measurement is the foundation

The subject of “measurement” is of HUGE concern when considering “quality.” Why? Do not we simply measure our process, manipulate the data, and discover the extent of the variability? Well, it is not as straightforward as that. Actually, measurement systems themselves are RESPONSIBLE for a portion of the variation under consideration. Always. No exceptions. Only the magnitude of such error differs for various measurement systems under consideration.

Why is this? Are not calibrated gages always accurate? Precise? In a measurement system, calibration is expected (we will not delve into this subject here). However what we are considering here is repeatability and reproducibility. But is this not the same as calibration? Absolutely not. Repeatability is concerned with the ability of one operator – or in the case of on-line measurement, one system – to repeat the same set of measurements on the same parts. Of course if we present an operator with say ten parts and ask they be measured 3 times each, repeatable measurements are inevitable if the parts are measured with any pattern.

However, if the parts are randomly measured, without operator knowledge of any identification whatsoever, the measuring results will most often take on a totally different dataset. Depending upon the discrimination of the gage (how “small” a dimension it can measure), one can rest assured the measurements will not repeat. It is only a matter of the magnitude of this measurement variation – and, once again, gauge discrimination.

Conversely, reproducibility is concerned with multiple operators and multiple sets of parts. One way to tell if there is a reproducibility issue in a plant is when only a certain individual is “allowed” to make a particular measurement. All trained operators - or in-line systems – should return nearly the same measurements. It is important to note that we are considering not only the gage, but personnel and the environment. We then can elevate from a simple (and crude) “calibration” assurance to a Gage Repeatability and Reproducibility study; or a “Gage R&R.” This is the critical factor in a measurement system, as it considers all that affects that system.

Is Gage R&R really so important? Without its application – on almost any measurement system – it is not possible to know the true value of the measurements being collected. Many problems are actually exacerbated by measurement systems, especially with very tight tolerances. Without a proper Gage R&R – as part of a Measurement Systems Analysis - one is essentially “measuring in the dark.”

MSA focuses in upon the system of measurement; this is where most problem-solving efforts begin and where the most surprises occur. Very often, measurement systems that are assumed to be acceptable can easily be shown to be incapable for the task at hand; even "off-the-shelf" solutions. Do not take our word for it: have us come in and perform MSA on one of your systems.

A Gage R&R incorporates many factors, such as calibration (traceability to a standard), linearity (“accuracy” within a range of measurement values), discrimination (how “fine” is the measurement), bias (whether the measurement consistently differs from a standard), the sop as performed by operators, the environment in which the measurement is taken, and the precision to tolerance ratio (how the GR&R relates to a stated customer specification).

Repeatability focuses upon one operator’s ability to consistently measure the same set of parts. Intuition might say this is a moot point, but the experience of Genesis shows that this is a very important factor, especially if the operator is given the parts in continuous random order, thereby not having knowledge of which part is being measured. (The operator will not know what his last measurement was of that particular part, so will not be unduly influenced by such).

Reproducibility is concerned with the ability of multiple operators to consistently measure multiple sets of parts. This helps negate the role of “feel” or subjectivity in a measurement system. It is also important within this phase of the analysis to maintain anonymity among parts, but also among the measurements from each operator: operators are not privy to each other’s measurements until the end of the analysis.

Shown at the left is MiniTab (http://www.minitab.com) output showing a “poor” GR&R: the %R&R is responsible for most of the measured variation in this study. The actual measured Part-to-Part variation is very low: this measurement system is useless.

- click here to view the math behind gr&r -

Conversely, on the right is an example of a “good” GR&R: the measured Part-to-Part variation is very high, which is desirable. We want to be assured that most of the variation we are measuring is actually coming from the parts, not the measurement system.

- click here to view the math behind gr&r -

Total GR&R is a measure of the percentage of variation contributed by the measurement system over the samples examined during the study. It does not address the specification – or tolerance – that must be held.

Shown at the left (top) is a normal curve illustrating the variation that might be measured during a GR&R study; it is usually 5.15 x the standard deviation (explained later). The 20%, 50%, and 75% r&r shown pictorially represent several possible variation levels – any value is possible - caused by the measurement system itself; the rest of the variation actually comes from the parts. Notice though, that there has not yet been mention of an actual specification, or tolerance.

All we can know from this data is that over the range of parts we have measured at the discrimination (“fineness” of the gage available) we have used, is the %r&r, or what the gage has contributed to that measured variation. Now we must look at the next step and consider our actual specification.

Enter the concept of % tolerance (or precision to tolerance ratio), which takes that same measurement system variation and compares it to the actual required tolerance. THIS IS SEPARATE AND DISTINCT FROM THE %R&R. Shown on the right are three examples of possible p/t ratios. NOTICE THE TOLERANCE IS SIMPLY A LINEAR MEASURE; IT IS NOT A STATISTICAL DISTRIBUTION.

If somehow by (incredible) chance our actual required tolerance is equal (or close enough) to the measurement system variation, the amount of tolerance we have “used up” via this variation will equal the %R&R, as illustrated here at the left.

However, the chances of that happening are slim and none.

Looking at the two equations on the top line on the right, we see that %R&R and %tolerance are mathematically two different measures. Looking further into the ratio between the two, we have the equation in the middle, algebraically simplified, which leads us to the last equation, illustrating the LACK OF A LINEAR RELATIONSHIP BETWEEN THE TWO.

As shown on the left, If we are fortunate enough to have the actual required tolerance exceed our measured variation, the %tolerance will be less than the %R&R, which is “good” (assuming the %R&R was “acceptable” to begin with).

However, if the inverse is true (the required tolerance is less than the measured variation) this will work against us. The %tolerance may or may not be “acceptable” even if the %R&R was. It all depends upon how “tight” is our tolerance; this is illustrated on the right.

- click here to view the math behind gr&r -