Final answer:
A statistical process control (SPC) tool, such as a control chart, is used in manufacturing to track the mean diameter of tubing to ensure product quality and consistency.
Step-by-step explanation:
Understanding Statistical Process Control in Manufacturing
A manufacturing process that produces copper tubing would utilize a statistical process control (SPC) tool to track the mean diameter of the tubing. This tool is typically a control chart, which is used to monitor whether the process is in a state of control by tracking specific sample statistics over time.
For example:
- A manufacturer produces screws with specified diameter measurements.
- The screws have a uniform distribution within a certain range.
- Using the central limit theorem, if sample sizes are sufficiently large, the distribution of sample means will approximate a normal distribution.
This analysis would involve calculating the mean diameter and standard deviation for the sample, as well as finding the probability of a sample being within stated tolerance levels. Such data provides insights into the consistency and reliability of the manufacturing process and whether the company's diameter claims are plausible.
By applying statistical tools and principles, manufacturers can maintain quality control and ensure their product meets the necessary specifications.