fstats_msa Module

Performs a gauge repeatability and reproducibility (gauge R&R) study by means of the analysis of variance (ANOVA) method.

A gauge R&R study apportions the observed variation between the parts being measured and the measurement system itself. The measurement system contribution is split into repeatability, the variation seen when one operator measures one part repeatedly, and reproducibility, the variation seen between operators. Three study designs are supported.

Crossed

Every operator measures every part, and each combination is measured repeatedly. Because each part is seen by every operator, the operator-by-part interaction can be separated from the residual, and the measurements are described by $$y_{ijk} = \mu + P_{i} + O_{j} + (PO)_{ij} + \epsilon_{ijk}$$ where $P$ is the part effect, $O$ the operator effect, $(PO)$ their interaction, and $\epsilon$ the residual. The interaction describes the tendency of operators to differ from one another by differing amounts from part to part, and it contributes to reproducibility. This is the appropriate design whenever the measurement is non-destructive, and it is the design assumed by default. Supply an M-by-P-by-O array and, optionally, GAUGE_RR_CROSSED_STUDY.

Nested

Each operator measures its own distinct set of parts, so no part is shared between operators. This is the appropriate design when the measurement destroys or alters the part, or when the parts cannot otherwise be circulated. Since no part is common to two operators there is no information with which to separate an interaction from the part effect, and the parts are said to be nested within the operators $$y_{ijk} = \mu + O_{j} + P_{i(j)} + \epsilon_{ijk}$$ where $P_{i(j)}$ denotes the effect of the i-th part measured by the j-th operator. Reproducibility is therefore the operator term alone. Supply an M-by-P-by-O array together with GAUGE_RR_NESTED_STUDY; the P parts measured by one operator are understood to be different from those measured by any other.

Expanded

A third factor, such as the day, the setup, the fixture, or the measurement site, is varied alongside the parts and the operators in a fully crossed arrangement. All two-way interactions and the three-way interaction are estimated $$y_{ijkl} = \mu + P_{i} + O_{j} + C_{k} + (PO)_{ij} + (PC)_{ik} + (OC)_{jk} + (POC)_{ijk} + \epsilon_{ijkl}$$ where $C$ is the third factor. This design answers whether the measurement system is stable with respect to an influence that a conventional study would leave confounded with the repeatability. Every term other than the part term describes variation introduced by the measurement system, so all of them contribute to reproducibility. Supply an M-by-P-by-O-by-C array; the study type follows from the rank of the argument.

The analysis of variance table underlying a gauge R&R study. Terms that do not appear in the study design are zeroed.

Components

Describes a single variance component of a gauge repeatability and reproducibility study.

Components

Contains the results of a gauge repeatability and reproducibility study.

Components