Run Charts and SPC for Surgeons

A department's surgical site infection rate was 2.1% last quarter and 3.4% this quarter. The audit meeting concludes that infection rates have risen, and a working group is convened.

Possibly. Or possibly nothing whatever has changed, and the difference is the ordinary quarter-to-quarter wobble of a small denominator. Nobody in the room can tell which, because two numbers cannot distinguish a real shift from routine variation — and acting on the difference costs the department a working group, several people's time, and a change that may make things worse.

This is the most common analytical failure in surgical quality work, and the fix is a chart you can draw in ten minutes. This post sits within our governance series and pairs with PDSA Cycles That Actually Finish.

Two kinds of variation

The foundational idea, from Walter Shewhart and later W. Edwards Deming, is that variation comes in two flavours and they demand opposite responses.

Common cause variation is the ordinary noise inherent to a stable process. Your infection rate fluctuates from month to month even when nothing has changed, because case mix, denominators and chance all move. A process showing only common cause variation is stable — which does not mean good, only predictable.

Special cause variation is a signal: something genuinely different has happened. A new prophylaxis protocol, a new surgeon, a broken steriliser, a change in how cases are coded.

The two errors follow directly, and Deming named them:

1. Treating common cause as special cause — reacting to noise. This is the working group convened over a difference that meant nothing. It is far more common than the reverse, it wastes enormous effort, and it can actively destabilise a process that was working.
2. Treating special cause as common cause — dismissing a real signal as random. Rarer, and more dangerous.

The entire purpose of a run chart is to tell you which one you are looking at before you decide what to do.

The run chart

The simplest useful tool in improvement work, and it needs no software beyond a spreadsheet.

How to build one:

1. Time on the horizontal axis — weeks, months, or consecutive cases. Never categories.
2. Your measure on the vertical axis — rate, count, or time.
3. Plot every point in time order. Do not aggregate into before-and-after.
4. Draw the median as a horizontal line across all points.
5. Annotate interventions with a vertical line at the point the change was made.

That last step is what turns a chart into evidence. A reader can see whether the process moved after you did something, which is a claim two bars can never support.

How many points? Ten to twelve as a working minimum for a run chart. Fewer than that and the rules below have no power.

Reading a run chart

Four standard rules identify special cause. If none is present, you are looking at a stable process and should not react to individual points.

Points on the median are ignored when counting shifts and runs.

The practical value is mostly negative, and that is not a criticism — most month-to-month movement satisfies none of these rules, which means the correct response is to do nothing. Learning to leave a stable process alone is a genuine skill, and it is the opposite of most clinical instinct.

Control charts

A control chart is a run chart with statistically derived limits, usually set three standard deviations either side of the mean. It answers the same question with more power and a formal basis.

Upper and lower control limits are calculated from your own data. They describe what this process actually does. A point outside them is a signal.

The single most important thing to understand about them:

A control limit is not a target. Control limits describe how your process behaves. A target describes what someone wants. Drawing your target on the chart as though it were a control limit is the most common error in healthcare SPC and it makes the chart meaningless.

Choosing the chart type matters more than surgeons expect, because it depends on the kind of data:

Using the wrong chart produces limits that are wrong, usually too narrow, generating false signals every few months and training everyone to ignore the chart.

How many points? Around 20 to 25 before control limits are trustworthy. Below that, use a run chart and wait.

Rare events

A specific trap in surgery. Never events, wrong-site incidents and deaths after elective arthroplasty are all rare enough that a conventional chart is useless — most months are zero, and a single event looks catastrophic.

For rare events, plot time between events rather than count per month. A lengthening interval is improvement; a shortening one is a signal. This is far more informative than a bar chart of mostly zeros with an occasional one.

Where surgeons go wrong

Rebasing the limits every time something changes. Recalculating control limits after every intervention guarantees the process always looks stable. Rebase only when you have deliberately and permanently changed the process, and mark clearly where you did it.

Treating every point outside the limits as a scandal. A stable process will occasionally produce an extreme point by chance. Investigate it; do not assume it.

Aggregating away the signal. Annual figures hide everything. Monthly is usually the right granularity for surgical data; weekly for process measures during an active project.

Ignoring the denominator. A rate built on 12 cases will swing wildly for reasons that have nothing to do with care quality. Small denominators need longer time periods or a different measure.

Comparing to other units without adjustment. Case mix differs. A raw comparison of infection rates between a tertiary revision centre and a district elective unit is not information.

Worth charting in an orthopaedic department

Good candidates: the data already exists, the process is yours, and the numbers move often enough to plot.

• Time to theatre for hip fracture — I-MR chart, individual patients
• VTE risk assessment completion — P chart, monthly proportion
• Prophylactic antibiotic timing compliance — P chart
• Surgical site infection rate — U chart, but beware small denominators
• Length of stay after primary arthroplasty — Xbar-S chart
• Fracture clinic non-attendance — P chart
• Theatre start time for the first case — I-MR chart, and reliably more revealing than anyone expects
• Days between never events — time-between-events chart

Why this is worth the effort

Beyond doing better work: a run chart with an annotated intervention is dramatically more persuasive than a pair of bars, at an audit meeting, in a business case, or at interview.

"We improved antibiotic timing from 71% to 89%" invites the obvious question of whether that is real. A chart showing twelve stable months around a median of 71%, a marked intervention, and then eight consecutive points above the median answers it before it is asked — that is a shift by the run chart rules, and it is evidence rather than assertion.

If you are presenting improvement work for ARCP or at consultant interview, this single skill separates a project that sounds credible from one that does not.

The short version

Plot your data over time, in order, with the median drawn. Mark where you intervened. Apply the four rules. If none fires, the process is stable and you should not react to individual points — however tempting.

Move to control charts once you have twenty-odd points, choose the chart type from the data type, and never draw your target as though it were a control limit.

Most of the value is in what this stops you doing. A great deal of effort in surgical departments is spent reacting to variation that means nothing, and the discipline of asking "is this actually a signal?" before convening a working group is worth more than any individual improvement project.