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The run chart is the most common chart of process data. It is easy to create and maintain and gives the process operators immediate insight when a process becomes unstable.

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Quick reference

Run Chart

The run chart is the most common chart of process data. It is easy to create and maintain and gives the process operators immediate insight when a process becomes unstable.

When to use

If a run chart does not already exist, it should be immediately started during the Measure phase. The run chart should be maintained from that point forward until it is replaced by control charts in the Control phase.

Instructions

A run chart is very easy to create and multiple run charts can be created for different process output parameters. The horizontal scale for the run chart is normally based upon a time increment such as hours or days, although it can also be sequential units. The vertical scale is based on the parameter being tracked on the run chart.

The data points for the parameter are plotted. As soon as 15 points have been recorded, a median for the data set should be determined and shown as a horizontal line on the chart. The median can be recalculated periodically (monthly or after a significant number of additional units are included) but it should not change significantly unless there has been a process change or there is the presence of special cause variation.

The run chart indicates special cause variation if one of these five conditions exists:

  1. Nine consecutive points on the same side of the median
  2. Six consecutive points changing in the same direction (becoming larger or smaller)
  3. An astronomical point (a judgment call that the point is well beyond the normal expected values)
  4. Fourteen consecutive points of alternating higher then lower than the immediately preceding point in a sawtooth manner.
  5. Too many or too few “runs” based upon the number of “useful observations.” A useful observation is any point that is not the value of the median. A run is a set of one or more points on the same side of the median. The minimum and maximum number of runs that are consistent with only common cause variation must be looked at from a consecutive run table.

