Run Charts

Overview
Run charts are one of the most useful tools in quality improvement. They allow us to:

  • Monitor the performance of one or more processes over time to detect trends, shifts or cycles.
  • Allow us to compare a performance measure before and after implementation of a solution to measure its impact.
  • Focuses attention on truly vital changes in the process.
  • Assess whether improved performance has been sustained.

Run charts are a valuable tool at the beginning of a project, as it reveals important information about a process before you have collected enough data to create a Stewhart control chart.

Characteristics of a run chart

  • On the X axis you have data in some sort of chronological order e.g. Jan, Feb, Mar
  • On the Y axis you have the measure of interest e.g. %, count
  • Once the data points are connected you put a centre line (CL) between the graph. For a run chart the CL is called the Median.

The median is the number in the middle of the data set when the data are reordered from the highest to the lowest value. If the number of observations is even, the median is the average of the two middle values.

typical run chart 1

A typical run chart

How to create a run chart

Step 1 – State the question that the run chart will answer and obtain data necessary to answer this question.

For example, if you were looking at how long it takes to travel to work in the morning you will make note of the time taken (in minutes) to get to work over a period of a month.

Step 2 – Gather data, generally collect 10-12 data points to detect meaningful patterns.

Step 3 – Create a graph with vertical line (y axis) and a horizontal line (x axis).

  • On the vertical line (y axis), draw the scale related to the variable you are measuring.

Please note: it is good practice to ensure the y axis covers the full range of the measurements and then some (e.g. 1 ½ times the range of data). This is to ensure the chart can accommodate any future results.

  • On the horizontal line (x axis), draw the time or sequence scale.

Step 4 – Plot the data, calculate the median and include into the graph.

Step 5 – Interpret the chart. Four simple rules can be used to distinguish between random and non-random variations.

 

Interpreting a run chart

There are four rules that can be used to interpret a run chart. Non-random variation can be recognised by looking for:

  • Rule 1 – Shift
    Six or more consecutive points either all above or all below the centre line (CL). Values that fall on the CL do not add to nor break a shift. Skip values that fall on the median and continue counting.
interpreting a run chart 1 - shift

Rule 1 – shift

Rule 2 – Trend

Five or more consecutive points all going up or all going down. If the value of two or more successive points is the same (repeats), ignore the like points when counting.

interpreting a run chart2 - trend

Rule 2 – trend

 

  • Rule 3 – Too many or too few runs

A non-random pattern is signalled by too few or too many runs, or crossings of the median line. If there are too many or too few runs, this is a sign of non-random variation. To see what an appropriate number of runs for a given number of data sets, refer to following statistical table. An easy way to count the number of runs is to count the number of times the line connecting all the data points crosses the median and add one. If the number of runs you have are:

  • Within the range outlined in the table, then you have a random pattern.
  • Outside the range outline in the table, then you have a non-random pattern or signal of change.
interpreting a run chart3 - too many or too few runs

Rule 3 – Too many or too few runs

 

  • Rule 4 – An astronomical data point

This is a data point that is clearly different from all others. This is a judgement call. Different people looking at the same graph would be expected to recognise the same data point as astronomical.

interpreting a run chart4 - astronomical point

Rule 4 – An astronomical data point

By applying each of the four rules, you can evaluate the run chart for a signal for change (through a non-random variation). However, it is not necessary to find evidence of change with each of the four rules to determine that a change has occurred. Any single rule occurring is sufficient evidence of a non-random signal of change.

Additional resources 

 

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