# Types of data for control charts

## What type of data do I have?

The control chart that you use depends on whether you collect continuous data or attribute data. If you have multiple continuous variables, consider whether you have multivariate data. Attribute data has two subtypes: binomial and Poisson.

Continuous variables can have an infinite number of values, such as 234.8 or 0.01. The values for attribute variables are restricted to specified categories or discrete values. For example, attribute values can include the categories "pass" and "fail". The number of defects in a sample can also be an attribute variable.

Continuous measurements usually provide more information than attribute data. However, attribute data are generally easier to collect. Thus, attribute data are often collected when continuous measurements are difficult to obtain. Attribute data are often subjective ratings that are assigned by operators or quality control personnel.

## Continuous process data

Continuous data measures a characteristic of a part or process, such as length, weight, or temperature. The data often include fractional (or decimal) values.

For example, a food manufacturer wants to investigate whether the weight of a cereal product is consistent over time. To collect data, a quality analyst records the weights from a sample of cereal boxes.

If you have continuous data collected in subgroups, use one of the control charts in Stat > Control Charts > Variables Charts for Subgroups.

If you have continuous data collected as individual observations, use one of the control charts in Stat > Control Charts > Variables Charts for Individuals.

## Multivariate process data

You have multivariate data if you collect more than one continuous variable from the same process. You can monitor multiple variables on one multivariate control chart when variables are correlated. For example, you can monitor both temperature and pressure for a process that produces injection-molded plastic parts.

To determine whether you should use a univariate or multivariate control chart, create a correlation matrix of your variables. If the variables are correlated, consider creating a multivariate control chart.

If the data include correlated variables, then it is misleading to create separate control charts for each variable, because the variables jointly affect the process. If you use separate univariate control charts in a multivariate situation, then the following are not equal to their expected values:
• Type I error
• The probability of a point correctly falling within the control limits

The distortion of these values increases with the number of measurement variables.

If you have multivariate data, then multivariate control charts provide the following advantages:
• They represent the actual control region of the related variables (elliptical for bivariate case).
• They let you maintain the specified rate of type I error.
• They let you monitor all the correlated process variables on a single chart, often with a single control limit.

However, multivariate control charts are more difficult to interpret than classic Shewhart control charts. For example, the scale on multivariate control charts is unrelated to the scale of any of the variables. Also, out-of-control signals on multivariate control charts do not reveal which variable (or combination of variables) caused the signal.

If you have continuous data collected from two or more correlated variables, use one of the control charts in Stat > Control Charts > Multivariate Charts.

## Attribute process data

For control charts, attribute data are usually counts of nonconformities (also called defects) or nonconforming units (also called defectives). A nonconformity refers to a quality characteristic and a nonconforming unit refers to the overall product. A unit may have many nonconformities, but the unit itself is either conforming or nonconforming. For example, a scratch on a metal panel is a nonconformity. If several scratches exist, the entire panel may be considered nonconforming.

Poisson data
Values for Poisson date are often counts of defects or events. Poisson data are often used to model an occurrence rate, such as defects per unit.
For example, inspectors sample 5 beach towels every hour and examine them for discolorations, pulls, and incorrect stitching. They record the total number of defects in the sample. Each towel can have more than one defect, such as 1 discoloration and 2 pulls (3 defects).
Binomial data
Values for binomial data are classified into one of two categories such as pass/fail or go/no-go. Binomial data are often used to calculate a proportion or a percentage, such as the percentage of sampled parts that are defective.
For example, an automated inspection process examines samples of bolts for severe cracks that make the bolts unusable. For each sample, analysts record the number of bolts inspected and the number of bolts rejected.

If you have attribute data, use one of the control charts in Stat > Control Charts > Attributes Charts.

## Rare event process data

Control charts for rare events show the amount of time or the number of opportunities between events. Plotted points that are higher on a control chart for rare events indicate a longer time between events. Plotted points that are lower on the chart indicate less time between events.

Some events occur so infrequently that you cannot use a traditional control chart, such as an Xbar-R or P chart, to monitor your data. Examples of rare events include hospital-acquired infections, medication errors, or manufacturing processes that have a low defect rate.

If you have rare event data, then use one of the control charts in Stat > Control Charts > Rare Event Charts.

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