FEATURED ARTICLE
# About Measurement System Analysis (MSA)

### Errors

### Analytics for Gauge R&R

### Effect of these errors

### The need for a Measurement System Analysis (MSA)

Measuring some characteristic is done with measuring equipment, also called a gauge. A gauge can be defined as an instrument that measures and display the value of something. Examples of something include weighing scales, thermometers, calipers, refractometers, rulers, viscometers and countless more.

No measuring device is perfect. There will always be a small amount of error, some due to faults and imperfections with the equipment, some due to robustness problems with ambient conditions, some due to inadequate training, and many other reasons, hence the reason for a **measurement system analysis**.

There are five major types of error.

**BIAS**

Bias in the measurement system analysis (MSA) is the difference between the average of measured values and the actual value of a part. The actual value of the part is called the reference value. Ideally the bias should be zero

The above image shows the variation in the different measurements on the same part and the deviation of the average from the reference value. In this instance the bias is negative.

Bias can be dependent on the actual measured value. A Linearity is normally used to identify this dependency. However, bias may also be partially random, or follow some nonlinear patter. This is usually due to faulty instruments

Bias can have the most significant effect on the reliability of the reported measurement values.

**REPEATABILITY**

Gauge repeatability in a measurement system analysis (MSA) is a measure in terms of standard deviations of how close repeated measurements on the same part using the same gauge by the same appraiser are. It is not about closeness to target (accuracy) which is about bias. It is about precision. The first two images below show similar close clustering, but even though one is off target, the repeatability is similar. The third image shows bad repeatability.

**APPRAISER REPEATABILITY-REPRODUCIBILITY**

Historically this error has generally been ignored, possibly because it was not understood.

Gauge repeatability standard deviation is not necessarily due to the instrument alone. Repeatability can be appraiser dependent, i.e. repeatability is not reproducible by different appraisers. Some appraisers may obtain poorer repeatability than others. This is analogous to different shooters using the same rifle or bow and arrow. Some shooters will have greater scatter than others, even though all use the same ‘equipment’.

A Gauge R&R study must include a test for repeatability when performing a measurement system analysis (MSA). The analyst should not assume that each appraiser has the same variability. Sometimes the reason for the difference is simply training. For example, one tester may not wait for scales to stabilize which will cause greater variability. Another tester may not have steady hands causing variability with calliper measurements.

**EQUIPMENT REPEATABILITY-REPRODUCIBILITY**

Different measuring devices used to measure the same characteristic can have different repeatability, i.e. repeatability may not be reproducible using different measuring devices, even if the same model.

**APPRAISER REPRODUCIBILITY**

An appraiser reproducibility analysis concerns itself with differences in bias. There are two types of bias. Once is due to the instrument itself and the other is due to appraisers. If the bias is due to the instrument only, then all appraisers will obtain the same bias. Appraiser reproducibility analysis will identify differences in bias caused by appraisers. For this type of analysis, it is not necessary to know the reference value. Just establishing differences in the average measurements obtained by the appraisers establishes differences in bias. If that is the case, then the instrument may not be robust to different appraisers or some appraisers have not been trained enough.

To explain why appraiser reproducibility is actually bias reproducibility consider a part with reference value 10.0 Appraiser 1 obtains an average of 11.0 and Appraiser 2 an average of 10.0. By definition of Bias, Appraiser one has a bias of 1.0 and Appraiser 2 a bias of zero. Reproducibility is thus about bias.

**EQUIPMENT REPRODUCIBILITY**

Historically Gauge R&R has been about appraiser variation only and pure instrument variability, with little consideration to variation between instruments, or equipment, yet instrument variation can be a big component of variation. It is common for companies to have several measuring devices to choose from to measure the same characteristic. It is important that consistency between the different devices are tested for.

Gauge R&R has prior to the availability of modern computing power and software been performed mainly by using control charts. These are time consuming to apply and have several problems associated with them, which are beyond the scope of this article.

Today Gauge R&R is often performed with Analysis of Variance, Analysis of Co Variance and Regression Analysis applied to at least the following applications:

"Attributes Studies; Bias (Simple); Gauge Capability & Repeatability; Gauge Performance; Gauge R&R (One Equipment; One Part; Multiple Appraisers); Gauge R&R (Multiple Equipment; One Part; One Appraiser); Gauge R&R (Multiple Parts; One Equipment; Multiple Appraisers); Linearity; Repeatability-Reproducibility; Stability; Bias (One Equipment; One Appraiser; Multiple Parts); Bias (Multiple Equipment; One Appraiser; One Part); Bias (Multiple Parts; One Equipment; Multiple Appraisers); Gauge R&R (Multiple Equipment; Multiple Appraisers; One Part); Linearity (Bias) (Multiple Equipment; One Appraiser); Nested Gauge R&R (Multiple Equipment; Multiple Appraisers; One Part)"

There are some important considerations. One is the assumption of normality which normally holds. The other is the variance model. Three types of models can be applied. One is pure random, where all effects, such as appraiser effects are random. The same goes for equipment effects. Another model is fixed and a third is mixed. The random model seems to be predominantly used. The random model may however, not be the most appropriate. If a company uses three appraisers all the time, not randomly selected from a pool of appraisers, then a fixed model is more appropriate which affects significance testing and Gauge R&R statistics. The same applies to equipment.

The effect of these errors depends on the magnitude of errors. Several authors have concluded that if the Gauge R&R Sd is less than 20% the effect on process capability is negligible. Our own research has shown similar. Indeed, a measurement error as high as 50% of the process standard deviation does not have a major impact. This assumes a normal distribution and a random appraiser effects model. If a fixed appraiser effects or equipment effects model is used the effect on process capability becomes more significant.

As the norm appears to be using a random-effects model the effect on process capability analysis can be underestimated. But if the effect is fixed, the effect can be quite significant. The magnitude of the effect can be estimated with the BISNET Special Analysis App.

The following simulations demonstrate the effect of 20% Gauge R&R on the Cp index

Process Capability Histogram without measurement error
Cp = 1.30

Process Capability Histogram with Measurement Error added equal to 20% of the process variation.
Cp =1.29

Although the effect on process capability is relatively small if the Gauge R&R Sd is even up to 50%, it cannot be assumed that the measurement error is low. There are many case studies where measurement error was equal to the process variation.

The purpose of a measurement system analysis (MSA) is to provide assurance that the Measurement System is adequate. Once adequacy has been established an MSA needs to be performed periodically to identify deterioration in the Measurement System and whether there is a need to retrain appraisers or service existing measurement devices.

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