# IR Chart with SigmaXL

### What is an IR Chart?

The IR chart (also called individual-moving range chart or I-MR chart) is a popular control chart for continuous data with subgroup size equal to one.

- The I chart plots an individual observation as a data point.
- The MR chart plots the absolute value of the difference between two consecutive observations in individual charts as a data point.

If there are n data points in the I chart, there are n –1 data points in the MR chart. The I chart is valid only if the MR chart is in control. The underlying distribution of the I-MR chart is normal distribution.

### I Chart Equations

I Chart (Individuals Chart)

Data Point:

Center Line:

Control Limits:

Where: n is the number of observations.

### MR-Chart Equations

MR Chart (Moving Range Chart)

Data Point:

Center Line

Upper Control Limit:

Lower Control Limit: 0

Where: n is the number of observations.

### Use SigmaXL to Plot I-MR Charts

Data File: “IR” tab in “Sample Data.xlsx”

Steps to plot IR charts in SigmaXL:

- Select the entire range of data
- Click SigmaXL -> Control Charts -> Individuals & Moving Range
- A new window named “Individuals and Moving Range” appears with the selected range automatically populated into the box below “Please select your data”.

- Click “Next>>”
- A new window named “Individuals and Moving Range Chart” pops up.
- Select “Measurement” as the “Numeric Data Variable (Y)”

- Check the checkbox of “Test for special causes”
- Click “OK>>”
- The IR charts appear in the newly generated tab “Indiv & MR Charts (1)”.

#### I-MR Charts Diagnosis

Model summary: The I-MR Chart (Individuals’ Chart) above shows that test 6 and 5 fail and the table above calls out the data observations that failed these tests. Also, since the MR chart is out of control, the I chart is invalid. In the MR Chart (Moving Range Chart): Two data points fall beyond the upper control limit. This indicates the MR chart is out of control (i.e., the variations between every two contiguous individual samples are not stable over time). We need to further investigate the process, identify the root causes that trigger the outliers, and correct them to bring the process back in control.