Gage Repeatability & Reproducibility Results - Advanced Tab

Click the Range method variance estimate button to display a spreadsheet with the estimates for the variance components (Sigma and Sigma squared); that is, for the repeatability (error due to differences between trials), reproducibility (error due to differences between operators or appraisers), combined repeatability and reproducibility, and part-to-part variability. For computational details refer to Technical Notes.

Click the Range method percent tolerance button to display a Percent Tolerance Analysis spreadsheet, which is computed using the settings of the options on the Gage Repeatability & Reproducibility Results dialog -

Options

tab, where you specify the tolerance value for parts and the number of Sigma intervals. The computational formulas for most of these computations are described in Technical Notes. In short, the tolerance value will be used to compute the percent tolerance values, that is, to express the variability due to reproducibility and repeatability errors relative to the engineering tolerance. The number of Sigma intervals parameter will be used to determine the range of repeatability and reproducibility errors; by default (number of Sigma intervals = 5.15), this range contains 99% of the errors, assuming the normal distribution. The Percent Tolerance Analysis spreadsheet contains variability estimates and percentage values; (for an example, see ASQC/AIAG, 1990, pages 71,72).

In the spreadsheet, the first column contains the estimates of Sigma (for repeatability, reproducibility, etc.) times the number of Sigma intervals. The second column contains the percentage values (for the ranges in the first column) relative to the total (study) variation range; the third column contains the percentage values relative to the total variance (% Total Contribution), and the fourth column contains the percentage values relative to the tolerance values. If the percent of total variation range or tolerance for repeatability and/or reproducibility is less than 10%, the gage system is usually considered acceptable; percentage values between 10% and 30% may be acceptable based upon the importance of the respective application, cost of gage, cost of repairs, etc. (see ASQC/AIAG, 1991, page 127).

Note: Experiments with single trials. If the current R & R study includes only a single trial for each operator and part (i.e., it is a short study), then some of the variance components cannot be estimated. Specifically, the repeatability and reproducibility components cannot be estimated separately, and only the combined R & R component will be reported.

This check box pertains to the computation of the reproducibility variance estimate via the Range method. It is provided mostly in order to allow you to compute the appraiser (reproducibility or between-operator) variability from ranges using the two formulas widely cited in the literature (see also Technical Notes). Specifically, if the Adjust appraiser variability (AIAG) check box is selected, the variance for the reproducibility is estimated from ranges as (see ASQC/AIAG, 1991):

σ_reprod.² = (X-bar_diff/d2)² - σ_repeat²/(n*r)

In this formula, X-bar_diff is the range of the mean measurements across operators, d2 is the mean relative range (as tabulated in most industrial statistics text books; e.g., see Duncan, 1974, table D3), σ_repeat is the estimated Sigma for the repeatability, and n and r are the number of parts and trials, respectively. Some textbooks (e.g., Montgomery, 1991, page 394; DataMyte, 1992, page 6-21) use a simplified version of this formula, dropping the second part (past the minus sign) from this equation. To reproduce results compatible with the formulas reported in those text books, clear the Adjust appraiser variability check box. To produce results compatible with the ASQC/AIAGFundamental Statistical process control reference manual (referenced as ASQC/AIAG, 1991, throughout this text; see also ASQC/AIAG, 1990), select this check box (the default setting).

ANOVA method variance estimate. This button is only available if the current experiment contains more than one trial. Click the ANOVA method variance estimate button to display a spreadsheet with the estimates for the variance components (Sigma and Sigma squared); that is, for the repeatability (error due to differences between trials), reproducibility (error due to differences between operators or appraisers), combined repeatability and reproducibility, and part-to-part variability. If the No 2-way interaction check box (see below) is not selected, then a separate variance estimate will be computed for the operator by part interaction component. For all Sigma estimates, the lower and upper confidence limits (according to the Proportion for confidence interval value - see below) will also be reported. For computational details refer to Technical Notes.

This button is only available if the current experiment contains more than one trial. Click the ANOVA method percent tolerance button to create a Variance Components spreadsheet, which is computed using the settings of the options on the Gage Repeatability & Reproducibility Results dialog -

Options

tab, where you specify the tolerance value for parts and the number of Sigma intervals. In the spreadsheet, the first column contains the estimates of Sigma (for repeatability, reproducibility, etc.) times the number of Sigma intervals; the second and third column contains estimates of the lower and upper confidence limits for these ranges. The fourth column contains the percentage values (for the ranges in the first column) relative to the total (study) variation range; the fifth column contains the percentage values relative to the total variance (% Total Contribution), and the sixth column contains the percentage values relative to the tolerance values. If the percent of total variation range or tolerance for repeatability and/or reproducibility is less than 10%, then the gage system is usually considered acceptable; percentage values between 10% and 30% may be acceptable based upon the importance of the respective application, cost of gage, cost of repairs, etc. (see ASQC/AIAG, 1991, page 127).

Click the Complete ANOVA table button to display two spreadsheets (if there is more than one measurement trial; only the first one will be displayed if the current experiment involves only a single measurement trial). The first spreadsheet will report a complete ANOVA table, where all variability is partitioned into main effects, two-way interactions, and the three-way interactions. It is customarily assumed in R & R experiments that no interactions exist between parts and trials, operators and trials, or parts, operators, and trials. Thus, it is assumed that there are no interactions by trials, which appears reasonable. For example, it is difficult to imagine how the measurement of some parts will be systematically different in successive trials, in particular when parts and trials are randomized. The second spreadsheet will report an ANOVA table where only the operator by parts interaction is estimated separately (unless the No 2-way interaction check box is selected - see below), and where all remaining variability is treated as error variance. You can then perform an F test of the Statistical significance of the operator by part interaction. If significant, you may conclude that some (but not all) operators measured some (but not all) parts with systematically different results, which is usually not desirable as it contributes to the overall measurement reproducibility error. If the operator by parts variability is not significant, then you should select the No 2-way interaction check box (see below). In that case, the second spreadsheet will not contain any two-way interactions (see Technical Notes; see also ASQC/AIAG, 1990, Duncan, 1974).

The selection of the No 2-way (Operator-Part) interaction check box determines whether the operator by parts interaction will be included in the computation of the variance components and their confidence limits (see AIAG/ASQC, 1990, page 71). If the No 2-way (Operator-Part) interaction check box is not selected, then the Variance Estimate option will compute separate estimates for the operator variability and the operator by parts variability.

Enter the value that will determine the confidence interval that will be computed for the Sigma estimates (Range method variance estimate button) and Sigma spreads (Range method percent tolerance button). For computational details refer to ASQC/AIAG (1990, pages 67-71) or Duncan (1974, pages 726-730).

See also, Unbiasing Constants c4, c5, d2, d3, d4.