Measurement system analysis (MSA) or Gage R & R is a method that is used to determine whether the measurements from a process are valid. Several parts are measured repeatedly by different tools or operators, and the results are analyzed statistically. The analysis is usually performed using measurement system analysis software, that produces a graphical and text summary of the results. Variance is linked to the variance - the standard deviation squared. Throughout this article, σ² means the "variance".
MSA Total Variability: Repeatability and Reproducibility
The variation produced by the measurement tools should be small compared to the variation produced by the parts. The MSA calculates how much of the variation comes the parts, and how much comes from the machine / tool / operator. There are two main types of gauge error:
Repeatability - how much variation is there when the same part is measured by the same person on the same machine
Reproducibility - how much variation is caused by using different operators, machines, set-ups, long-term variation etc.
Measurement System Analysis Set-Up
When setting up a gauge study, there are three main points to remember that will greatly increase the effectiveness of the study:
1. Number of parts × number of operators / machines × (number of measurements per setup -1) should be at least 30.
2. Choose parts that represent the full range of likely measurements. For example, if parts from the process usually measure 100 to 150 units, do not select parts for the gauge study that are all in the range 120 to 130
3. Randomize the order of measurement, where possible
Measurement System Analysis Definitions and Equations
Precision = σ²[repeatability] + σ²[reproducibility]
Tolerance = Upper Specification Limit - Lower Specification Limit
Resolution = Number of decimal places that the measurement system uses. e.g. No point using millimeters to measure the width of a hair
The basic mathematical relationship that defines the gauge capability is:
σ²[total] = σ²[parts] + σ²[repeatability] + σ²[reproducibility]
Note that σ²[measurement system] = σ²[repeatability] + σ²[reproducibility]
To evaluate whether a measurement system contributes significantly to the overall process variation, the P / T (Parts to Tolerance) ratio is used:
P / T = 6 × σ[measurement system] / Tolerance. Usually stated in percentage form, this is just a way to ask "how much of the specification is taken up by variation due to the measurement system?"
%R & R = 100 × σ²[measurement] / σ²[total]. Usually stated in percentage form, this is just a way to ask "how much of the total variation is due to the measurement system?"
Measurement System Analysis Summary
Measurement System Analysis software is used to decide how much of a process variation is due to the actual measurement system, compared to the parts that are being measured. It is desirable that the P/T ratio and %R&R are as small as possible. This is because no improvements to a product can be attempted before checking whether the measurement values being produced can actually be believed.
Gauge R&R References
" The Lean Six Sigma Pocket Toolbook: A Quick Reference Guide to 100 Tools for Improving Quality and Speed" by George, Maxey, and Rowlands, is a handy short reference, and the equations in the section on measurement analysis were used in this article.
Martin Bell - Martin holds a B.Sc. degree in chemical engineering, and an M.Sc. degree in electronics and computing. He has spent more than 25 years ...
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