SPC sampling: subgroup size and frequency for control charts

How many parts per subgroup and how often to sample: rational subgroups, how subgroup size changes the chance of detecting a shift, how many subgroups you need for limits and how to choose the interval.

Updated 2026-10-28

Start with the rational subgroup

A subgroup is a small set of parts measured together. It is rational when the variation inside it is only the everyday (common cause) variation and any change over time, such as tool wear, a new material lot or a new operator, shows up between subgroups. That is why a subgroup is normally consecutive parts from one machine, one stream and one moment, not a mix of machines or shifts.

If a subgroup spans two causes of variation (two cavities, two spindles, two shifts), the range inside it is inflated, the control limits become too wide and real shifts are hidden. Chart each stream separately, or use individuals.

How many parts per subgroup

• n = 1 (I-MR chart): slow or expensive measurements, batch processes, destructive tests, one value per shift or lot.
• n = 3 to 5 (X̄-R chart): the usual choice for parts made in series. Five is common, four is easier to compute and plot by hand.
• n up to 8 with the range, larger with the standard deviation (X̄-S chart): the range loses efficiency as n grows.

What subgroup size does to detection

A larger subgroup averages out noise, so a shift of the mean stands out more. With standard 3σ limits, the chance that the first subgroup after a shift of the mean signals is:

The average number of subgroups until the signal (the average run length) is the reciprocal: a 1.5 σ shift with n = 5 is caught after about 1.6 subgroups, with n = 1 after about 15. This is why individual values need the run rules (Nelson rules) to be useful. The numbers assume a normal, independent process and only the 3σ rule.

How often to sample

The interval decides how many parts you make before a shift is found. Parts at risk are roughly interval × average run length. Example: a subgroup of 5 every 50 parts and a 1.5 σ shift is caught after about 1.6 subgroups, so about 78 parts are made before the signal. If a bad part costs a customer complaint, sample more often or reduce the shift you must catch.

• Tie the interval to events, not only to the clock: start of the shift, after set-up or tool change, after a material lot change, after a stop.
• Tool wear: sample several times during one tool life so the drift is visible before it reaches the limit.
• Stable and capable for months: the frequency can be reduced step by step, with a rule to return to the higher frequency after any out-of-control signal.
• New or critical characteristics: start frequent, then relax with data.

How many subgroups for the limits

Calculate trial control limits from at least 20 to 25 subgroups (100 or more readings in total), remove subgroups with a known special cause, and recalculate. Fix the limits afterwards and recalculate only after a deliberate change of the process. Limits that are updated with every new point follow the process instead of judging it. The capability tool calculates the limits and the Nelson signals from your data.

Sample size for capability is a different question

The subgroup of a control chart watches stability over time. A capability study needs enough parts to make Cpk reliable: Cpk from 30 parts is far less certain than from 300 (see What is a good Cpk?). Use the sample size calculator to see how many parts you need to demonstrate a requirement.

Common mistakes

• Subgroups that mix machines, cavities or shifts.
• Measuring five parts at the same moment and calling it five hours of data.
• Sampling once per shift out of habit although the process drifts within the shift.
• Limits recalculated every day, or limits taken from the specification.
• Chart for attributes (defects) with subgroups too small to expect any defect: use larger samples (attribute charts).