Final answer:
Statistical process control uses standard deviation to determine when a process is out of control, utilizing control charts and control limits typically set at three standard deviations from the mean.
Step-by-step explanation:
Statistical process control (SPC) commonly uses the standard deviation to determine when a process diverges from its usual operational steps. The standard deviation is a statistical measure that describes the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. When utilizing tools such as a TI-83, 83+, or 84+ calculator, one would select the appropriate standard deviation symbol (σx or sx) from the summary statistics to perform the calculations necessary for SPC analysis.
To gauge control of the process, SPC makes use of control charts where the standard deviation helps to establish control limits. These control limits are typically set at three standard deviations (3σ) from the process mean. If the process data falls outside these control limits, it is an indication that the process may be out of control and intervention might be needed to correct this. By monitoring and maintaining processes within these set limits, organizations can ensure consistent quality and performance.