450-millimeter high and 200-millimeter wide in another aluminum plate. If the gasket passes through this slit, the part is too thin.
So, in order to pass, a part must pass through the first slit and fail to pass through the second. A portion of the data table is shown in the table, “Partial Data for Gasket Attribute Study.”
Here is how to read the data table:
Part. Part identifier for the actual gasket being measured.
Standard. Whether the part passes (1) or fails (0) based on an independent measurement system of higher quality. (See RefValue below.)
Code. A “+” indicates all measurement of this part correctly identified it as in specification. A “-” indicates that all measurements correctly identified this part as out of specification. An x indicates that some measurements of this part were incorrect.
A, B and C. Pass (1) and fail (0) measurements for each of the operators.
RefValue. The thickness of the gasket as measured by a higher quality gage.
Notice that the overall percent effectiveness is about 94%. The percent miss rate (misses) is 6.25% for operators A and B, and 12.5% for operator C. The percent false alarm rate (false alarms) is 4.9% for operator A, 1.96% for operator B and 8.82% for operator C. Based on these results, the measurement system looks good for percent effectiveness, fair for percent false alarm rate (based on the worst operator result) and poor for percent miss rate (for all operators).
Improving this technique will start with determining why all of the operators are passing out of specification parts-they all have a high percent miss rate. The table, “Partial Data: Misses,” includes the pertinent data.
Notice that most of the miss errors are made by passing gaskets that are too thick. Examining the gage shows that it has a taper, starting at 0.5429 millimeter at one end and progressing to 0.5650 millimeter at the other end. Thus, depending on where in the 200-millimeter wide gage the 25-millimeter wide gasket is inserted, it may or may not pass through.
A similar taper was discovered on the narrower gage as well. New gages were produced by the company machine shop with no measurable taper using the previous inspection method. A new attribute gage study was performed and the results are shown in the table, “Effectiveness Report After Correcting the Gage.”
Notice that the now overall percent effectiveness is about 97.6%. The percent miss rate (misses) is 0% for operator A, and 2.08% for operators B and C. The percent false alarm rate (false alarms) is 2.94% for operator A, 0.98% for operator B and 4.90% for operator C. Based on these results, the measurement system looks good overall after correcting the taper problems with the gage.
Measurement system analysis helps to judge whether an attribute gage is trustworthy meeting inspection needs. After the gage is evaluated and found to be satisfactory, the gage helps increase profitability by reducing false alarms, and increase customer satisfaction by reducing the number of misses. By performing GR&R studies before introducing any gage to production or inspection we can be assured that our decisions are based on good data. Q
Tech TipsMeasurement system analysis helps to judge whether an attribute gage is trustworthy meeting inspection needs.
Good data come from measurements that are as free from variation as possible and are accurate.
By performing GR&R studies before introducing any gage to production or inspection, we can be assured that our decisions are based on good data.