Hints & tips

  • There is no reason to delay the start of a run chart – so don’t.
  • If you have historical data, you can create a run chart from that data to see if there is special cause variation.
  • Place the run chart at the point of data collection and plot it immediately so that the information is always up to date.
  • Statistical process control charts should only be used with processes that are stable and under statistical control. That doesn’t apply to a run chart, so feel free to use it.
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  • 00:04 Hi, I'm Ray Sheen.
  • 00:06 Let's take a few minutes to talk about run charts.
  • 00:09 This basic statistical tool is helpful for both problem solving and process control.
  • 00:16 So what is a run chart?
  • 00:18 It is a display of the process performance over time.
  • 00:21 We can take any key output parameter and plot it on a run chart.
  • 00:25 Run chart is a special case of the line graph.
  • 00:28 The vertical scale is based upon the output parameter values, and
  • 00:33 the horizontal scale is a time increment or unit number of process output.
  • 00:38 Since it is a line graph, each data point is connected with a line to the points
  • 00:42 immediately preceding and following that point in the sequence.
  • 00:46 One thing that can be clearly seen from a run chart is trends.
  • 00:50 Is the output parameter getting larger or smaller over time?
  • 00:54 Another element of most run charts is a horizontal line that is drawn at the value
  • 00:59 of the median.
  • 01:00 The median is used for several reasons.
  • 01:02 First, it is not significantly influenced by outliers.
  • 01:05 Second, we don't know if we have a normal distribution.
  • 01:09 Recall that the mean is used with a normal distribution and
  • 01:12 the median is used with non-normal distributions.
  • 01:16 If the distribution is normal, the median and mean will be virtually identical.
  • 01:20 So we don't lose anything by using the median and
  • 01:23 we are protected against non-normal data.
  • 01:25 The value of the run chart is that it is the voice of the process.
  • 01:30 Now earlier, we discussed the voice of the customer, now,
  • 01:33 we're talking about the voice of the process.
  • 01:36 Let's take a minute to discuss how to create and use a run chart.
  • 01:40 They are incredibly easy to create.
  • 01:43 Just take a measure of the output and
  • 01:45 record it on the chart at the next point in the sequence.
  • 01:48 One of the ways we use the chart is to provide a picture of what is happening in
  • 01:53 the process for our stakeholders and our team members.
  • 01:56 The run chart lets them visualize what is happening.
  • 01:59 Now I mentioned that the run chart uses the median value.
  • 02:02 When you first start to plot the process output, there is no median.
  • 02:06 Don't try to determine that until you have at least 15 data points,
  • 02:10 then you can periodically update the median over time.
  • 02:13 There are several uses of the run chart information and the insight it provides.
  • 02:18 Of course, an obvious one is that the run chart shows when a shift has occurred in
  • 02:22 process performance.
  • 02:23 This can be useful both in problem solving and
  • 02:26 by helping to identify when something negative occurred.
  • 02:29 And it can be an excellent way to demonstrate the impact of a process
  • 02:33 improvement as it illustrates the before and
  • 02:36 after condition of the process parameter.
  • 02:39 In addition, there are five rules that we can use to determine if there are special
  • 02:43 causes present in the process.
  • 02:45 Recall that we want to eliminate all special cause variation so
  • 02:49 that we only have common cause variation, and therefore, our process is stable and
  • 02:53 predictable.
  • 02:54 Let's look at each of the special cause rules that can be observed on a run chart.
  • 02:59 The first is 9 consecutive points on the same side of the median.
  • 03:03 This demonstrates a shift in performance.
  • 03:05 If this was not a planned shift, then something special has happened.
  • 03:09 This shift could be good or bad from an overall process performance perspective.
  • 03:13 That is why we need to determine the cause.
  • 03:16 The second is an astronomical point.
  • 03:19 This means a point that is an outlier.
  • 03:21 It is far removed from the typical values of the process parameter.
  • 03:25 How far off?
  • 03:25 Well, right now, that's a judgment call.
  • 03:28 You don't have a standard deviation or
  • 03:30 control limits to help you like you will on the control chart.
  • 03:33 So we leave that to your judgment.
  • 03:35 Third is a trend, this is when there are at least 6 consecutive points that
  • 03:40 are changing in the same direction as compared to the preceding point.
  • 03:44 These don't need to be above or below the median,
  • 03:47 they just all need to be going in the same direction.
  • 03:49 This indicates that there is a new effect impacting the process parameter.
  • 03:54 Fourth is sawtooth pattern.
  • 03:56 In this case, there are at least 14 points that alternate going higher or
  • 04:00 lower than the preceding data point.
  • 04:02 This effect is often due to some external effect attempting to over control
  • 04:07 the process rather than the normal process performance occurring.
  • 04:11 The fifth way of identifying special causes is called consecutive runs.
  • 04:15 It's a tricky one and it's based upon too many or too few runs in the data.
  • 04:20 Of course, you're probably asking, what's a run?
  • 04:22 A run is one or
  • 04:23 more consecutive useful observations that are on the same side of the median.
  • 04:28 And the definition of a useful observation is that of any value that
  • 04:32 is not equal to the median.
  • 04:33 Based upon the total number of useful observations, there is a minimum and
  • 04:38 maximum number of runs that are expected.
  • 04:40 Too few or
  • 04:41 too many indicates a special cause is overriding the process performance.
  • 04:46 So let's take a look at this run chart.
  • 04:48 There are 27 data points, but 4 of them are on the median, so
  • 04:52 there are only 23 useful observations.
  • 04:55 The first point is on the median.
  • 04:57 The next two are below, so that constitutes a run.
  • 05:00 Then there are three points above the median which constitutes another run.
  • 05:04 That is followed by a point on the median, and
  • 05:07 then three more points below the median for the third run.
  • 05:10 There are then four points above the median for
  • 05:13 run number four before we have another point on the median.
  • 05:17 Then 3 points below, 4 points above, 4 points below for runs 5, 6,
  • 05:22 and 7, finally a point back on the median.
  • 05:25 This is a total of 7 runs.
  • 05:27 When we go to the table at the right, we find that for 23 useful observations,
  • 05:32 we should have a minimum of 8 runs and a maximum of 16 runs.
  • 05:36 Since we are below the minimum,
  • 05:38 we know that some special cause is overriding the normal process performance.
  • 05:44 The run chart is one of the easiest and most practical data gathering and
  • 05:48 data analysis techniques that is available to a Lean Six Sigma team.

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