GR&R Passes Every Year, but the Customer Wants a Cg/Cgk? —— Five Steps for Gauge Capability Study

When submitting PPAP for a new project, the measurement system section typically includes three GR&R reports, with %GRR all below 10%. However, the customer returned the documents with an additional note: "Please provide Cg/Cgk for key characteristics gauges." The quality engineer reviewed the entire factory's gauge ledger and found only calibration certificates and GR&R reports, none of which could answer the question, "Is this gauge itself actually qualified?"

GR&R and Cg/Cgk are not the same and cannot replace each other. GR&R (Class 2 study) evaluates the variation of the measurement system relative to process variation or tolerance, involving multiple parts and operators, naturally mixing part-to-part and operator-to-operator variations. Cg/Cgk (Class 1 study) involves repeatedly measuring a single reference part to assess the gauge's own repeatability and bias relative to the reference value. In short: GR&R answers whether the measurement system can be used to control the process, while Cg/Cgk answers whether the gauge itself can be used for the characteristic. Gauge acceptance and the release of new equipment rely on the latter.

1. What Cg and Cgk Are Looking At

Two indices, two perspectives.

Cg looks at dispersion. It compares the "part of the tolerance allowed for measurement" with the "actual dispersion of the gauge": 20% of the tolerance band is reserved for the measurement system, and the gauge's own repeatability must fall within this 20% in a 6σ range. The larger the Cg, the narrower the gauge's dispersion relative to the tolerance.

Cgk looks at dispersion plus bias. It uses half of 10% of the tolerance band as the allowable deviation, then subtracts the systematic bias between the measurement mean and the reference value. For the same data set, Cgk will always be less than or equal to Cg—whenever there is a systematic bias, the difference between the two will be greater.

The criterion is 1.33. If Cg ≥ 1.33 and Cgk ≥ 1.33, the gauge capability is qualified. If Cg is qualified but Cgk is below 1.33, it indicates that the repeatability is fine but the gauge has a systematic bias; calibration or zero adjustment should be performed followed by a re-measurement of 25 times for confirmation. If Cg itself is below 1.33, it suggests that the dispersion is too large; the gauge should be replaced or the measurement method changed, rather than勉强 using it. Some industries adopt a more lenient threshold of Cgk ≥ 1.0, but the same report must clearly state the standard used, and the two criteria should not be mixed.

2. Five Steps for Gauge Capability Study

Step 1: Select the reference part and determine the reference value. The reference part should be stable, close to the center of the tolerance or the daily processing center, and not be one that is already at the edge of the tolerance. The reference value must be provided by a higher-grade gauge or calibration certificate (CMM, higher-level metrology lab, standard part) and should never be the average value of the gauge being evaluated—this would be circular reasoning, and the bias would never be calculated, effectively making Cgk a duplicate of Cg.

Step 2: Fix conditions and repeat measurements more than 25 times. The same operator, the same reference part, the same measurement position, and continuous measurement within a short time. Twenty-five times is the minimum; for key characteristics or narrow tolerances, 50 measurements are recommended. Note that different positions on the part inherently have dimensional differences, which belong to part variation rather than gauge repeatability, so the positioning method and clamping direction must be consistent each time. All data must be retained and not deleted because it "looks wrong."

Step 3: Calculate the standard deviation, bias, and substitute into the formulas. Let the tolerance band width T = USL − LSL, s be the standard deviation of repeated measurements, x̄ be the measurement mean, and x_ref be the reference value, with bias = |x̄ − x_ref|:

• Cg = 0.2 × T ÷ (6 × s)
• Cgk = (0.1 × T − bias) ÷ (3 × s)

The Cg formula can also be read as: 6s ÷ T is the proportion of measurement variation to tolerance (%EV), and Cg is 0.2 divided by this proportion. Cg = 1.67 corresponds to %EV = 12%, and Cg = 2.0 corresponds to %EV = 10%, aligning with the interpretation criteria of GR&R.

Step 4: Interpret and handle the results. Three outcomes correspond to three actions: if both indices pass, the gauge is released; if Cg passes but Cgk does not, perform calibration or zero adjustment and re-measure 25 times for confirmation; if Cg does not pass, investigate from the directions of resolution, clamping stiffness, temperature, vibration, and operation method. If no issues are found, replace the gauge. In any case, measurement records and conclusions must be retained and not just written as "合格" (qualified) in the report.

Step 5: Update the ledger and set re-evaluation triggers. Write the Cg/Cgk conclusions into the gauge ledger and specify when re-evaluation is required: after calibration or maintenance, after gauge relocation, after changes in production processes, or when the same type of gauge is used for a new product with stricter tolerances. Without this step, Cg/Cgk would only be a one-time review document.

3. A Numerical Example

For a shaft diameter characteristic, the tolerance band T = 0.100 mm (25.050 / 24.950), and the reference part's reference value is 25.003 mm. Using the gauge to be evaluated, 25 consecutive measurements yield a mean x̄ = 25.011 mm and a standard deviation s = 0.002 mm.

• Bias = |25.011 − 25.003| = 0.008 mm
• Cg = 0.2 × 0.100 ÷ (6 × 0.002) = 0.020 ÷ 0.012 ≈ 1.67
• Cgk = (0.1 × 0.100 − 0.008) ÷ (3 × 0.002) = 0.002 ÷ 0.006 ≈ 0.33

The conclusion is not "the gauge is不合格" (unqualified), but rather "the dispersion is good, but the systematic bias is high." Cg = 1.67 indicates that the repeatability is sufficient (%EV = 6 × 0.002 ÷ 0.100 = 12%), and the issue lies in the 0.008 mm systematic bias—this is usually a problem of zero drift or calibration. After performing a zero adjustment and re-measuring, assume the mean returns to 25.004 mm and s remains unchanged, the bias reduces to 0.001 mm, and Cgk = (0.010 − 0.001) ÷ 0.006 = 1.50, allowing the gauge to be released.

This example illustrates why both numbers should be considered together: looking only at Cg would misjudge the gauge as "excellent," while looking only at the bias would not clarify whether the bias is significant relative to the tolerance. Together, Cg and Cgk distinguish between "stable but inaccurate" and "unstable and inaccurate."

4. Four Common Misuses

Using the mean of the gauge being evaluated as the reference value. The bias is defined as zero, making Cgk always equal to Cg, and completely masking the systematic bias.

Reporting only Cg and not Cgk. Qualified dispersion does not mean accurate measurement. Many gauges on the shop floor that "always measure the same result" are actually consistently biased, but no one has compared them to the reference value.

Using existing GR&R data to calculate Cg/Cgk. The data conditions for the two types of studies are different: Class 1 study involves repeated measurements of a single part more than 25 times under controlled conditions, while GR&R involves nested data from multiple parts and operators. The two indices cannot be derived from each other.

Not replacing the reference part for a long time or selecting it at the edge of the tolerance. The reference part can wear out or rust, causing the reference value to drift. Selecting a part at the edge of the tolerance can either amplify or reduce the bias, leading to distorted conclusions in both cases.

A gauge must be both "stable" and "accurate"—Cg looks at dispersion, Cgk looks at dispersion plus bias, and both indices must exceed 1.33 for the gauge to be truly accurate.

Knowledge code: 6.2.1

Version: v20261007

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