Meaning
Non-parametric calculation techniques estimate distribution bounds without assuming normal curve symmetry. The Clements percentile method uses Pearson curves fitted to sample skewness and kurtosis to determine upper and lower specification limits. Non-normal distributions in precision machining or chemical batching yield incorrect fallout predictions under Gaussian assumptions.
Calculating bounds with Pearson family curves aligns reject estimates with observed process behavior across non-symmetrical distributions.
Distribution Skewness
Asymmetrical probability functions alter tolerance boundaries when tool wear or material batching skews dimensional drift. Skewness shifts the center of probability mass relative to upper and lower limits. Applying the Clements percentile method corrects boundary estimates on the heavy tail side.
Correcting the calculation using third and fourth moment coefficients establishes accurate tolerance bounds.
Tolerance Bound
Mathematical determination of lower and upper limits provides explicit rejection thresholds for production validation. Using the Clements percentile method converts sample statistics into standardized Pearson parameters for direct mapping to target percentiles.
Operational Fallout
Yield predictions fail when non-normal tail probability is understated prior to full scale ramp up. Evaluating fallout with the Clements percentile method prevents releasing a process tool into high volume assembly with undetected scrap risks. Miscalculating boundary fallout propagates assembly mismatches into downstream production lines.
Correct calculation prevents premature tool signoff before meeting capability targets.
