by Paul A. Keller, CQE, CQA
As discussed in the recent column on Calibration Studies, a Calibration provides just one element of measurement uncertainty for the measurement system. Additional sources of uncertainty exist that must be separately analyzed. An R&R Study provides a technique for estimating two components: Repeatability and Reproducibility.
Repeatability is the ability of the measurement system to provide consistent readings when used by a single technician or operator on a given piece. Repeatability is sometimes referred to as Equipment Variation. Reproducibility is the ability for multiple technicians or operators to achieve consistent results, and is sometimes called Appraiser Variation.
At first glance, many of us would expect any reliable measurement system to have zero error associated with Repeatability and Reproducibility. We purchase inspection equipment, and if there is error in the measurements, there must be something wrong with the equipment. But R&R Studies measure much more than the error of the particular gage: they measure the error in the measurement system, of which the particular gage is one component.
When conducting an R&R Study, it is imperative to use production parts, or parts that are similar to production parts (such as when performing pre-production evaluations). You must not use reference standards, since the ability of the measurement system to precisely measure the standards is not a good indicator of whether the system will precisely measure parts in production. Remember the purposes of the measurement system: to evaluate the suitability of given product for release to (internal or external) customers, and/or to evaluate the stability (i.e. statistical control) and capability of the process producing the parts.
Using production parts allow us to include error associated with measurement fixturing (used to hold the part or gage during measurement), as well as variation within the production pieces themselves. Each of these generally contribute to increased Repeatability errors, since all the operators contend with these problems. However, it might be that select operators have improved techniques for dealing with the poor fixturing or the within-piece variation, so that their Repeatability error is less than the repeatability error from other operators. Recognizing this, when it occurs, can lead to system improvements, as we will see in later articles.
Of course, these techniques are not limited to mechanical inspections, nor to material parts. They can also be applied to optical inspections, chemical analyses, or any other measurement system. In chemical analyses, sample preparation may be a critical component of the measurement. Just as we use production parts above, this preparation should be done using actual product, so that sample preparation is done using “real-world” conditions.
R&R Studies are conducted by obtaining a sample of parts, and having representative operators inspect each part (called a piece) multiple times (each inspection is termed a trial). A typical study involves having 3 operators measure 10 pieces 3 trials each. The number of pieces, operators, and trials can vary from case to case, but we need multiple trials to estimate Repeatability and multiple operators to estimate Reproducibility. Multiple parts allows us to obtain better estimates of Repeatability and Reproducibility, as well as to estimate Part Variation.
When we conduct the R&R Study, keep these things in mind:
· use production pieces (see above)
· randomize the order of the pieces presented to each operator
· number each part (example 1-10), but try to keep this hidden from the operator (some operators have astounding memories!)
Repeatability Reproducibility Analysis for an example analysis.