Final answer:
The most accurate statement is that tolerances are mathematically defined while control limits are statistically determined. Tolerances involve design requirements, and control limits reflect process variation used in quality control charts.
Step-by-step explanation:
The statement that is most accurate regarding tolerances and control limits is that tolerances are typically mathematically defined specifications that products must meet during the manufacturing process, whereas control limits are statistically determined boundaries used in process control charts to determine the natural variability of a process. Therefore, the correct answer is that tolerances are typically mathematically defined whereas control limits are typically statistically defined (option 4). It is important to distinguish between the two, as tolerances relate to design requirements and control limits are associated with the process variation.
To elaborate, tolerances are the permissible limits of variation in a physical dimension or physical property of a material. They are established by design specifications and do not change unless the design specification changes. In contrast, control limits, which appear on control charts, are calculated from the process data and provide a visual representation of the process variation over time. They help to determine whether the process is in 'control' or if there is an assignable cause for variation that needs investigation.