Gage rnr model

`daspi.anova.model.GageRnRModel(source, target, part, gage, u_av=None, u_gv=None, u_t=None, u_stab=None, u_obj=None, u_rest=None, fit_at_init=True)` ¶

Bases: LinearModel

A linear regression model for Gage Repeatability and Reproducibility (Gage R&R) analysis.

PARAMETER	DESCRIPTION
`source`	Pandas DataFrame as tabular data in a long format used for the model. TYPE: `pandas DataFrame`
`target`	Column name for source data holding the measurement values. TYPE: `str`
`part`	Column name for the parts variable (unit under test). TYPE: `str`
`gage`	The provided GageStudyModel instance contains the measurement system's statistics. This class corresponds to measurement system analysis type 1. To calculate the uncertainty for linearity, provide multiple reference parts in the `GageStudyModel` instance. TYPE: `GageStudyModel`
`u_av`	Column name of the variable that identifies the operator for type 2 Gage R&R. If the operator has no influence (MSA Typ III) and was therefore not included in the data acquisition, set `u_av` to `None`. In this case, it is recommended to record multiple locations, multiple part holders, or other possible changes to the measuring system and specify them in `u_gv`. Default is None. TYPE: `str \| None` DEFAULT: `None`
`u_gv`	Specifies the measurement uncertainty of gage ss, which reflects the comparability of the measurement system. This uncertainty is determined based on the data. To account for this uncertainty, provide the column name containing the categorical variables for the different measurement systems, test nests, or similar. If not specified, the default value is 'None'. TYPE: `str \| None` DEFAULT: `None`
`u_t`	Indicates the measurement uncertainty related to temperature dependence. This uncertainty can be assessed using the data (Method A) or specified directly if known (Method B). Method A: Enter the column name containing the categorical variables for different temperatures. Method B: Specify a MeasurementUncertainty instance directly. If neither method is applied, the default value is 'None'. TYPE: `MeasurementUncertainty \| str \| None` DEFAULT: `None`
`u_stab`	Represents the measurement uncertainty related to the stability of the measurement system. This uncertainty is determined from the data. To include this uncertainty, enter the column name containing the categorical variables for the relevant conditions. If not specified, the default value is 'None'. TYPE: `str \| None` DEFAULT: `None`
`u_obj`	Specifies the measurement uncertainty associated with the inhomogeneity of the object. This uncertainty can be determined from the data (Method A) or directly specified if known (Method B). Method A: Provide the column name containing the relevant categorical variables for calculation from the data. Method B: Specify a MeasurementUncertainty instance directly. If neither method is applied, the default value is 'None'. TYPE: `MeasurementUncertainty \| str \| None` DEFAULT: `None`
`u_rest`	Accounts for uncertainties not covered by the parameters above. This parameter considers additional sources of uncertainty that may impact the overall measurement, such as environmental conditions, operator influences, or other unknown variables. If known, specify the uncertainty here; otherwise, the default value is 'None'. TYPE: `MeasurementUncertainty \| None` DEFAULT: `None`
`fit_at_init`	If True, the model is fitted at initialization. Otherwise, the model is fitted after calling the `fit` method. Default is True. TYPE: `bool` DEFAULT: `True`

Examples:

If you run the following code in a Jupyter Notebook cell, all tables will be calculated and output in an HTML format:

import daspi as dsp
df = dsp.load_dataset('grnr_layer_thickness')
gage = dsp.GageStudyModel(
    source=df,
    target='result_gage',
    reference='reference',
    u_cal=df['U_cal'][0],
    tolerance=df['tolerance'][0],
    resolution=df['resolution'][0],)
rnr_model = dsp.GageRnRModel(
    source=df,
    target='result_rnr',
    part='part',
    gage=gage,
    u_av='operator')
rnr_model # or print(repr(rnr_model))

References

The calculations are done based on the following references:

[1] Dr. Bill McNeese, BPI Consulting, LLC (09.2012) https://www.spcforexcel.com/knowledge/measurement-systems-analysis-gage-rr/anova-gage-rr-part-2/

[2] Minitab, LLC (2025) https://support.minitab.com/de-de/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/crossed-gage-r-r-study/methods-and-formulas/gage-r-r-table/

[3] Curt Ronniger, Software für Statistik, Schulungen und Consulting (2025) https://www.versuchsmethoden.de/Mess-System-Analyse.pdf

[4] VDA Band 5, Mess- und Prüfprozesse. Eignung, Planung und Management (Juli 2021) 3. überarbeitete Auflage

`part = part` `instance-attribute` ¶

Column name of the part (unit under test) variable.

`has_operator = bool(u_av)` `instance-attribute` ¶

Indicates whether the model has an operator variable.

`u_map = {old: new for old, new in (zip(u_old, u_new)) if isinstance(old, str)}` `instance-attribute` ¶

Dictionary for mapping original names of uncertainties in the source data to the uncertainty abbreviations used in the model.

