# What is an I-MR-R/S (Between/Within) chart?

## What is an I-MR-R/S chart?

Use an I-MR-R/S chart to monitor the mean of your process and the variation between and within subgroups when each subgroup is a different part or batch.

The I-MR-R/S chart consists of:
I chart
The I chart monitors the process mean. The control limits of the I chart are calculated using the between-subgroup variation, but not the within-subgroup variation.
MR chart
The moving range chart plots a moving range of the subgroup means. Therefore, the MR chart only monitors the between-subgroup component of variation, not the within-subgroup variation.
R chart or S chart
The R or S chart monitors within-subgroup variation.

### Example of an I-MR-R/S chart

A manufacturer of steel beams coats each beam with an anti-corrosion treatment. Engineers measure the thickness of the coating at 5 positions on each beam. Because the engineers want to monitor the variation in the coating thickness both within a single beam and across all beams, they use a I-MR-R/S chart.

## When should I use an I-MR-R/S chart?

Use an I-MR-R/S chart when your within-subgroup variation includes more than just common-cause variation. If you do not account for variability in your sampling technique, your process may appear to be in control when it is not. Use an I-MR-R/S chart when you need to consider both between-subgroup and within-subgroup variation on the same chart.

When you collect data in subgroups, common-cause variation, or random error, should be the only source of within-subgroup variation. For example, if you sample five parts in close succession every hour, the only differences should be due to random error. Over time, the process could shift or drift, so the next sample of five parts may be different from the previous sample. Under these conditions, the overall process variation is due to both between-sample variation and random error.

Variation within each sample also contributes to overall process variation. Suppose you sample one part every hour, and measure five positions across the part. While the parts can vary hour to hour, the measurements taken at the five positions can also be consistently different in all parts. Perhaps one position almost always produces the largest measurement, or is consistently smaller. This variation due to position is not accounted for, and the within-sample standard deviation no longer estimates random error, but actually estimates both random error and the position effect. This results in an estimated standard deviation that is too large, causing control limits that are too wide, with most points on the control chart placed very close to the center line.

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