Data considerations for Acceptance Xbar-R Chart

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The data should be continuous

Continuous data are measurements that can have any numeric value within a range along a continuous scale, including fractional or decimal values. Common examples include measurements such as length, weight, and temperature.

The data should be in time order

Because control charts detect changes over time, the order of the data is important. You should enter the data in the order it was collected, with the oldest data at the top of the worksheet.

The data should be collected at appropriate time intervals

Collect data at equally spaced time intervals, such as every hour, every shift, or every day. Select a time interval that is short enough that you can identify changes to the process soon after the changes occur.

The data should be in rational subgroups

A rational subgroup is a small sample of items that are similar, that are produced in a short period of time under the same conditions (such as operator, equipment, or supplier), and that are representative of the output from a process. If the subgroups are not rational subgroups, the estimated control limits might be too narrow.

The subgroup size should be 8 or fewer observations

For subgroups that have 9 or more observations, use Acceptance Xbar-S Chart.

If you do not have subgroups, use Acceptance I-MR Chart.

Collect an appropriate amount of data

The appropriate amount of data depends on the subgroup size.

• If the subgroup size is less than or equal to 2, collect at least 100 observations.
• If the subgroup size is 3, collect at least 80 observations.
• If the subgroup size is 4 or 5, collect at least 70 observations.
• If the subgroup size is 6 or greater, collect at least 60 observations.

If you have fewer than the recommended number of observations, then you can still use the control chart, but the results are preliminary because the control limits might not be precise. If you use the chart regularly, re-estimate the standard deviation and the control limits after you collect the recommended number of observations.

The data do not need to be normally distributed

Although most control charts for variables data are formally based on the assumption of normality, you can still obtain good results with nonnormal data if you collect data in subgroups. The degree of nonnormality in the data determines the required subgroup size.

The observations within each subgroup should not be correlated with each other

If consecutive observations within each subgroup are correlated, the within-subgroup standard deviation might be underestimated. As a result, the acceptance control limits might be too wide, and the chart might incorrectly show some out-of-control points as in control.