Cpk and Gage R&R for Mark Contrast and Adhesion Measurement

Cpk and Gage R&R for Mark Contrast and Adhesion Measurement

Key Takeaways

• Qualify the measurement before the process. A capability index calculated with an incapable gauge is arithmetic, not information.
• Destructive tests need matched-sample designs, because the same specimen cannot be measured twice.
• Attribute methods have their own agreement study — classification schemes are gauges too.
• Capability assumes stability. Compute Cpk on a process that is in control, or the number describes nothing repeatable.

Capability studies on decorating and marking processes are often performed diligently and interpreted incorrectly, because a step is skipped. The measurement system is assumed to be adequate, capability is computed from the observed variation, and a disappointing index is attributed to the process. Frequently most of that variation belongs to the gauge.

Observed Variation Has Two Sources

Every measurement contains process variation and measurement variation combined. Where the measurement contributes a large share of the total, several practical consequences follow immediately: capability indices are pessimistic, acceptable parts are rejected and unacceptable ones accepted, process changes cannot be detected reliably, and improvement effort aimed at the process produces no visible result because the noise dominates.

Establishing the split is the purpose of measurement system analysis, and doing it first changes what the subsequent work should be. A process whose measurement consumes most of the tolerance does not have a process problem yet; it has a metrology problem, and fixing that is usually cheaper.

The Destructive Test Problem

Standard gage repeatability and reproducibility studies rely on measuring the same part several times. Adhesion testing destroys the specimen, so the design has to change.

The usual approach is matched samples: parts produced adjacently under conditions as identical as achievable are treated as a group of nominally equivalent specimens, and the analysis compares variation within groups against variation between operators and between groups. The assumption of equivalence within a group is load-bearing, and any genuine part-to-part variation inside it will be attributed to the measurement system.

That is a limitation to state rather than to hide. It means destructive-test gage studies establish an upper bound on measurement variation rather than an exact value, which is still useful — if the upper bound is acceptable, the measurement is adequate.

Attribute Methods Are Gauges Too

Adhesion classification schemes and visual mark assessments are measurement systems, and they deserve the same scrutiny. An attribute agreement analysis presents assessors with a set of parts spanning the acceptance boundary, repeated in randomised order, and records whether each assessor agrees with themselves on repeat presentation and with the other assessors.

Results on borderline parts are routinely worse than people expect, and that is precisely the region where acceptance decisions are made. Where agreement is poor, the corrective options are better reference standards, clearer classification criteria, training against known samples, or replacing the attribute method with an instrumental one.

The Specific Measurements

Mark contrast. Instrumental measurement is reproducible provided the conditions are fixed: instrument type, illumination geometry, aperture, and measurement location relative to the mark and to a defined background reference. Surface texture, curvature and gloss all affect readings, so parts with three-dimensional marked surfaces need a defined fixturing arrangement as part of the method.

Code verification. Machine-readable code grading to a recognised standard is among the better-behaved measurements in this area, because the standards specify aperture, wavelength and geometry tightly. Repeatability is generally good; reproducibility between different verifier models is less so, which is why the specification should name the equipment class.

Adhesion. Tape and cross-hatch methods are sensitive to tape lot, application pressure, dwell and removal rate and angle. Pull-off testing is more quantitative but sensitive to dolly alignment, adhesive cure and loading rate. Both benefit substantially from fixturing that removes operator technique from the result.

Surface energy. Dyne testing is fast, inexpensive and technique-dominated: ink age, applied quantity, reading interval and the operator’s judgement of when a film has broken all shift the answer, and the stepwise nature of the ink set limits resolution. Where surface energy is a controlled parameter with a tight window, contact angle instrumentation gives resolution and repeatability that dyne inks cannot.

Capability Requires Stability First

A capability index computed on an unstable process describes a mixture of states rather than a process, and it will not predict future output. Control charting the measurement over a period, confirming the absence of shifts, trends and special causes, is a prerequisite rather than a refinement.

