Measure: Baseline, MSA, and Capability
Measure: Baseline, MSA, and Capability
Measure establishes a trustworthy baseline: the measurement system must be adequate, the sample must represent the process, and the process must be stable before capability is judged. The exam tests data types, sampling, Gage R&R, attribute agreement, Cp/Cpk, DPMO, and RTY.
Core rules and concepts
- Operational definition: unambiguous procedure for assigning a value, including equipment and decision criteria.
- Data types: continuous (time, length, concentration) versus discrete (pass/fail, count). Match the tool to the type.
- Sampling: define population, frame, size, frequency, and randomization; avoid convenience samples and non-independent subgroups.
- MSA: for continuous data use Gage R&R; %study variation below 10% is acceptable, 10-30% conditional, above 30% unacceptable; number of distinct categories (ndc) of 5 or more is desirable. For attribute data use attribute agreement analysis.
- Stability first: use a control chart to confirm a stable baseline; capability indices are misleading for unstable processes.
- Capability: Cp/Cpk use within-subgroup variation; Pp/Ppk use overall variation. Cpk penalizes centering. Common minimum is 1.33; 1.67 for critical characteristics.
- DPMO = defects / (units x opportunities) x 1,000,000. RTY = product of step yields.
Worked example
A filling process has mean 10.0 oz, s = 0.5, LSL 8.5, USL 11.5. Cpk = min(11.5-10.0, 10.0-8.5)/(3 x 0.5) = 1.5/1.5 = 1.0. That is below 1.33, so the process is not capable. But Gage R&R %SV = 28%: the measurement system is conditional at best. Reasoning: fix the gauge or fixture and retrain before trusting the 1.0; a noisy measurement system can understate or overstate capability.
Traps that cost marks
Calculating capability before stability, using %tolerance when %study variation was asked, skipping attribute MSA, treating control limits as specification limits, and reporting sigma level without checking conversion assumptions.