A run chart displays observed data as they evolve over time. Just a basic graph that displays data values in a time order. Can be useful for identifying trends or shifts in process but also allows you to test for randomness in the process.

A run chart can reveal shifts and trends, but not points out of control (A run chart does not have control limits; therefore, it cannot detect out of control conditions.) You can turn a run chart into a control chart by adding upper and lower control limits.

Use it to:

- track improvements (and determine success)
- display outputs to look for stability or instability

## Run Chart Analysis

(These examples are from the wonderful download Developed by Richard Scoville, PhD. (richard@rscoville.net))

### Testing a change

- Plot the baseline
- Extend the median and begin the test
- Continue to plot data following the change
- Apply the rules
- If there was a signal, re-plot with new median

## Decision Rules

Signals of an effective change:

**Runs**– Are there too many or too few for just common cause variation.- A run is a series of consecutive points that all lie on the same side of the line.
- Ignore the points exactly on the line!

**Clustering**– too few runs.**Mixtures**– too many runs.**Shift**– 6 or more consecutive points above or below the median.- A general rule of thumb is when seven or eight values are in succession above or below the average of the group, a shift has occurred.

**Trend**– 5 or more consecutive increasing or decreasing points.- A basic rule of thumb is when a Run Chart exhibits seven or eight points successively up or down, then a trend is clearly present in the data.

**Astronomical Point**– A dramatically different value.

Run Chart Signals

### Counting Runs

Counting Runs

How Many Runs?

Expected Runs Table

## Comments (6)

Is there perhaps some SAS code that would create the graph in step 5 above. I see that the SAS support document refers to Shewhart Charts.

Sorry, Jacques. I’m not familiar with SAS code.

How many data points a run chart should include before applying

any of the decision rules ?

I like having 15 or more data points, Arthur.

If the 6 consecutive points come below or above mean line. Then it is trend or not?

I think you’re looking for the rule of 7 here, Hunny.