Evaluating Gradual Change Detection Capability and the Useful Region of Failure-Count Charts on Outgoing c=0 Reliability Test Data

Purpose: Reliability in volume production can degrade gradually with lot-to-lot variation, and monitoring this statistically requires a separate test on every lot, which costs time and money. The c=0 outgoing gate test, by contrast, is already run for lot disposition and yields a failure count for every lot. This study examines whether across-lot gradual change can be monitored from these data without additional testing and over what region such monitoring is useful.Methods: Two previously proposed charts, GCCC and Bernoulli CUSUM, were used as evaluation tools in a simulation across a range of conditions. Both charts were designed for step changes while actual degradation is gradual, and they were evaluated with those designs left unchanged.Results: Bernoulli CUSUM attained the target ARL₀ of 500 and, among the conditions where GCCC could be matched to the same ARL₀, gave a higher probability of successful detection than GCCC in all 48 combinations of gradual-change conditions. Detection capability depends on the expected number of failures per lot and on the size of the change: at a ramp length of 50, 8 of the 16 combinations of these two met the 80% usefulness criterion. A twofold increase reached 79.9% at 0.1 expected failures per lot, close to the criterion, whereas a 1.5-fold increase reached only 70.9% even at the largest value of 0.3 and did not meet the criterion. Longer ramps lowered detection and narrowed the useful region.Conclusion: A failure-count chart cannot signal before the first failed lot, which is already out of specification (OOS), so the method detects trends rather than giving early warning, and ARL₀ calibration and initial estimation require care. Where the usefulness criterion is met, a supplementary monitoring scheme can be built from gate data without additional testing.