XmR Chart (Individuals and Moving Range)
Monitor a process when measurements come one at a time and cannot be subgrouped. The XmR chart, also called the I-MR chart, plots individual values and the moving range between consecutive points, estimating variation without subgroups.
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An XmR chart, also known as an I-MR chart (Individuals and Moving Range), monitors a process using individual measurements rather than subgroups. It is used when data naturally arrives one value at a time, for a batch process, a slow-cycle measurement, an accounting figure, or any situation where forming rational subgroups is impractical.
It consists of two charts. The Individuals (X or I) chart plots each single measurement to monitor the process level. The Moving Range (mR) chart plots the absolute difference between consecutive measurements, which serves as the estimate of short-term variation in the absence of subgroups.
Because variation is estimated from the moving range of consecutive points, the XmR chart assumes the data is reasonably independent and, ideally, not strongly non-normal. It is remarkably versatile and widely used, but it is generally less sensitive at detecting small shifts than a subgrouped chart, which is the trade-off for working with individual values.
In plain terms: When you only get one measurement at a time, monthly figures, batch results, you can't form subgroups. The XmR chart handles this: it plots each value, and it estimates the spread from how much consecutive values differ (the moving range). It's the go-to chart for individual data.
The Two Charts
Individuals (X) Chart
Plots each individual measurement to monitor the process level over time.
Moving Range (mR) Chart
Plots the absolute difference between consecutive measurements, the estimate of short-term variation without subgroups. Read this first.
When to Use
Best when data arrives one value at a time and rational subgrouping is impractical.
Key Formulas
Reading the Charts
Read the moving range chart first, since the individuals chart's limits are derived from the average moving range. If the mR chart is out of control, the variation estimate is unstable and the individuals limits cannot be trusted.
The XmR chart is less sensitive to small, sustained shifts than subgrouped charts, so pattern rules (runs, trends) are especially valuable for early detection. Because it relies on the moving range, it is also more affected by non-normal data than subgrouped charts, so markedly skewed data may warrant a transformation.
Assumptions & Validation
Individual Measurements
Data is collected one value at a time.
If violated: If rational subgroups are available, a subgrouped chart is more sensitive.
Independence
Consecutive measurements are reasonably independent.
If violated: Autocorrelated data distorts the moving range; use time-series methods.
Approximate Normality
The data is not strongly non-normal.
If violated: Transform strongly skewed data before charting.
⚠️ Check assumptions first
The XmR chart estimates variation from the moving range of consecutive points, which makes it more sensitive to non-normality and autocorrelation than subgrouped charts. Check that consecutive values are reasonably independent and not strongly skewed. It is also less able to detect small shifts than an X-bar chart, so rely on pattern rules for early warning and read the moving range chart before the individuals chart.
When NOT to Use XmR (I-MR) Chart
Subgroups Available
When rational subgroups can be formed, an X-bar R or X-bar S chart detects shifts more sensitively.
Attribute Data
For counts or proportions of defects, use a P, NP, C or U chart.
Strong Autocorrelation
For heavily autocorrelated data, use time-series control methods rather than a standard XmR chart.
Industry Applications
Batch Processes
Monitor one measurement per batch where subgrouping is not possible.
Low-Volume or Slow Cycles
Track processes that produce infrequent measurements.
Business & Transactional Metrics
Monitor periodic figures such as monthly costs, cycle times or error counts.
Individual Test Results
Chart destructive or expensive tests that yield single values.
Frequently Asked Questions
What is an XmR chart used for?
An XmR chart, also called an I-MR chart, monitors a process using individual measurements rather than subgroups. It is used when data naturally comes one value at a time, such as batch results, slow-cycle measurements, or periodic business figures, where forming rational subgroups is impractical. It plots each individual value and the moving range between consecutive values to monitor the process level and its variation.
What is the moving range?
The moving range is the absolute difference between consecutive individual measurements. Because an XmR chart has no subgroups from which to estimate spread, the moving range serves as the estimate of short-term variation. The average moving range is used to calculate the control limits of both the individuals chart and the moving range chart, which is why the moving range chart is read first.
When should I use an XmR chart instead of an X-bar R chart?
Use an XmR chart when measurements arrive one at a time and cannot be sensibly grouped into rational subgroups, for example one reading per batch or one figure per month. When rational subgroups can be formed, an X-bar R or X-bar S chart is preferred because subgrouped charts are more sensitive at detecting shifts. The XmR chart is the tool for genuinely individual data.
Is the XmR chart less sensitive than subgrouped charts?
Yes. Because it works with individual values and estimates variation from the moving range, the XmR chart is generally less able to detect small, sustained shifts than a subgrouped X-bar chart, which averages out noise within each subgroup. This is the trade-off for handling individual data. Using pattern rules for runs and trends helps compensate by catching gradual changes earlier.
Does the XmR chart assume normal data?
The XmR chart is more sensitive to non-normality than subgrouped charts, because subgrouping tends to make subgroup means more normal through the Central Limit Theorem, whereas individual values do not benefit from that averaging. Moderately non-normal data is often acceptable, but strongly skewed data can produce misleading limits and may warrant a transformation before charting.
Why read the moving range chart before the individuals chart?
The control limits of the individuals chart are calculated from the average moving range. If the moving range chart is out of control, the estimate of variation is unstable, so the individuals chart's limits are not reliable. Assessing the moving range chart first confirms that the variation estimate is sound before the individuals chart is used to judge the process level.
Monitor Processes One Value at a Time
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