Pneumatic-Trainer Leak-Rate Estimation in Engineering Education Fluid-Power Laboratories: A Pressure-Decay Evaluation Linking Seal-Compression Loss to Circuit-Response Reliability Bounds

Leak-rate estimation in student fluid-power laboratories is typically treated as a maintenance concern rather than a measurement problem, yet the pressure-decay test that underpins it is itself a statistical design whose operating characteristics are rarely characterised. The analysis is a replication-based evaluation of the before-after-control-impact estimator under a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), with power estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The results indicate that 52 clusters are required to detect a 5-percentage-point effect at 80% power, and that the minimum detectable effect falls steeply as cluster count rises from 8 to 32. The framework proposes that seal-compression loss be treated as a circuit-level covariate whose decay signature bounds the reliability of downstream response measurements, and it specifies the conditions under which pressure-decay estimates can be trusted in teaching laboratories. The contribution is a design-theoretic account of leak-rate estimation that replaces ad hoc pass/fail thresholds with explicit power and detection bounds.