When calculating the variance for a data set the sum of the squared differences between each measurement and the mean is calculated and then divided by the degrees of freedom ( n – 1).
The calculation of variance components and standard deviations using ANOVA is equivalent to calculating variance and standard deviation for a single variable but it enables multiple sources of variation to be individually quantified which are simultaneously influencing a single data set. The ANOVA then allows the individual sources of variation in the measurement data to be identified the part-to-part variation, the repeatability of the measurements, the variation due to different operators and the variation due to part by operator interaction.
In one common crossed study, 10 parts might each be measured two times by two different operators. Several methods of determining the sample size and degree of replication are used. 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. 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. Įxamples of gauge R&R studies can be found in part 1 of Czitrom & Spagon. Īnova gauge R&R is an important tool within the Six Sigma methodology, and it is also a requirement for a production part approval process (PPAP) documentation package. 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. 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. 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. If the P/T ratio is low, the impact on product quality of variation due to the measurement system is small. 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. Gauge R&R addresses only the precision of a measurement system. It is important to understand the difference between accuracy and precision to understand the purpose of Gauge R&R. Reproducibility: the variation induced when different operators, instruments, or laboratories measure the same or replicated specimen.Repeatability: The variation in measurements taken by a single person or instrument on the same or replicate item and under the same conditions.There are two important aspects of a Gauge R&R: A measurement system may be good for measuring steel block length but not for measuring rubber pieces, for example. Parts or specimens (what is being measured), some items are easier to be measured than others.The range or the engineering tolerance does not affect the measurement, but is an important factor in evaluating the viability of the measurement system.
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