A run chart is a graphical display of data over time. Run charts are used to visually analyze processes according to time or sequential order. They are useful in assessing process stability, discovering patterns in data, and facilitating process diagnosis and appropriate improvement actions.
To start a run chart, some type of product, service, or process must be available on which to take measurements for analysis. Measurements must be taken over a reasonable period of time using a calibrated measurement tool that is being monitored with a calibration control chart. A measurement error study must indicate that the measurement process is acceptable during the data collection process. The data must be collected and stored in chronological or sequential order. You may start at any point in the data set and end at any point. To get meaningful results, at least 25 or more samples must be taken over a long enough period of time so all the components of variation are included.
Once the data have been collected in chronological or sequential order, they must be divided into ordered pairs of x and y values. The values for x represent time or sequence number, and the values for y represent the measurements taken from the product, service, or process.
Plot the y values versus the x values by hand or by using a computer program. Select an appropriate scale that will make the points on the graph visible. Next, draw vertical lines for the x values to separate time intervals such as observation number or time unit (e.g., days, weeks, months). Then draw horizontal lines to help distinguish where nonrandom observations appear (e.g., trends, shifts, spikes, cycles) in the process or operation. Your chart should look like the example in figure 1.
To visually analyze a run chart, you should do the following:
Use your computer to draw a linear regression trend line from the beginning to the end of the data on the run chart. If the line is approximately horizontal, then the mean of the process can be considered stationary over this time interval. If not, then the process mean is considered nonstationary, or unstable. Remember that drawing this inference requires sufficient data, usually 50 or more observations (i.e., two points are not sufficient). There is a statistical test to determine if you can reject the null hypothesis that the slope of the linear trend line is zero.
Look at the run chart. Does it appear that the variation in the data is increasing or decreasing over time (i.e., does the overall pattern or data envelope appear funnel-shaped or like a snake that swallowed a pig)? If the answer is yes, then the process variance can be considered nonstationary. If the answer is no, then the process variance can be considered stationary. You can use your computer to generate the two-point moving ranges and plot them. Then plot the linear trend line for the two-point moving ranges. If the trend line is approximately horizontal, then the variance is considered stationary over the interval.
Are the points on the run chart scattered evenly and randomly around the trend line? If the answer is yes, then the data are not significantly auto-correlated (i.e., they are reasonably independent). If the data values tend to follow each other like a snake, then the data are auto-correlated (i.e., they may not be statistically independent). So you should ask: Is there a logical reason why this would be the case?
Is there a pattern in the run chart’s data (e.g., cyclic, trend, shift, spike, funnel shape)? To help spot a change, draw a horizontal line from the beginning of the data to the end, dividing the data in half. This is called the center line (CL) or median of the data. If you find cases where eight or more consecutive points are above or below the median line, or if eight points are steadily increasing or decreasing, then the process is probably unstable. If this is the case, then you should look for the causes. If it is not the case, then proceed to the next visual analysis test.
Is there a point or points on the run chart that appear to be isolated from the rest of the data? If the answer is yes, then investigate this rare observation to determine if it is valid and if so, then try to determine the causes.
The process mean shown in figure 1 may be slightly nonstationary (i.e., the trend line is going down), but the small number of observations and the large amount of variation in the data make it impossible to validate this trend with a high degree of confidence. We should continue to monitor the process to see if the trend continues and becomes significant.
The process variance appears to be stationary, as the envelope of variation seems to be fairly consistent.
There appears to be auto-correlation in the data because the points do not appear to be randomly distributed around the trend line.
There appears to be a cyclic pattern of period 5 in the data. There does not appear be a trend, shift, spikes, or any other unusual systematic patterns in the data.
There do not appear to be any rare event points (i.e., outliers) in the data.
The run chart can be a very effective tool in understanding process behavior. The smart engineer will make it one of his commonly used tools.