`n_levels = source[features].nunique().rename(self.u_map)` `instance-attribute` ¶

Series with the number of levels for each variable. The amount of replications are stored under equipment variation 'EV'.

`n_samples` `property` ¶

The number of samples used in the Gage R&R study (read-only).

`gage` `property` ¶

The provided GageModel instances contains the measurement system's statistics. This classes corresponds to measurement system analysis type 1 (read-only).

`df_u` `property` ¶

Get the data frame with the whole uncertainty budget as the combination of the data frames of MS and MP (df_ums and df_ump). If the uncertainties are not calculated yet, the method uncertainties() is called (read-only).

`df_ums` `property` ¶

Get the data frame with the measurement uncertainty of the measurement system as gage study type 1. If the uncertainties are not calculated yet, the method uncertainties() is called (read-only).

`df_ump` `property` ¶

Get the data frame with the measurement uncertainty of the measurement process as gage study type 2 or 3. If the uncertainties are not calculated yet, the method uncertainties() is called (read-only).

`k` `property` `writable` ¶

The coverage factor for the expanded measurement uncertainty.

`interactions` `property` ¶

Get the interaction parameter names if interaction is present in the fitted model (read-only).

`tolerance` `property` ¶

The tolerance of the specification (read-only).

`u_evo` `property` ¶

Get the measurement uncertainty of the equipment variation (repeatability) on the object (read-only).

`u_av` `property` ¶

Get the measurement uncertainty of the appraiser ss (comparability of operators) (read-only).

`u_gv` `property` ¶

Get the measurement uncertainty of the gage ss (compareability of measurement system) (read-only).

`u_ia` `property` ¶

Get the measurement uncertainty of the interaction (read-only).

`u_t` `property` ¶

Get the measurement uncertainty of the temperature (read-only).

`u_stab` `property` ¶

Get the measurement uncertainty of the stability over time (read-only).

`u_obj` `property` ¶

Get the measurement uncertainty of the inhomogeneity of the object (read-only).

`u_rest` `property` ¶

Get the measurement uncertainty of the remaining (read-only).

`u_ms` `property` ¶

Get the measurement uncertainty of the measurement system (read-only).

`u_mp` `property` ¶

Get the measurement uncertainty of the measurement process (read-only).

`rnr(evaluate_ia='auto')` ¶

Get the Gage R&R analysis results as table.

The table contains the following rows:

R&R: The sum of repeatability and reproducibility.
EV: The repeatability component (Equipement Variation).
AV or GV: The reproducibility component (Appriser or Gage Variation).
Part: The part-to-part component.
Total: The sum of the repeatability, reproducibility, and part-to-part.

The table contains the following columns:

MS: The variance estimation.
MS/Total: The estimated variance divided by the total variance.
s: The standard deviation as square root of the variance.
6s: The 6 times the standard deviation.
6s/Total: The 6 times the standard deviation divided by the total 6 times the standard deviation.
6s/Tolerance: The 6 times the standard deviation divided by the tolerance.

PARAMETER	DESCRIPTION
`evaluate_ia`	Whether to include the interaction term in the analysis. If 'auto', the interaction term is included if it is significant. Otherwise, the interaction term is excluded and the model is refit without the interaction term. TYPE: `bool \| Literal['auto']` DEFAULT: `'auto'`

RETURNS	DESCRIPTION
`DataFrame`	The Gage R&R analysis results as table.

Examples:

import daspi as dsp
df = dsp.load_dataset('grnr_layer_thickness')
gage = dsp.GageStudyModel(
    source=df,
    target='result_gage',
    reference='reference',
    u_cal=df['U_cal'][0],
    tolerance=df['tolerance'][0],
    resolution=df['resolution'][0],)
rnr_model = dsp.GageRnRModel(
    source=df,
    target='result_rnr',
    part='part',
    gage=gage,
    u_av='operator')
print(rnr_model.rnr())

                 MS  MS/Total         s        6s  6s/Total  6s/Tolerance
R&R    6.736111e-07   0.02248  0.000821  0.004924  0.149932      0.164148
EV     6.736111e-07   0.02248  0.000821  0.004924  0.149932      0.164148
AV     0.000000e+00   0.00000  0.000000  0.000000  0.000000      0.000000
Part   2.929174e-05   0.97752  0.005412  0.032473  0.988696      1.082437
Total  2.996535e-05   1.00000  0.005474  0.032844  1.000000      1.094812

Notes

The mean squarse used for the calculation of the variances are computed using the anova method. The variance components are then calculated as follows:

With interaction term:

\[ s^2_{EV} = MS_{EV} = MS_{residual} \]

\[ s^2_{operator} = \frac{MS_{operator} - MS_{IA}}{n_{parts} n_{replication}} \]

\[ s^2_{IA} = \frac{MS_{IA} - MS_{EV}}{n_{replication}} \]

\[ s^2_{Part} = \frac{MS_{Part} - MS_{IA}}{n_{operator} n_{replication}} \]

\[ s^2_{AV} = s^2_{operator} + s^2_{IA} \]

Without interaction term:

\[ s^2_{EV} = MS_{EV} = MS_{residual} \]

\[ s^2_{operator} = \frac{MS_{operator} - MS_{EV}}{n_{parts} n_{replication}} \]

\[ s^2_{part} = \frac{MS_{part} - MS_{EV}}{n_{operator} n_{replication}} \]

Variance summary:

\[ s^2_{RnR} = s^2_{EV} + s^2_{AV} \]

\[ s^2_{total} = s^2_{RnR} + s^2_{part} \]

`uncertainties()` ¶

The uncertainties of the measurement system.

