Analyzing Data over Time

We can identify common and special causes by plotting data over time on a run chart. Run charts let us see the "story" behind the data.  Examine the following table of numbers. What do you see?

Registration Times
15 67 4 14 10
12 54 3 7 11
14 83 54 17 20
10 53      
These are actual times it took triage level 2 patients to register in the Emergency Department of a hospital.

You could find the mean, range, mode, median, etc.   However, these numbers would tell you very little about the process.

Now look at the same data arranged on a run chart.

Having plotted the data, you see that a group of patients get seen quickly while others do not.  If you know which patients the numbers represent, you might investigate the process and see what is happening.  Run charts do not give answers, just smarter questions.

Run Charts

Definition: A line graph of data plotted in the order in which they occurred.

Purpose: To indicate the presence of special causes of process variation in the form of trends, shifts, or other non-random patterns in a Quality Characteristic or Process Variable.

How to Construct:

  1. Draw a vertical and a horizontal axis on a piece of graph paper.
  2. Label the vertical axis with the name of the value being plotted.
  3. Label the horizontal axis with the unit of time or order in which the data were collected.
  4. Determine the scale of the vertical axis. Pick a number 20% larger than the largest value and 20% smaller than the smallest value. Label the axis in equal intervals between these two numbers.
  5. Plot the data on the graph point by point, preserving the order in which they occurred.
  6. Connect the points on the graph.
  7. Find the median (or mean) of the plotted numbers.
  8. Draw the median (or mean) on the graph.
    9.

Computing Statistics

Mean: , the arithmetic average of a set of numbers.

Median: , the midpoint of a set of numbers after they have been ordered from largest to smallest.

  1. Order the data from the largest value to the smallest.
  2. For an odd number of data points, X = the middle value.
    For an even number of data points, X = the average of the center two values.
    3.

Range:  , the difference between the highest and the lowest values in a set of data.

Rules for Detecting Special Causes on a Run Chart

Rule 1: Shift
Eight or more consecutive points either above or below the median is an indicator of a possible shift in the level of the process. Ignore values on the median.

Rule 2: Trend
 Seven points that all go up or down sequentially.  If two successive points are the same, this does not break the trend.

Rule 3: Zigzag pattern
 The line between successive points alternately going up and down 13 times. If the values of two or more points are the same, this breaks the pattern and it is not a special cause.

Rule 4: Point outside the control limits
 This rule is used with control charts.  Any point unusually high or low relative to the median may signal a special cause.  Such a point is called an outlier.  If a point looks like it could be an outlier, constructing a control chart will allow you to see whether that point lies outside the control limits.

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