Run charts and statistical process control
What question does this help answer?
Is the week-to-week variation in this measure consistent with the process's normal variation, or is there a signal that something has changed, for better or worse?
When to use it
Use these charts in quality improvement to monitor a process or outcome measured repeatedly, to see whether tested changes are followed by a shift, and to check that an improvement is sustained. They suit learning in real time from data that arrive in sequence.
When not to use it
They do not by themselves show that an intervention caused a change, and they do not replace an interrupted time series or a controlled design when the aim is to estimate an effect for publication or policy. Charts built on very few points, or on measures whose definition or denominator changed, can signal change that is an artefact.
Run charts
A run chart plots the measure in time order with the median as the centre line. Rules based on probability look for non-random patterns, such as an unusually long run of points on one side of the median or unusually few crossings of it. Published rule sets differ, and some commonly taught rules perform poorly; one simulation study found a rule counting consecutive rising or falling points nearly useless for detecting gradual drift. Choose the rules before looking at the chart.
What a shift looks like
Control charts
- A control chart adds a centre line and control limits calculated from the process's own variation, conventionally set about three standard deviations from the centre line.
- The chart type must match the data: for example a p-chart for proportions, a u-chart for rates with changing denominators, a c-chart for counts over equal opportunities, and an individuals chart for single continuous values.
- Common-cause variation is the expected variation of a stable process. Special-cause variation is a signal, such as a point outside the limits or a prespecified run pattern.
- Limits are estimated from a baseline period and recalculated only when there is evidence of a real, sustained change, with the reason recorded.
Assumptions and pitfalls
- Points are assumed to be broadly independent over time; strong autocorrelation or seasonality produces false signals.
- Definitions and denominators stay consistent. A coding change looks like a process change.
- Small or varying subgroup sizes widen the limits and change which chart is appropriate.
- Watching many charts, or applying many rules, raises the chance of a false signal somewhere.
Clinical example
A ward charts the weekly proportion of admitted patients with a completed thrombosis risk assessment within 24 hours, using a p-chart because weekly admissions vary. After a change to the admission checklist, a run of points above the centre line meets the rule chosen in advance. The team records the signal, checks whether the way completion is recorded changed, and keeps charting to see whether the shift lasts. This example is illustrative.
What to watch out for
A signal on a run chart or control chart says the process has probably changed, not why it changed. Control limits describe the variation of the process being charted; they are not targets or a test of whether an intervention caused the change, and limits recalculated after every apparent shift can hide the change the chart was meant to show.
Before using this in your workspace
Record the numerator and denominator, the sampling interval, the chart type and why, the baseline period for the limits, the signal rules chosen in advance, a dated note for each tested change, and which design will be used if an effect claim is needed.
- Statistical process control as a tool for research and healthcare improvement (opens in a new tab) · Qual Saf Health Care · doi 10.1136/qhc.12.6.458
- The run chart: a simple analytical tool for learning from variation in healthcare processes (opens in a new tab) · BMJ Qual Saf · doi 10.1136/bmjqs.2009.037895
- Plotting basic control charts: tutorial notes for healthcare practitioners (opens in a new tab) · Qual Saf Health Care · doi 10.1136/qshc.2004.012047
- Run charts revisited: a simulation study of run chart rules for detection of non-random variation in health care processes (opens in a new tab) · PLoS One · doi 10.1371/journal.pone.0113825