What is a run chart?

A run chart represents your process data over time. Use a run chart to look for evidence of special-cause variation in your process.

Example of a run chart

A manufacturing engineer wants to assess the production process for a new product made of plastic. The engineer samples 5 products every hour for 20 hours to test the strength of the plastic and creates this run chart.

Except for one observation, the points vary randomly around the center line (median). The approximate p-values for clustering, mixtures, trends, and oscillation are all greater than the significance level of 0.05. Therefore, there is no indication of special-cause variation or non-randomness.

What do the points and center line on a run chart mean?

A run chart plots the individual observations in the order that they were collected. The gray points represent the individual values. The blue points represent either the subgroup means or subgroup medians.

The horizontal center line is drawn depending on which option you choose in the Run Chart dialog box. (To open the Run Chart dialog box, choose Stat > Quality Tools > Run Chart.) If you select:
  • Plot subgroup means, the center line is the median of all the subgroup means and the blue plotted points are the subgroup means.
  • Plot subgroup medians, the center line is the median of all the subgroup medians and the blue plotted points are the subgroup medians.
Note

If the subgroup size = 1, the center line is the median of all data, regardless of the option you select for the plotted points.

Even with skewed data, the median of the subgroup means is usually close to the median of the subgroup medians. The y-axis has a wide range because the raw data are also plotted, so the difference is usually not noticeable.

Run charts help detect special-cause variation

Variation occurs in all processes. Common-cause variation is a natural part of the process. Special-cause variation, comes from outside the system and causes recognizable patterns, shifts, or trends in the data. The run chart shows graphically whether special causes are affecting your process.

Run charts also provide tests for randomness that provide information about non-random variation due to trends, oscillation, mixtures, and clustering in your data. Such patterns indicate that the variation observed is due to special-cause variation.

Nonrandom patterns that a run chart can identify

There are four basic patterns of nonrandomness that a run chart will detect.

Mixture patterns

A mixture is characterized by frequent crossing of the center line. Mixtures often indicate combined data from two populations, or two processes operating at different levels. If the p-value for mixtures is less than 0.05, you may have mixtures in your data.

If the p-value for mixtures is less than 0.05, you may have mixtures in your data. In this chart, the mixture may indicate that the data come from different processes.

Cluster patterns

Clusters may indicate variation due to special causes, such as measurement problems, lot-to-lot or set-up variability, or sampling from a group of defective parts. Clusters are groups of points in one area of the chart.

If the p-value for clustering is less than 0.05, you may have clusters in your data. In this case, the circled data may represent clusters of data.

Oscillating patterns

Oscillation occurs when the data fluctuates up and down, indicating that the process is not steady.

If the p-value for oscillation is less than 0.05, you may have oscillation in your data. In this case, the circled data seem to vary up and down frequently.

Trend patterns

A trend is a sustained drift in the data, either up or down. Trends may warn that a process is or likely will soon go out of control, and may be due to such factors as worn tools, a machine that will not hold a setting, or periodic rotation of operators.

If the p-value for trends is less than 0.05, you may have a trend in your data. In this case, the upward trend is circled and easily visible.

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