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Continuous data is essentially a measurement such as length, amount of time, temperature, or amount of money. Discrete data, also sometimes called attribute data, provides a count of how many times something specific occurred, or of how many times something fit in a certain category. For example, the number of complaints received from customers is one type of discrete data. The proportion of technical support calls due to installation problems is another type of discrete data.
In the first example, you are simply counting occurrences of something, in this case customer complaints. In the second example, you are taking each data point, in this case a technical support call, and bucketing the individual points into separate categories. Learn more about data types in our article, Six Sigma Data Types.
Some people refer to both of these types of data as attribute data, while others call the first type discrete-count data and the second discrete-attribute data. We will take a look at using control charts for both subtypes of data.
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Six Sigma project teams use control charts to analyze data for special causes, and to understand the amount of variation in a process due to common cause variation. With this information they can make the right decision about how to implement process improvements, whether that involves addressing the process itself or dealing with external factors that affect process performance. Learn more about control charts in our Introduction to Control Charts.
The most basic type of control chart, the individuals chart, is effective for most types of continuous data. With attribute data, however, other types of control charts are more powerful. The control limits are calculated differently to provide better detection of special causes based on the distribution of the underlying data.
For discrete attribute data, use the p chart. Recall that discrete attribute data results when you categorize or bucket each instance you are measuring. For example, you might track defective and non-defective components in a manufacturing process. This chart plots the proportion ("p") of the data falling into the relevant category over time.
When each data point is based on the same sample size, a special version of the p chart can be used. The np chart follows the same principle as the p chart, but actually plots the number of instances in a category over time rather than the proportion in the category. The name "np" derives from the convention of using "n" to refer to sample size. By multiplying sample size by proportion (n x p) you get the actual number in a category.
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The c chart is similar to the np chart, in that it requires equal sample sizes for each data point. For example, in evaluating errors on loan applications, you would use this chart if you sampled the same number of applications each week. But instead of plotting the proportion of data in a certain category, as does the np chart, the c chart plots count data, such as number of errors. As with the other control charts, special cause tests check for outliers and process shifts.
The u chart is a more general version of the c chart for use when the data points do not come from equal-sized samples. For instance, if you review all loan applications each week, and the number submitted differs on a weekly basis, you could still count errors and plot the number of errors by week over time. Because of the difference in sample sizes, the control limits will not be constant for each data point. Thus while the same special cause tests apply as for other charts, the outlier test checks specifically for whether a given data point is outside its own control limits.
Special use of p charts
Most control charts plot data over time. The p chart has an additional use, however, for data that is being compared across conditions rather than over time. For instance, a project team might be analyzing resolution rates for different technical support teams or different types of support problems. In such a situation, a p chart calculates control limits separately for each data point, and any data point lying outside its own control limits represents special cause. The project team would then investigate why performance for that specific category was higher or lower than expected based on typical process performance.
Read more about it
We have additional charts explained in More Types of Control Charts available on Bright Hub PM.
The Basics of Attribute Control Charts
Control charts are a powerful tool for Six Sigma projects, allowing analysis of special cause and common cause process variation. Learn about the different types and their uses.