## Table of contents

Estimated reading time: 6 minutes

## What is an I-MR Chart?

Walter Shewart introduced the IMR chart; control charts are therefore also known as Shewart Charts. An I-MR chart (also called an XMR chart) is a combination of two charts (Individual Range and Moving Range), which are used to track process variability based on samples taken over a time period.

When continuous data are not collected into subgroups, an Individual Moving Range (IMR) chart can be used. Collect only one observation at a given time. A graphical I-MR chart shows the process variations over time. A graphical IMR chart can help identify when a process is out of control, and where to focus attention on the cause.

## Definition of I-MR

The IMR chart is a combination of two charts: the Individuals (I-) chart and the Moving Range (MR-) chart.

**I Chart:** An individual chart displays individual data points and monitors the average and changes in the process as the data is collected regularly. This chart can help identify common causes and their assignable values in the process.

**Moving Range Chart:** The Individual chart monitors process mean while the Moving Range chart monitors process variation when data points are collected regularly. The moving range chart shows the absolute difference between each measurement from its previous measurement.

## Uses of an I-MR Chart

- Check for any signs of causes that could lead to a process going out of control.
- Monitor the performance of the process before and after implementing process improvements.
- If the shop floor is slow and it’s difficult to get more samples.
- The cost of the measurement system is too high (like destructive tests).
- Most commonly used in batch processing.

## Differences Between an I-MR Chart and an X-R Chart

I-MR (Individuals Moving Range) charts and X-R (Range) charts are both types of control charts used in statistical process control to monitor and control the variability of a process. They are commonly employed in quality management to identify whether a process is in control or experiencing variations that may require investigation and correction. Here are the key differences between I-MR charts and X-R charts:

**Data Type**

**I-MR Chart:**The I-MR chart is used when individual observations (measurements) are taken from a process, and the moving range between consecutive observations is calculated.**X-R Chart:**The X-R chart is used when subgroups of data are collected, and the range (difference between the maximum and minimum values) within each subgroup is calculated.

**Chart Components**

**I-MR Chart:**It consists of two charts – an Individuals (I) chart and a Moving Range (MR) chart. The Individuals chart displays the individual data points, while the Moving Range chart shows the variability between consecutive data points.**X-R Chart:**It also consists of two charts – an X chart (for the subgroup averages) and an R chart (for the subgroup ranges). The X chart monitors the central tendency of the process, while the R chart monitors the variability within each subgroup.

**Sample Size**

**I-MR Chart:**It can be used with individual data points, and the moving range is calculated between consecutive points.**X-R Chart:**It requires data to be collected in subgroups, and the range is calculated for each subgroup.

**Application**

**I-MR Chart:**Suitable for processes where it is feasible or necessary to collect data one point at a time, such as measurements taken from a continuous process.**X-R Chart:**Commonly used in situations where it is practical to collect data in groups or batches, such as sampling from a production line.

**Sensitivity to Changes**

**I-MR Chart:**Generally more sensitive to small shifts in the process mean.**X-R Chart:**Tends to be more sensitive to changes in process variability.

**Calculations**

**I-MR Chart:**Involves the calculation of individual data points and the moving range between consecutive points.**X-R Chart:**Requires the calculation of subgroup averages (X-bar) and subgroup ranges.

**Assumptions**

**I-MR Chart:**Assumes that the process is stable and that individual observations are independent.**X-R Chart:**Assumes that the process is stable and that subgroup samples are representative of the process.

In summary, the choice between an I-MR chart and an X-R chart depends on the nature of the data and the sampling method used in a particular process. Both charts are valuable tools for quality control and process improvement, providing insights into process stability and identifying areas where intervention may be needed.

## How to use an I-MR Chart

An Individual-Moving Range (IMR) chart is a statistical tool used in quality control and process improvement to monitor the stability and variability of a process over time. The chart consists of two parts: the I-chart (Individuals chart) and the MR-chart (Moving Range chart). The I-chart displays individual data points, while the MR-chart shows the moving ranges between consecutive data points. Here’s a step-by-step guide on how to use an I-MR chart:

### Collect Data

- Gather data points from your process. The data should be collected in a chronological order.

### Calculate Moving Ranges

- Calculate the difference between consecutive data points to obtain the moving range. The formula for the moving range (MR) is usually (|X_i – X_{i-1}|).

### Plot the I-MR Chart

- Use statistical software or tools like Excel to create the I-MR chart. Plot the individual data points on the I-chart and the corresponding moving ranges on the MR-chart.

### Determine Control Limits

- Calculate the average (X̄) and the standard deviation (σ) of the individual data points. Use these values to determine control limits for both the I-chart and the MR-chart. For the I-chart:
- Upper Control Limit (UCL) = (X̄ + 3 \times \sigma)
- Lower Control Limit (LCL) = (X̄ – 3 \times \sigma) For the MR-chart:
- UCL_MR = (2.66 \times \text{average moving range}) (for smaller sample sizes, the constant may vary)

### Interpret the Chart

- Points on the I-chart falling within the control limits indicate a stable and predictable process. Points outside the limits may suggest special causes of variation that need investigation.
- Observe the MR chart for stability. Large or increasing moving ranges might indicate issues with the process.

### Respond to Out-of-Control Points

- Investigate and address any data points that fall outside the control limits. These points may indicate a special cause of variation that needs to be identified and eliminated.

### Continuous Monitoring

- Periodically update the IMR chart with new data to monitor the ongoing stability of the process.

### Tips

- Ensure that the data points are collected at random intervals and represent the natural variation of the process.
- If there are patterns, trends, or cycles in the data, further investigation may be needed.

The I-MR chart is a valuable tool for identifying variations in a process and determining whether the process is under control. Regular use of this chart can help maintain and improve the quality of a process over time.