# Gage R & R (Measurement System Assessment)

### Description

Performs Gage R&R analysis for the assessment of the measurement system of a process. Related to the Measure phase of the DMAIC strategy of Six Sigma.

### Usage

1 2 3 |

### Arguments

`var` |
Measured variable |

`part` |
Factor for parts |

`appr` |
Factor for appraisers (operators, machines, ...) |

`lsl` |
Numeric value of lower specification limit used with USL to calculate Study Variation as %Tolerance |

`usl` |
Numeric value of upper specification limit used with LSL to calculate Study Variation as %Tolerance |

`sigma` |
Numeric value for number of std deviations to use in calculating Study Variation |

`data` |
Data frame containing the variables |

`main` |
Main title for the graphic output |

`sub` |
Subtitle for the graphic output (recommended the name of the project) |

`alphaLim` |
Limit to take into account interaction |

`errorTerm` |
Which term of the model should be used as error term (for the model with interation) |

`digits` |
Number of decimal digits for output |

### Details

Performs an R&R study for the measured variable, taking into account part and appraiser factors. It outputs the sources of Variability, and six graphs: bar chart with the sources of Variability, plots by appraiser, part and interaction and x-bar and R control charts.

### Value

Analysis of Variance Table/s. Variance composition and %Study Var. Graphics.

`anovaTable` |
The ANOVA table of the model |

`anovaRed` |
The ANOVA table of the reduced model (without interaction, only if interaction not significant) |

`varComp` |
A matrix with the contribution of each component to the total variation |

`studyVar` |
A matrix with the contribution to the study variation |

`ncat` |
Number of distinct categories |

### Note

The F test for the main effects in the ANOVA table is usually made
taken the operator/appraisal
interaction as the error term (repeated measures model), thereby computing F as
$MS_factor/MS_interaction$, e.g. in appendix A of AIAG MSA manual,
in Montgomery (2009) and by statistical software such as Minitab.
However, in the example provided in page 127 of the AIAG MSA Manual, the
F test is performed as $MS_factor/MS_equipment$, i.e., repeatability.
Thus, since version 0.9-3 of the SixSigma package, a new argument
`errorTerm`

controls which term should be used as error Term, one of
"interaction", "repeatability".

Argument `alphaLim`

is used as upper limit to use the full model, i.e.,
with interaction. Above this value for the interaction effect, the
ANOVA table without the interaction effect is also obtained, and the variance
components are computed pooling the interaction term with the repeatibility.

### Author(s)

EL Cano with contributions by Kevin C Limburg

### References

Automotive Industry Action Group. (2010). Measurement Systems Analysis (Fourth Edition). AIAG.

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012.
*Six Sigma with R. Statistical Engineering for Process
Improvement*, Use R!, vol. 36. Springer, New York.
http://www.springer.com/statistics/book/978-1-4614-3651-5.

Montgomery, D. C. (2009). Introduction to Statistical Quality Control (Sixth Edition ed.). New York: Wiley & Sons, Inc.

### See Also

`ss.data.rr`

### Examples

1 2 3 4 | ```
ss.rr(time1, prototype, operator, data = ss.data.rr,
sub = "Six Sigma Paper Helicopter Project",
alphaLim = 0.05,
errorTerm = "interaction")
``` |