Process Analysis Gage Repeatability and Reproducibility - Introductory Overview
Gage repeatability and reproducibility analysis addresses the issue of precision of measurement. The purpose of repeatability and reproducibility experiments is to determine the proportion of measurement variability that is due to 1) the items or parts being measured (part-to-part variation), 2) the operator or appraiser of the gages (reproducibility), and 3) errors (unreliabilities) in the measurements over several trials by the same operators of the same parts (repeatability). In the ideal case, all variability in measurements will be due to the part-to-part variation, and only a negligible proportion of the variability will be due to operator reproducibility and trial-to-trial repeatability.
To return to the piston ring example (see also, Sampling Plans Overviews), if we require detection of deviations from target specifications of the magnitude of .01 millimeters, then we obviously need to use gages of sufficient precision. The procedures described here allow the engineer to evaluate the precision of gages and different operators (users) of those gages, relative to the variability of the items in the population.
STATISTICA computes the standard indices of repeatability, reproducibility, and part-to-part variation, based either on ranges (as is still common in these types of experiments) or from the analysis of variance (ANOVA) table (as, for example, recommended in ASQC/AIAG, 1990, page 65). The ANOVA table will also contain an F test (statistical significance test) for the operator-by-part interaction, and report the estimated variances, standard deviations, and confidence intervals for the components of the ANOVA model.
Finally, the program will compute the respective percentages of total variation, and report so-called percent-of-tolerance statistics. These measures are briefly discussed in the following sections of this introduction. Additional information can be found in Duncan (1974), Montgomery (1991), or the DataMyte Handbook (1992); step-by-step instructions and examples are also presented in the ASQC/AIAG Measurement systems analysis reference manual (1990) and the ASQC/AIAG Fundamental statistical process control reference manual (1991).
- R & R data sheets
- To further facilitate the data entry and computations for R & R studies, STATISTICA will print and save standard R & R data sheets (see ASQC/AIAG, 1990, pages 49, 62, 63; ASQC/AIAG, 1991, pages 124, 128); those files do not need to contain any grouping or coding variables, and they can later be analyzed with this module.
- Very large designs, random effects, and components of variance
- Note that there are several other modules of STATISTICA that can also analyze these types of designs; see the section on Methods for Analysis of Variance for details. In particular the Variance Components and Mixed Model ANOVA/ANCOVA module is very efficient for very large designs (e.g., with more than 200 levels overall), or hierarchically nested designs (with or without random factors).