| Adding the element of time will help clarify your | | | | them. Another way of doing this is to count the |
| understanding of the causes of variation in your | | | | number of times the run-line crosses the median, and |
| processes. A run chart is a line graph of data points | | | | then add one. Compare the number of runs you count |
| organized in time sequence and centered on the | | | | to the accompanying chart. |
| median data value. The patterns in the run chart can | | | | • Numbers of runs outside the range shown for the |
| help you find where to look for assignable causes of | | | | number of data points are statistically unusual. |
| variation. | | | | • Too few runs (below the lower limit) generally |
| What can it do for you? | | | | indicate that something cyclic is systematically shifting |
| Histograms or frequency plots can show you the | | | | the process average. |
| general distribution or variation among a collection of | | | | • Too many runs could point to a problem of |
| data points representing a process, but one histogram | | | | consecutive, over-compensating process adjustments |
| or one frequency plot can not show you trends or help | | | | or indicate that the data points actually came from two |
| pinpoint unusual events. Sometimes, a normal-looking | | | | sources with different process averages. |
| distribution will hide trends or other unusual data. To | | | | • Look for sequences of ascending or descending |
| spot those trends, the data must be considered in time | | | | values. Seven or more continuously increasing or |
| order. Plotting data on a run chart can help you identify | | | | continuously decreasing points indicates a trend that is |
| trends and relate them to the time they occurred. This | | | | shifting the process average. When counting points, |
| will help you in your search for the special causes that | | | | ignore any points that repeat the previous value. |
| may be adding variation to your process. | | | | Repeated values neither add to the length of the run |
| Run charts are especially valuable in the measure and | | | | nor break it. |
| analyze phases of Lean Six Sigma methodology. | | | | • Search for seven or more consecutive points on |
| How do you do it? | | | | the same side of the median line or 10 of 11 points or |
| 1. Select a characteristic from one of your processes. | | | | 12 of 14 or 16 of 20. (Ignore any points that are exactly |
| This characteristic could be presenting a problem | | | | on the median.) Such a sequence indicates that |
| because excessive variation often drives it outside of | | | | something has occurred to shift the process average |
| specification limits, or it could be a cause of customer | | | | in that direction. |
| complaints. | | | | • A sequence of 14 or more data points alternating |
| 2. Measure the characteristic over time intervals and | | | | up and down suggests a variation related to sampling |
| record the data. Note the time or the time period that | | | | (such as one reading early in the day and one reading |
| is associated with each data point. | | | | toward the end) or that the data is coming from two |
| 3. Find the median data value. To do this, list the data | | | | sources with different process averages (such as |
| values in numeric order. Include each data point, even if | | | | from two machines making the same part.) In looking |
| it is a repeat value. If the number of data points is odd, | | | | for up-and-down alternation, ignore any points that are |
| the median is the middle value. If the number of data | | | | exactly the same as the preceding point. |
| points is even, the median is halfway between the two | | | | • A sequence of seven or more points with exactly |
| values nearest the middle. For example, if the collected | | | | the same value usually should signal you to look for a |
| data points were: 5, 1, 18, 8, 12, 9, the ordered values | | | | special cause. While it is possible that your process |
| would be: 1, 5, 8, 9, 12, and 18. The middlemost values | | | | has improved to the extent that the existing |
| are 8 and 9. The median is the average of those | | | | measurement technique is no longer sensitive enough |
| values, or 8.5. (Remember, the numerically-ordered | | | | to measure variation, it is usually more probable that a |
| data is only for determining the median. The data must | | | | gauge is stuck or broken or that someone is making |
| be plotted in time order on the run chart to be of any | | | | up the data. |
| value.) | | | | Now what? |
| 4. Set up the scales for your run chart. The vertical | | | | Run charts can be very valuable in helping your search |
| scale will be the data values, and the horizontal scale | | | | for sources of variation. They are easy to plot and |
| will be the time. Make the horizontal scale about two to | | | | easy to interpret. The sampling is uncomplicated, and |
| three times the distance of the vertical scale. | | | | there are no statistical computations to make. They |
| 5. Label the vertical scale so that the values will be | | | | can also be applied to almost any process or any |
| centered approximately on the median and so the | | | | data. |
| scale is about 1 ½ to 2 times the range of the | | | | On the other hand, they are not an instant indicator. |
| collected data. | | | | They are best used for spotting trends; short shifts in |
| 6. Draw a horizontal line representing the median value. | | | | the process cannot always be detected with run |
| 7. Plot the data points in sequence. Connect each point | | | | charts. In addition, special causes that produce general |
| to the next point in the sequence with a line. | | | | piece-to-piece variation will not be readily detected on |
| Some special cause variation reveals itself in unusual | | | | run charts. |
| run-chart patterns. These clues can direct you in your | | | | Finally, a simple run chart cannot establish the natural |
| search for causes. Count the number of runs. Runs | | | | capabilities of a process, so it isn’t possible to use |
| are sequences of points that stay on one side of, | | | | one to predict what specifications a process can |
| either above or below, the median line. One way of | | | | actually meet. To do that, you need to create a control |
| counting the runs is to circle these sequences and tally | | | | chart, a run chart with statistical control limits. |