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Gage R&R (Measurement System Analysis)

Source: R/precision.R
measure_gage_rr.Rd

Performs a Gage Repeatability and Reproducibility study to assess measurement system variation.

Usage

measure_gage_rr(
  data,
  response_col,
  part_col,
  operator_col,
  tolerance = NULL,
  conf_level = 0.95,
  k = 5.15
)

Arguments

data

A data frame containing Gage R&R study data.

response_col

Name of the column containing the measurements.

part_col

Name of the column identifying parts/samples.

operator_col

Name of the column identifying operators/analysts.

tolerance

Optional specification tolerance for calculating %Study variation and %Tolerance.

conf_level

Confidence level. Default is 0.95.

k

Multiplier for study variation calculation. Default is 5.15 (99%).

Value

A measure_gage_rr object containing:

  • Variance components (Repeatability, Reproducibility, Part-to-Part)

  • %Contribution of each component

  • %Study Variation (using k * sigma)

  • %Tolerance (if tolerance provided)

  • Number of distinct categories (ndc)

Details

Gage R&R decomposes total measurement variation into:

  • Repeatability (EV): Equipment variation - variability from repeated measurements by the same operator on the same part

  • Reproducibility (AV): Appraiser variation - variability between operators measuring the same parts

  • Part-to-Part (PV): True variation between parts

Acceptance Criteria (typical guidelines)

  • %R&R < 10%: Measurement system acceptable

  • %R&R 10-30%: Measurement system may be acceptable depending on application

  • %R&R > 30%: Measurement system needs improvement

The number of distinct categories (ndc) should be >= 5 for a capable measurement system.

See also

measure_repeatability(), measure_intermediate_precision()

Other precision: measure_intermediate_precision(), measure_repeatability(), measure_reproducibility()

Examples

# Gage R&R study with 10 parts, 3 operators, 2 replicates each
set.seed(123)
data <- expand.grid(
  part = 1:10,
  operator = c("A", "B", "C"),
  replicate = 1:2
)
data$measurement <- 50 +
  (data$part - 5) * 2 +  # Part-to-part variation
  ifelse(data$operator == "A", 0.5,
         ifelse(data$operator == "B", -0.3, 0)) +  # Operator effect
  rnorm(nrow(data), 0, 0.5)  # Repeatability

result <- measure_gage_rr(
  data,
  response_col = "measurement",
  part_col = "part",
  operator_col = "operator",
  tolerance = 20
)
print(result)
#> measure_gage_rr: Measurement System Analysis
#> ──────────────────────────────────────────────────────────────────────────────── 
#> 
#> Study design:
#>   Parts: 10 
#>   Operators: 3 
#>   Replicates: 2 
#> 
#> Variance Components:
#>   Repeatability: 0.2381 (0.6% contribution)
#>   Reproducibility: 0.1875 (0.5% contribution)
#>   Total R&R: 0.4256 (1% contribution)
#>   Part-to-Part: 36.28 (99% contribution)
#> 
#> % Study Variation:
#>   Repeatability: 8%
#>   Reproducibility: 7%
#>   Total R&R: 11%
#>   Part-to-Part: 99%
#> 
#> % Tolerance:
#>   Repeatability: 13%
#>   Reproducibility: 11%
#>   Total R&R: 17%
#>   Part-to-Part: 155%
#> 
#> Number of Distinct Categories (ndc): 13 
#> 
#> Assessment:
#>   Measurement system MAY BE ACCEPTABLE (%R&R 10-30%)