Capability Index
Statistical evaluation of manufacturing limits determines how closely a process runs to its design specifications. When used on the factory floor, cpk calculation measures the relationship between process variability and the width of the tolerance band. It establishes a quantitative score that predicts the likelihood of producing out-of-specification circuit boards.
Mathematical Formulation
The formula utilizes both the process mean and the standard deviation to evaluate the distance from the average performance to the nearest specification limit. A high standard deviation narrows the index, showing that the process is closer to producing scrap material. Production engineers calculate this value by taking the minimum of the upper tolerance minus the mean divided by three standard deviations, and the mean minus the lower tolerance divided by three standard deviations.
This dual-sided calculation ensures that both drift and spread are reflected in the final output.
Process Analysis
Modern surface mount placement lines require a minimum score of one point three three for standard components and one point sixty-seven for critical assemblies. A lower score demands immediate recalibration of the pick and place machines to prevent defective boards. Continuous monitoring of this index maintains quality levels without 100 percent manual inspection.
