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GR&R - Variables Data

Gauge R&R analysis is based on a type of ANOVA model called a Random Effects model, also known as a Variance Components model.

The standard GR&R model supposes that each specimen or part can be tested or measured multiple times without changing the characteristic being measured and without destroying the part.  If this is not the case, then a Destructive GR&R (DGR&R) model might be considered.

Standard GR&R models might be fit using either the Range method or the ANOVA method.  The ANOVA method will often provide more information for the same amount of effort; such as determining if any interactions (e.g. Operator x Part, Operator x Gauge) are significant.  The ANOVA method also allows model diagnostics, such as analysis of model residuals.

The ANOVA method used for GR&R is the Random Effects ANOVA model (vs. the Fixed Effects ANOVA model).  See the Montgomery SQC text, among others.

Planning the study.

See notes on randomization and collection of specimens.  (3 stage process)

What goes into the report?
  (see report template for ANOVA)

Study design

Sampling and randomization plan

GR&R Results
  • Random Effects ANOVA analysis
    • get GR&R variance components AND interaction(s)
    • can include any blocking term related to restrictions on randomization (as fixed effect)
  • Values for Repeatability and Reproducibility
  • Total GR&R as a percent of process variation
    • Prefer "as percent of process variation", for example if using results of measurements for SPC
    • Depending on application, might accept "percent of Tolerance"
  • Number of Distinct Categories (or equivalent)
  • Depending on risk, also consider calculating the confidence intervals around each GR&R component.

Model diagnostics
  • EMS table
    • Check the computer generated EMS table against the manually created EMS table
    • Check the allocation of degrees of freedom
    • Check the denominator synthesis
  • Residuals -> homogeneity, iid N(0.1))

Supplementary analysis
  • Impact of any blocking variables
  • Fixed Effects ANOVA analysis of GR&R study data to explore:
    • Differences in means between levels of factors (operators, gauges, facilities, etc.)
      • Associated means plots (prioritize interaction terms)
    • Levene's test (or equivalent) to check for differences in variances between levels of factors
      • Plot of means vs. variances (prioritize interaction terms)
    • Blocking variables
      • Cavity
      • Test sequence ID
      • Position
        • 12, 3, 6, 9 clock positions
        • Position across a web of film or barrier perform