What is measurement system analysis?
Every measurement contains error. Measurement system analysis quantifies that error so you know whether a gauge can support decisions such as part acceptance, capability studies or SPC. Accuracy is about bias, linearity and stability. Precision is about repeatability and reproducibility, which you assess with a Gage R&R study.
Type 1 gage study
Measure one master part of known value 25 to 50 times, under normal conditions. The tool calculates the bias and tests it with a one-sample t-test, and calculates Cg (repeatability against 20% of the tolerance) and Cgk (repeatability and bias). Both should be at least 1.33. Run a Type 1 study before a Gage R&R: if the gauge alone is not capable, operators cannot fix it.
Linearity and bias study
Choose about five parts whose reference values span the operating range, and measure each 10 to 12 times. The tool regresses the bias of every reading on the reference value. A slope significantly different from zero means a linearity problem; the bias at each reference is also tested. %Linearity is |slope| × 100, and %Bias compares the average bias with the process variation.
Examples
Type 1: a height gauge measures a 10.000 mm master 50 times against a 0.10 mm tolerance. Cg = 1.99 and Cgk = 1.62: the gauge is capable. The average reading is 0.0019 mm high, statistically significant (p below 0.001) but under 2% of the tolerance, so a correction at the next calibration is enough.
Linearity: an oven thermocouple is compared with a reference thermometer at 100, 150, 200, 250 and 300 °C. The bias falls from +0.35 °C at 100 °C to −1.14 °C at 300 °C, a highly significant slope (p below 0.001). A single-point calibration cannot fix this; the thermocouple needs a multi-point calibration or replacement.
How to use this Measurement System Analysis tool
- Choose the study. Pick a Type 1 study for bias and repeatability on one master, or a linearity study across the range.
- Enter the references. For Type 1, enter the reference value and the tolerance; for linearity, the process variation if you have it.
- Paste the readings. Paste the repeated readings, or reference and reading pairs for a linearity study.
- Read the results. Check Cg, Cgk and the bias test, or the slope and the bias at each reference.
- Act and export. Recalibrate or improve the gauge where needed and export the study to PDF or Excel.
Frequently asked questions
What is measurement system analysis (MSA)?
MSA evaluates how much of the variation you see in your data comes from the measurement system itself (gauge, method, operator and environment) rather than from the parts. The main properties are bias, linearity, stability, repeatability and reproducibility. The AIAG MSA manual is the standard reference.
What is a Type 1 gage study?
A Type 1 study measures one reference part (master) 25 to 50 times with the same gauge and operator. It checks bias (the difference between the average reading and the reference value) and repeatability, summarized by Cg and Cgk. A gauge is usually considered capable when both are at least 1.33.
How are Cg and Cgk calculated?
With the common VDA 5 / Bosch definitions: Cg = 0.2 × T / (6 × s) and Cgk = (0.1 × T − |bias|) / (3 × s), where T is the tolerance and s the standard deviation of the repeated readings. Some companies use 4s instead of 6s or 0.15 instead of 0.2; check your customer requirements.
What is gauge linearity?
Linearity is a change in bias across the operating range of the gauge. A linearity study measures several reference parts (typically 5) across the range, each 10 to 12 times, and regresses the bias against the reference value. A significant slope means the gauge reads differently at the low and high end.
How is MSA different from Gage R&R?
Gage R&R is one part of MSA. It measures repeatability and reproducibility using several parts and operators. Bias and linearity studies, covered by this tool, check accuracy against reference values. A complete MSA usually includes both.