Which control chart do you need? The chart follows the data, not the reverse. What you measure, how it arrives, and the size of the shift you need to catch decide the chart. The wrong choice either raises false alarms or misses the drift you built the chart to see.

Every control chart plots a statistic against control limits and asks one question: is the process still behaving the way it did when the limits were set? What changes from chart to chart is the statistic on the axis. That follows from three decisions you make before any data are plotted.

The types of control chart

Nine charts cover almost everything, in three families.

Chart	Data	What it plots
Xbar-R	Variables, in subgroups	Subgroup mean and range, for small subgroups
Xbar-S	Variables, in subgroups	Subgroup mean and standard deviation, for larger subgroups
I-MR	Variables, one at a time	Individual values with the moving range
p	Attribute, defective units	Proportion defective, varying sample size
np	Attribute, defective units	Number defective, constant sample size
u	Attribute, defects	Defects per unit, varying sample size
c	Attribute, defects	Count of defects, constant sample size
CUSUM	Time-weighted	Cumulative sum of deviations from target
EWMA	Time-weighted	Exponentially weighted moving average, tunable to the shift size

Three decisions pick one out of the nine, and the rest of this guide takes them in order.

First: is the measurement a variable or an attribute?

A variable is something you measure on a continuous scale: a thickness, a concentration, a time. An attribute is something you count: defective units, or defects per unit. The distinction decides the whole family. Variables data carry far more information per point and support tighter, more sensitive charts. Where you can measure rather than count, measure.

Second: do the data arrive in subgroups or one at a time?

For variables, the question is whether you collect rational subgroups: several units produced under the same conditions, or single observations. Subgroups let you separate within-subgroup variation from between-subgroup variation. That is what makes a chart able to distinguish a real shift from ordinary noise.

With subgroups you plot the subgroup mean on an Xbar chart, paired with an R chart (range) for small subgroups, up to about eight or ten, or an S chart (standard deviation) for larger ones, where the range would waste information.

Where the process yields one value at a time (a batch assay, a daily figure) you use an I-MR chart: individuals with a moving range. In a clinical laboratory the individuals half of that chart, run on a stable control material with limits taken from that material’s own mean and standard deviation, is the Levey–Jennings chart. Always read the spread chart first. If the R or S chart is out of control, the limits on the mean chart are not trustworthy.

For attributes, the count type sets the chart. Counting defective units gives a p chart (proportion, varying sample size) or an np chart (number, constant sample size), both built on the binomial distribution. Counting defects, where one unit can carry several, gives a u chart (defects per unit, varying size) or a c chart (count, constant size), built on the Poisson distribution. Choosing a defective-unit chart when you should be counting defects, or the reverse, puts the wrong distribution behind your limits.

Third: how small a shift must you catch?

A Shewhart chart (Xbar, I-MR, p, and the rest) reacts quickly to a large, sudden shift but is slow to notice a small, sustained drift. Each point is judged on its own. When the failure mode is gradual (reagent degradation, tool wear, calibration drift) a time-weighted chart catches it far sooner by accumulating information across points.

A CUSUM chart sums deviations from target, so a persistent small bias builds into a clear signal. An EWMA chart plots an exponentially weighted moving average, tunable to the shift size you care about. Run one of these alongside the Shewhart chart rather than instead of it. The pair catches both the sudden shift and the slow drift.

Getting the limits right

Whatever the chart, the control limits must come from a period when the process was stable, and from enough of it. Commonly twenty to twenty-five subgroups, or upward of a hundred individual points, for the estimate of the spread to settle.

The limits describe how the process actually varies, not the specification. Limits set over a period that already contains a shift are widened by it, until they no longer detect the very problem you are charting. Where the process runs in distinct periods (before and after a change) use separate control limits per phase rather than one set spanning both.

Downloads

Download the Xbar-R control chart example (.xlsx) — copper plating across three phases with detection rules and operator stratification, ready to open in the Analyse-it trial.

Common mistakes

Counting when you could measure. Attribute charts need large samples to match the sensitivity a variables chart gets from a handful. If the characteristic can be measured, an Xbar or I-MR chart will see trouble sooner.

Reading the mean chart before the spread chart. An out-of-control R or S chart invalidates the limits on the mean. Settle the spread first.

Expecting a Shewhart chart to catch a slow drift. Small sustained shifts are what CUSUM and EWMA are for. A Shewhart chart will get there eventually, but often too late.

Setting limits from an unstable period. Limits computed over data that already contain the problem are too wide to detect it. Establish them on a stable period.