## Confidence Limit Calculations for Variance Components

The following calculations of confidence limits are used for GR&R Reports based on the GR&R and ANOVA test types.

### ANOVA Confidence Limit Calculations

DataPage+ uses the non-additive model when the interaction between parts and operators is significant; it uses the additive model when interaction is not significant.

Non-Additive Model

This model is used when the interaction between parts and operators IS SIGNIFICANT.

Variance Component | Confidence Limit (CL) | Degrees of Freedom
(repeatability) |  |
(interaction) |  |
(part-to-part) |  |
(R&R) |  |

, , , and are notations for the master variance components.

Additive Model

This model is used when the interaction between parts and operators is INSIGNIFICANT.

Variance Component | Confidence Limit (CL) | Degrees of Freedom
(repeatability) |  |
(reproducibility) |  |
(part-to-part) |  |
(R&R) |  |

Degrees of Freedom: Degrees of freedom for the ANOVA test type are based on:

Operator

Parts

Oper X Parts

Gage (Error)

where n is the number of parts measured; r is the number of times the part was measured; and k is the number of operators

For the ANOVA test type, degrees of freedom for errors associated with variance components will differ depending upon whether the additive or non-additive model is used (i.e., whether the interaction between parts and operators is significant or insignificant). Refer to the tables above for the calculations used in each model.

### GR&R Confidence Limit Calculations

| Lower Limit | Upper Limit
Repeatability (EV) |  |
Reproducibility (AV) |  |
Gage GR&R |  |

Degrees of Freedom: For reports using the GR&R test type, degrees of freedom (n) are based on the number of samples (g) and the size of the samples (m). Refer to the Table of d*2 Values & Degrees of Freedom for specific values.