Distribution shape matters as well. Adhesion and contrast data are frequently skewed or bounded — a classification scale has a ceiling, contrast has physical limits — and normal-theory indices applied to strongly non-normal data can be substantially wrong in either direction. Plotting the data before computing anything is the cheapest safeguard available.

Most requirements here are one-sided: contrast above a minimum, adhesion above a threshold, surface energy above a level. The appropriate one-sided index applies, and it is worth stating explicitly which limit is being assessed rather than reporting a two-sided figure computed against an invented upper bound.

What to Do With a Poor Result

A weak capability result has three possible owners and the analysis should identify which. If measurement variation dominates, improve the measurement — fixturing, method discipline, better instrumentation, training. If the process mean sits close to the limit, centre it, which is usually the cheapest of the three. If process variation is genuinely wide, the sources have to be found, and for these processes they are typically material lot variation, treatment coverage and consistency, part-to-part geometry differences, and drift between maintenance intervals.

Distinguishing those three cases is the entire value of doing the measurement analysis first. Without it, every poor capability number produces the same response — tighten the process — and roughly a third of the time that response is aimed at the wrong thing.

Sampling That Reflects the Real Sources of Variation

A capability study is only as representative as the parts that went into it, and studies on decorating lines are frequently run on a single production run, from a single resin lot, on a single shift, with one operator, in a single week. The resulting index describes that run rather than the process.

The variation that actually matters on these lines is between resin and colourant lots, between cavities on a multi-cavity tool, between fixture positions, between shifts and operators, and across maintenance intervals. A sampling plan that deliberately spans those sources gives a capability figure that predicts future output; one that holds them all constant gives an optimistic number that will not be reproduced.

The practical approach is a rational subgrouping scheme: small subgroups taken frequently enough to capture short-term variation, over a period long enough to include the lot and maintenance cycles. It takes longer to complete than a single-run study and it is the difference between a number that supports a decision and a number that supports a report.

Related Reading

• Writing an Enforceable Specification
• IQ, OQ and PQ for Laser Marking
• Proving a Specification Was Met
• Dyne Testing and Surface Energy
• FMEA for a Marking or Decorating Line

Need help with this?

The Sabreen Group provides independent engineering support for measurement system analysis and process capability studies for decorating operations. Our engineering services team works with manufacturers on process development, material qualification and production troubleshooting. Contact us to discuss your application.

Frequently Asked Questions

Why does measurement system analysis come before capability?

Because observed variation is the sum of process variation and measurement variation. If the measurement system accounts for a large share of the tolerance, the calculated capability index mostly describes the gauge, and improvement efforts aimed at the process will not move it. Qualifying the measurement first tells you which problem you actually have.

How is gage R&R performed on a destructive test?

By using matched samples in place of repeated measurement. Parts produced adjacently under identical conditions are treated as nominally identical, and the analysis compares within-group and between-operator variation. The assumption that the group members are equivalent is doing real work and should be stated, because part-to-part variation within the group appears as measurement variation.

Do visual classification methods need this treatment?

Yes. A classification scheme such as a cross-hatch adhesion rating is a gauge, and an attribute agreement analysis establishes whether assessors agree with each other and with themselves on repeat viewing. Disagreement rates on borderline parts are frequently high and are worth knowing before the method is used for acceptance.

What makes surface energy measurement hard to qualify?

Dyne testing is quick and technique-dependent: ink age, application quantity, reading time and operator judgement all shift the result, and the measurement is stepwise rather than continuous, which limits resolution. Contact angle instruments give better resolution and repeatability where the application justifies them.

Is Cpk meaningful for a one-sided specification?

It is, using the relevant one-sided index, since most marking and adhesion requirements are minimum-only — contrast above a threshold, adhesion above a value. What matters more is that the process is stable and the distribution is understood, since adhesion and contrast data are frequently skewed and normal-based indices can mislead.

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