The process of determining the central tendency and variability within subgroups of continuous data, and subsequently charting these values to monitor process stability, involves several key calculations. The average value, representing the arithmetic mean of the data points within each subgroup, must be computed. Furthermore, either the range, representing the difference between the highest and lowest values in each subgroup, or the standard deviation, measuring the dispersion of the data around the mean, must be calculated. These values form the basis for establishing control limits on a graphical representation.
Monitoring process averages over time allows for the detection of shifts or trends that may indicate a process is becoming unstable or moving out of acceptable control limits. This enables proactive intervention to correct any issues before defective products are produced. This form of monitoring is fundamental to statistical process control, a methodology with roots in manufacturing quality control during the early 20th century, designed to improve product consistency and reduce waste.