The table contains the following rows:

RE: Resolution uncertainty
BI: Bias uncertainty
EVR: Equipment variation on the Reference (repeatability)
MS: Measurement System uncertainty
EVO: Equipement Variation on the Object(repeatability)
AV: Appraiser Variation uncertainty
IA: Interaction uncertainty
MP: Measurement Process (or Precision) uncertainty

The table contains the following columns:

u: The measurement uncertainty for the respective components
U: The expanded uncertainty as k * u
Q: The Quality Indicator serves as a quality indicator for the measurement process, reflecting how well the measurement system performs in relation to the specified requirements and tolerances.
rank: The rank of the uncertainty component, where a lower rank indicates a more significant contribution to the overall uncertainty.

RETURNS	DESCRIPTION
`u`	The uncertainties of the measurement system. TYPE: `DataFrame`

Examples:

import daspi as dsp
df = dsp.load_dataset('grnr_layer_thickness')
gage = dsp.GageStudyModel(
    source=df,
    target='result_gage',
    reference='reference',
    u_cal=df['U_cal'][0],
    tolerance=df['tolerance'][0],
    resolution=df['resolution'][0],)
rnr_model = dsp.GageRnRModel(
    source=df,
    target='result_rnr',
    part='part',
    gage=gage,
    u_av='operator')
model.uncertainties()
print(model.df_u)

                u         U         Q  rank
CAL      0.000100  0.000200  0.013333   5.0
RE       0.000289  0.000577  0.038490   3.0
BI       0.000196  0.000393  0.026173   4.0
LIN      0.000000  0.000000  0.000000   NaN
EVR      0.000688  0.001377  0.091785   2.0
MS_REST  0.000000  0.000000  0.000000   NaN
MS       0.000723  0.001446  0.096371   NaN
EVO      0.000821  0.001641  0.109432   1.0
AV       0.000000  0.000000  0.000000   NaN
GV       0.000000  0.000000  0.000000   NaN
IA       0.000000  0.000000  0.000000   NaN
T        0.000000  0.000000  0.000000   NaN
STAB     0.000000  0.000000  0.000000   NaN
OBJ      0.000000  0.000000  0.000000   NaN
MP_REST  0.000000  0.000000  0.000000   NaN
MP       0.000850  0.001700  0.113305   NaN

Gage rnr model

daspi.anova.model.GageRnRModel(source, target, part, gage, u_av=None, u_gv=None, u_t=None, u_stab=None, u_obj=None, u_rest=None, fit_at_init=True) ¶

part = part instance-attribute ¶

has_operator = bool(u_av) instance-attribute ¶

u_map = {old: new for old, new in (zip(u_old, u_new)) if isinstance(old, str)} instance-attribute ¶

n_levels = source[features].nunique().rename(self.u_map) instance-attribute ¶

n_samples property ¶

gage property ¶

df_u property ¶

df_ums property ¶

df_ump property ¶

k property writable ¶

interactions property ¶

tolerance property ¶

u_evo property ¶

u_av property ¶

u_gv property ¶

u_ia property ¶

u_t property ¶

u_stab property ¶

u_obj property ¶

u_rest property ¶

u_ms property ¶

u_mp property ¶

rnr(evaluate_ia='auto') ¶

uncertainties() ¶

`daspi.anova.model.GageRnRModel(source, target, part, gage, u_av=None, u_gv=None, u_t=None, u_stab=None, u_obj=None, u_rest=None, fit_at_init=True)` ¶

`part = part` `instance-attribute` ¶

`has_operator = bool(u_av)` `instance-attribute` ¶

`u_map = {old: new for old, new in (zip(u_old, u_new)) if isinstance(old, str)}` `instance-attribute` ¶

`n_levels = source[features].nunique().rename(self.u_map)` `instance-attribute` ¶

`n_samples` `property` ¶

`gage` `property` ¶

`df_u` `property` ¶

`df_ums` `property` ¶

`df_ump` `property` ¶

`k` `property` `writable` ¶

`interactions` `property` ¶

`tolerance` `property` ¶

`u_evo` `property` ¶

`u_av` `property` ¶

`u_gv` `property` ¶

`u_ia` `property` ¶

`u_t` `property` ¶

`u_stab` `property` ¶

`u_obj` `property` ¶

`u_rest` `property` ¶

`u_ms` `property` ¶

`u_mp` `property` ¶

`rnr(evaluate_ia='auto')` ¶

`uncertainties()` ¶