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A comparison of engineering specifications to chance causes of variations is done using which Six Sigma tool?

Design of experiments

Analysis of variance

Pareto analysis

Process capability study

The tool used for comparing engineering specifications to chance causes of variations is a process capability study. This study assesses how well a process can produce output within specified limits, thereby evaluating the capability of a process to meet or exceed those engineering specifications. It involves statistical analysis to determine the degree of variation in the process and compares that variability to the specifications established.

In a process capability study, key metrics such as Cp, Cpk, Pp, and Ppk are calculated to quantify the capability of a process. By analyzing these figures, one can understand whether the inherent variability of the process (which includes chance causes) falls within acceptable limits defined by the engineering specifications. This information is crucial for identifying whether a process is stable and under control, making it essential for quality management in Six Sigma.

Other tools mentioned serve different purposes. Design of experiments focuses on understanding how different variables influence outcomes to optimize processes. Analysis of variance examines differences between group means, but it doesn't specifically assess process capability against engineering specifications. Pareto analysis is employed to prioritize problems based on their frequency or impact, which again does not directly correlate with the comparison of process variability and engineering specifications.

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