MSA Bias Study

What this tool does

CM8-362 tests whether a measurement system reads consistently high or low. You measure a part whose value you already know, several times, and the tool works out the average offset, its confidence interval, whether it is statistically distinguishable from zero, and whether it is large enough to matter against your tolerance.

Everything runs inside this single file — no account, no upload, no network request of any kind.

What bias is

Bias is a systematic offset: the gauge reads 0.006 high, every time, on everything. It does not average out, it is not caught by looking at your process data, and it moves every measurement you have ever taken with that gauge in the same direction — including the ones that decided whether parts were scrapped or shipped.

It is also invisible without a reference. Ten thousand readings from a biased gauge look perfectly consistent, because they are.

This is not a gauge R&R study

Different question, different exercise:

• Bias asks whether the system reads the right value. It needs a known reference. That is this tool.
• Repeatability and reproducibility ask whether the system reads the same value twice, and whether two people get the same answer. It needs several parts and several operators, and no reference at all.

A gauge can be perfectly repeatable and badly biased — that is the most dangerous combination, because everything looks under control. Run both.

Choosing the reference

Everything here depends on the accepted value being right. Three acceptable sources, recorded per reading:

• A certified standard — a master ring, gauge block or check weight with a calibration certificate.
• A value established on a measurement system an order of magnitude better than the one being studied — a CMM for a hand gauge.
• A consensus value from several systems, which is the weakest of the three and should be said out loud when it is used.

If the reference is wrong, every number in this tool is wrong by exactly that amount and nothing in the arithmetic will hint at it. This is the one assumption the statistics cannot test.

Running the study

• At least ten readings on the same reference part. The tool reports the numbers below that but refuses to draw a conclusion, because a t-test on five readings mostly detects whether you were lucky.
• One person, one gauge, one method for the core study. Mixing appraisers turns a bias study into a poor R&R study.
• Measure normally. The point is the system as used, not the system used carefully because somebody is watching.
• Record the order. A steady drift across a session is a different finding from a constant offset — usually temperature, or a gauge warming up.
• Let everything reach the same temperature. On dimensional work this is the single most common source of a spurious bias.

The arithmetic in full

Every one of these appears in the calculation table with the figures filled in, so an auditor or a customer can reproduce the result without trusting this tool at all.

What the t-test does and does not say

The test asks one narrow question: could this offset plausibly have arisen by chance if the true bias were zero? If the 95% interval does not contain zero, the answer is no and the bias is real.

Two things it does not say, both of which get misread constantly:

• Significant does not mean important. With enough readings, a bias of one micron on a tolerance of a millimetre will come out significant. It is real and it does not matter.
• Not significant does not mean no bias. It very often means too few readings. The honest reading of a non-significant result is "this study could not detect a bias", and the width of the confidence interval tells you how large a bias could still be hiding in it.

Bias against tolerance

This is the question that decides what to do:

Use process variation — six standard deviations of the process — where you know it. It is the stricter and more conventional basis, because a gauge has to distinguish parts from each other, not merely fit inside a tolerance. Tolerance is the practical fallback when process variation is unknown.

Ten percent is the usual bar for acceptable, with up to thirty accepted where there is a documented reason and no alternative. Anything above thirty is a measurement system that should not be making decisions.

Two questions, two answers

The conclusion combines both tests, and all four outcomes occur:

• Significant and above the bar — real and it matters. Correct the gauge or replace it.
• Significant but below the bar — real and small. Record it and carry on; correcting it is usually not worth the effort.
• Not significant, narrow interval — good evidence of no meaningful bias.
• Not significant, wide interval — the study proved nothing. Take more readings.

Linearity

Bias measured at one point tells you about that point. A gauge can read high at the bottom of its range and low at the top, and a single correction would then make things worse at one end.

The linearity table lists the bias at each reference value in the study and fits a slope once there are three or more. Below that it says so rather than fitting a line through two points, which would always fit perfectly and mean nothing. To study linearity properly, use at least three reference parts spread across the working range — low, middle and high — with ten readings each.

What to do about bias

In rough order of preference:

• Find the cause. Zero-setting against the wrong master, temperature, measuring force, the part not seated, a worn anvil, the wrong probe compensation. Most bias has a physical cause that can be removed.
• Recalibrate or adjust. Only after the cause is understood; adjusting out a bias caused by technique simply moves the problem.
• Apply a correction — least preferred, and only where linearity has been shown to be flat. Corrections applied by people get forgotten, and corrections applied in software get applied twice.
• Reassess what has already been measured. This is the uncomfortable one. If the gauge has been reading 30% of tolerance high for six months, some of what was rejected was good and some of what shipped was not.

Limits worth knowing

• The reference is assumed correct. Nothing here can test that.
• The t-test assumes independent, roughly normal readings. Twelve readings taken by the same person in five minutes without re-seating the part are not independent, and the interval will be too narrow.
• Bias by appraiser is shown, but two appraisers differing is an R&R finding, not a bias one.
• Resolution matters. A gauge that displays to 0.01 cannot demonstrate a bias of 0.006 in any meaningful way; if all your deviations take three or four distinct values, resolve the measurement before drawing conclusions.

Printing and sharing

The Report tab prints the tiles, charts and both tables with a title block you fill in. The calculation table is the one that satisfies an auditor, because it shows the whole method rather than a verdict.

Saving your work

Readings are held in this browser, on this computer, and stay there between visits. Use the backup button to write a JSON file you control.

Accuracy & disclaimer

The formulas and the critical values are stated in full above so every figure can be checked. This tool is not a substitute for the measurement system analysis your customer or your standard requires, and it takes no view on whether your reference, your method or your gauge is fit for the job.