ANOVA gauge R&R
ANOVA gauge R&R (or ANOVA gauge repeatability and reproducibility) is a measurement systems analysis technique that uses an analysis of variance (ANOVA) random effects model to assess a measurement system.
ANOVA gauge R&R measures the amount of variability induced in measurements by the measurement system itself, and compares it to the total variability observed to determine the viability of the measurement system. There are several factors affecting a measurement system, including:
- Measuring instruments, the gauge or instrument itself and all mounting blocks, supports, fixtures, load cells, etc. The machine's ease of use, sloppiness among mating parts, and, "zero" blocks are examples of sources of variation in the measurement system. In systems making electrical measurements, sources of variation include electrical noise and analog-to-digital converter resolution.
- Operators (people), the ability and/or discipline of a person to follow the written or verbal instructions.
- Specification, the measurement is reported against a specification or a reference value. The range or the engineering tolerance does not affect the measurement, but is an important factor in evaluating the viability of the measurement system.
- Parts or specimens (what is being measured), some items are easier to be measured than others. A measurement system may be good for measuring steel block length but not for measuring rubber pieces, for example.
There are two important aspects of a Gauge R&R:
- Repeatability: The variation in measurements taken by a single person or instrument on the same or replicate item and under the same conditions.
- Reproducibility: the variation induced when different operators, instruments, or laboratories measure the same or replicate specimen.
It is important to understand the difference between accuracy and precision to understand the purpose of Gauge R&R. Gauge R&R addresses only the precision of a measurement system. It is common to examine the P/T ratio which is the ratio of the precision of a measurement system to the (total) tolerance of the manufacturing process of which it is a part. If the P/T ratio is low, the impact on product quality of variation due to the measurement system is small. If the P/T ratio is larger, it means the measurement system is "eating up" a large fraction of the tolerance, in that the parts that do not have sufficient tolerance may be measured as acceptable by the measurement system. Generally, a P/T ratio less than 0.1 indicates that the measurement system can reliably determine whether any given part meets the tolerance specification. A P/T ratio greater than 0.3 suggests that unacceptable parts will be measured as acceptable (or vice-versa) by the measurement system, making the system inappropriate for the process for which it is being used.
There is not a universal criterion of minimum sample requirements for the GRR matrix, it being a matter for the Quality Engineer to assess risks depending on how critical the measurement is and how costly they are. The "10×2×2" (ten parts, two operators, two repetitions) is an acceptable sampling for some studies, although it has very few degrees of freedom for the operator component. Several methods of determining the sample size and degree of replication are used.
- Richard K. Burdick, Connie M. Borror and Douglas C. Montgomery (2005). Design and Analysis of Gauge R and R Studies: Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models. American Statistical Association and the Society for Industrial and Applied Mathematics. p. 2. ISBN 0898715881.
- Richard K. Burdick, Connie M. Borror and Douglas C. Montgomery (2005). Design and Analysis of Gauge R and R Studies: Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models. American Statistical Association and the Society for Industrial and Applied Mathematics. p. 4. ISBN 0898715881.