MSA: Not Just a GR&R? —— Five Steps to Implement Bias, Linearity, and Stability Analysis

1. GR&R Passed, but the Gauge Made Two Shifts into Rivals

A certain electronics factory was inspecting the height of connector terminals. The gauge's GR&R report was always qualified, with %GRR only at 8%, and audits found no issues. However, after the shift change, a batch of parts deemed qualified by Shift A was re-measured by Shift B using the same gauge, and 5% were found to be out of tolerance. The two shifts argued every day. After thorough investigation, it was found that the gauge was calibrated within its validity period, but the problem lay in the "hands": the experienced workers in Shift A were accustomed to placing the parts lightly and reading the measurement, while the new workers in Shift B pressed the parts down firmly, causing a systematic shift of 0.02mm in the readings.

Ironically, the impressive GR&R report was based on sampling only the two "most stable hands" of the veteran employees, completely ignoring the new workers—naturally, the variation was small, but the real measurement system didn't work that way.

This is the most common blind spot in MSA. GR&R only answers whether the "repeatability and reproducibility variation is small enough," but it doesn't address three more hidden issues: how much the measurement results are biased overall (bias), whether the bias is consistent across different segments of the measurement range (linearity), and whether the bias remains stable over time (stability). Many companies treat MSA as "submitting one GR&R report per year," skipping these three crucial analyses. As a result, the data looks good, but decisions still go wrong. In essence, GR&R is just one indicator in a "health check package"; treating it as the entire health report is a fundamental misunderstanding.

2. The Three Skipped Analyses Each Guard Against a Hidden Risk

• Bias: The difference between the average measurement and the reference value, guarding against "systematic deviation." Even if the variation is small, a 0.02mm overall bias will cause all judgments to err in the same direction.
• Linearity: Whether the bias is consistent across the entire measurement range, guarding against "accurate for small parts, inaccurate for large parts." If the bias varies significantly at different ends of the measurement range, it indicates that the gauge is unreliable in certain intervals.
• Stability: The degree to which the bias drifts over time, guarding against "accurate today, inaccurate next month." Wear, temperature drift, and aging can cause the gauge to gradually deviate.

In short, GR&R manages "variation," while these three analyses manage "accuracy, consistency, and stability." Missing any one of them means the reliability of the measurement system is incomplete.

When should these three analyses be performed? The frequency is low, but the timing is critical: bias and linearity should be conducted when a new gauge is first put into use or after major repairs. They should be redone when the gauge is relocated, the operating method is changed, or environmental conditions significantly change. For gauges that are prone to wear and drift, stability must be continuously monitored. Additionally, when the same part is repeatedly judged as "marginally out of tolerance" or when different people in different shifts consistently disagree, it often indicates that these three analyses are sounding the alarm.

3. Five Steps to Implement the Three Analyses

Step One: Establish the Reference Before Measuring. Before taking any measurements, confirm whether the gauge's resolution is sufficient (generally, it should not exceed 1/10 of the tolerance). If the resolution is insufficient, all subsequent analyses will be based on a "blurry" ruler. Next, establish the reference: both bias and linearity must be compared to a "true value." The true value should be obtained from a higher-level metrological standard or a calibrated sample (such as a standard block with a nominal value of 10.000mm). It is crucial not to use the value measured by your own gauge as the reference, as that would be circular reasoning.

Step Two: Conduct Bias Analysis—One Sample, Multiple Measurements, Compare Averages. Select a reference piece that falls within the commonly used measurement range segment. Have the same person use the same gauge to measure it more than 10 times, then calculate the difference between the average value and the reference value. Perform a one-sample t-test on the difference: if the confidence interval crosses 0, the bias is not significant and acceptable; otherwise, evaluate whether to correct the readings or replace the gauge.

Step Three: Conduct Linearity Analysis—Multiple Standard Pieces, Across the Range. Select 3 to 5 standard pieces that cover the low, medium, and high segments of the measurement range. Measure each piece several times, calculate the bias at each point, and observe the trend of bias across the measurement range. Ideally, the bias should be independent of the measurement range. If the bias monotonically increases or decreases with the measurement range, it indicates that the gauge is only reliable in certain intervals, and the usage range should be limited or linearity compensation should be applied.

Step Four: Conduct Stability Analysis—Same Reference Piece, Periodic Re-measurement. Use a stable reference piece and measure it several times at regular intervals, such as weekly or monthly. Plot the average values over time (mean chart or range control chart). If the average value of any period falls outside the control limits, it indicates that the gauge has drifted, and immediate calibration, repair, or a shortened calibration cycle is required.

Step Five: Translate Conclusions into Management Actions, Not Just Reports. If the bias is significant, correct the readings or limit the measurement range; if the linearity is poor, label "only applicable to the X～Y range"; if the stability has deteriorated, reset the calibration cycle or increase periodic verification. The analysis itself does not generate value; the value comes from changing the usage and calibration rules of the gauge.

Returning to the initial case: the company conducted additional bias analysis and confirmed that Shift B had a systematic downward pressing bias. They then wrote "light placement and reading" into the work instruction and installed a poka-yoke limit, which eliminated the measurement discrepancies between the two shifts.

4. Four Common Misunderstandings

Misunderstanding One: A Qualified GR&R Means a Qualified Measurement System. GR&R only covers variation, while bias, linearity, and stability are separate dimensions. A "qualified" system is incomplete if these three are missing.

Misunderstanding Two: A Qualified Calibration Means No Need for Bias and Linearity Analysis. Calibration ensures that the gauge itself is traceable, but it does not guarantee accuracy under your actual usage method, measurement range segment, or environmental conditions.

Misunderstanding Three: Performing Each of the Three Analyses Once is Enough. Bias and linearity can be periodically re-evaluated, while stability must be continuously monitored, especially for gauges that are prone to wear and drift.

Misunderstanding Four: "Non-significant Bias" is a Free Pass. The significance of bias is a statistical judgment, and the sample size and sampling interval can influence the conclusion. To truly manage the gauge, it is crucial to standardize the measurement method, clearly document the work instructions, and include critical gauges in periodic verification.

5. One Sentence Summary

GR&R answers whether the "variation is small enough," while bias, linearity, and stability answer whether the system is "accurate, consistent, and stable." First, use standard pieces to establish the reference, then sequentially perform bias, linearity, and stability analyses, and finally, translate the conclusions into gauge usage and calibration rules. Only then is MSA truly closed-loop.

MSA is not just about one GR&R report; bias, linearity, and stability are the other half of the measurement system.

Knowledge code: 6.2.1

Version: v20260910

Author: QTank QTank is dedicated to providing systematic professional knowledge, methodologies, and practical tools for quality management practitioners, helping companies continuously improve their quality capabilities.