Final answer:
Machine Two has a higher capability index due to its smaller standard deviation indicating better consistency in meeting specifications compared to Machine One.
Step-by-step explanation:
Machine capability index, denoted as Cpk serves as a crucial metric in assessing the performance of manufacturing processes. It evaluates how well a process adheres to specified limits considering both the mean and standard deviation.
In this context the capability index is calculated by taking the minimum of the Cpk values corresponding to upper and lower specifications. Machine One and Machine Two both fall within the specified limits with means of 0.411 and 0.4105 respectively.
However the distinction lies in their standard deviations. Machine Two boasts a smaller standard deviation of 0.0005 as opposed to Machine Ones 0.0006.
A smaller standard deviation implies less variability in the manufacturing process leading to a higher Cpk. In practical terms this suggests that Machine Two demonstrates superior consistency in producing parts within the prescribed tolerances compared to Machine One.
Therefore the choice of Machine Two over Machine One aligns with the goal of achieving a more robust and reliable manufacturing process.