# QUALITY SOFTWARE & ANALYSIS: Gage R&R Improves Quality and Profitability

A gage repeatability and reproducibility study can determine if a measurement system is acceptable for the required measurement.

Gage repeatability and reproducibility (GR&R) studies provide information on measurement system performance by analyzing measurement error from various sources. If a large amount of variability is present in a measurement system, this can lead to poor quality product being shipped to customers by not being able to use the measurement system to differentiate between conforming and nonconforming parts. On the other hand, this situation also can reduce profitability by causing conforming parts to be rejected. Fortunately, a gage repeatability and reproducibility study can determine if the measurement system is unacceptable for the required measurement. By understanding the results, the system can be improved to make it trustworthy.

When determining if a measurement system is trustworthy, the sources of measurement variation are broken into three categories: part-to-part, repeatability or equipment, and reproducibility or appraiser.

Repeatability is the variability because of the gage itself. Reproducibility is the variability because of different operators using the gage differently. Repeatability and reproducibility together are called gage repeatability and reproducibility.

Ideally when calculated from measurement data in a study, the GR&R will be zero, but this is not possible in the real world. In light of this, the goal is to make GR&R as small as possible relative to the tolerance, the difference between the upper and lower specification limits. If successful, the measurement system will be trustworthy, resulting in the ability to accept conforming parts and reject nonconforming parts.

Gage Performance Curves

To visually understand the impact of an untrustworthy measurement system on a company's product quality and profitability, use gage performance curves along with typically calculated ratios. A gage performance curve shows the probability of accepting a part as good for a particular measurement system. The "Gage Performance Curves" illustration indicates that the chance for accepting bad parts increases as the percentage GR&R increases.

When the percentage GR&R is 7%, the probability of accepting a bad part or rejecting a good part is low except when the measurement result is close to an upper or lower specification limit. When percentage GR&R is greater than 30%, the probability of accepting bad parts and rejecting good parts is unacceptably high. When percentage GR&R is 32%, there is less than 90% probability of accepting parts that are well within the specification limits. This also corresponds to greater than 10% probability of accepting parts that are more than 5% outside of the specification limits. These errors lead to reduced profitability and poorer product quality. From this, to maintain profitability, measurement systems with low percentage GR&R ratios are important.

Trustworthiness

A gage repeatability and reproducibility study provides information not only if the measurement system is trustworthy, but it also indicates what needs to be improved in an untrustworthy measurement system by reviewing the components that make up the percentage GR&R. As previously mentioned, the percentage GR&R is separated into two components: repeatability and reproducibility. The larger of the two component percentages indicates where to focus improvement efforts.

The examples, "Gage Performance Curves for Fluoride Measurement" and "Gage Performance Curve for Copper Thickness Measurement" illustrate how repeatability and reproducibility percentage identify the largest source of variability in a measurement system graphically using gage performance curves.

The first example is a measurement system for quantifying the amount of fluoride in drinking water. In the figure "Gage Performance Curves for Fluoride Measurement," the curve on the left shows the effects of repeatability and reproducibility together. The center curve shows the effect of repeatability alone, while the curve on the right shows the effect of reproducibility alone. For this measurement system, repeatability is much larger than reproducibility. This condition indicates that the gage itself needs improvement. In fact, the reproducibility is so low it is difficult to measure the parts, indicating very consistent use of the gage by the operators. When repeatability is large relative to reproducibility, work on improving the gage.

The second example is a measurement system for determining the thickness of the copper walls in holes through printed circuit boards. For this measurement system as indicated in the figure "Gage Performance Curve for Copper Thickness Measurement," reproducibility is much larger than repeatability. The gage is quite good, but the operators are not using the gage consistently. When reproducibility is larger than repeatability, operators need training to learn to use the gage more consistently.

Gage repeatability and reproducibility studies provide guidance on how to improve a measurement system to make it trustworthy. By using gage performance curves in combination with calculated ratios for GR&R studies, the probabilities of accepting parts based on the repeatability and reproducibility components provide a simple tool on identifying how to improve the measurement system. After a measurement system is fine tuned by a GR&R study and making improvements, profitability and product quality will improve because conforming and nonconforming parts may be identified with greater confidence. Q

Quality Tech Tips

-Gage repeatability and reproducibility studies provide information on measurement system performance by analyzing measurement error from various sources.

-When determining if a measurement system is trustworthy, the sources of measurement variation are broken into three categories: part-to-part, repeatability and reproducibility.

-Ideally when calculated from measurement data in a study, the GR&R will be zero, but this is not possible in the real world.

-A gage performance curve shows the probability of accepting a part as good for a particular measurement system.

William D. Kappele is president of MathOptions Inc. (Bellingham, WA). He may be contacted through www.ObjectiveDOE.com. John Raffaldi is a test engineer at Micro Encoder Inc. (Kirkland, WA).