How to Read and Interpret I-MR Charts

I-MR Charts, otherwise known as Individual (I) and Moving Range (MR) Charts, are Control Charts that are used to examine continuous data. Used together, these charts provide complete information on process behaviors. If you need to examine and measure data for individuals, rather than an entire subgroup, then an I-MR chart is the ideal option.

Individual (I) Chart plots individual data points over a specified period and is very useful to detect the various trends and shifts that are evident in the process. It helps people visualize common causes and any unusual or special cause variations if they are present. The generated data should be sequential and presented in the same order in which it was collected against the time axis to best interpret trends compared to time performance.

The Moving Range (MR) Chart is developed by plotting values obtained from the sequential; time-ordered data. Every moving range point is calculated as Xn - Xn - 1 and therefore has one less data point than the Individual (I) Chart.

I-MR Chart Example
The I-MR chart allows process stability to be evaluated according to the variation between consecutive individual data points. The process is unstable whenever the points are out of control limits.
I-MR Chart Composition
I-MR charts are comprised of a top graph which is the Individual (I) Chart. This plots individual observational values and offers a way to evaluate the processing center.

The lower part of the chart is a Moving Range (MR) Chart which plots process variation as measured from 2 or more successive observational ranges.

Mean value: Represented by the green line
Upper and lower control limits: Represented by the red lines.
In control process: Reveals only random variations within control limits
Out of control process: Shows unusual variation possibly due to unique causes.

I-MR Charts have three fundamental uses:
Monitoring process stability so that if a problem is revealed because of changes, you can address it.
Identifying stability in a process, so you know if it is ready to be improved. Changes can't be correctly evaluated when an unstable process is changed so this chart can either confirm or deny process stability before implementing changes.
Showing improved process performance via a before and after I-MR Chart.

Interpreting I-MR Chart Results with an Example Scenario

Along with statistical institutions, pharmaceutical companies use I-MR Charts extensively. Let's pick an example from the pharmaceutical organization, where the company is developing a new product and has to determine if the pH value for a medication falls within normal and acceptable limits. The data can't be sub-grouped because the medication is made in batches and only 1pH measurement can be collected per batch.

To gain a measurement of the pH levels, 23 consecutive batches were measured through an I-MR Chart.

The I-MR chart results are simpler to interpret by looking at the charts separately, so we'll begin with the MR chart:

To start with, you have to figure out if the process variation is in control, so you must study the MR Chart.
The control limits on the I Chart will be inaccurate if the MR Chart is out of control.
Unstable variation causes lack of control in the I Chart.
If the MR Chart is in control, then changes in the processing center are causing an out of control I Chart.
In the above graph representation, the failed tests are indicated with a red symbol.
In this chart, the points display a random pattern, and none of the individual observations fall outside the lower and upper control limits. Therefore the process variation is in control.

Now we'll examine the I Chart:

The above graph representation reveals that three observations failed two tests, and the points were flagged at point 8 for Test 1, and points 20 and 21 for Test 2.
This I-MR Chart reveals instability in the process average and an out of control process, likely because of special causes.

Because of these findings, the pharmaceutical company understands that there is an issue that needs to be addressed and corrected before they release their new medication. Components that are contributing to the cause variation can now be examined in greater detail and eliminated so that the process can reach statistical control.

Agile Statistical Solutions from the Experts at Research Optimus

Great care should be applied toward performing all calculations, plotting results, and ensuring that the control limits are accurately calculated to avoid potential inconclusive of erroneous outcomes. It's important to rely on professional analysts with experience performing statistical modeling through the right software, critical thinking capabilities, and proven analytical methodologies.

Research Optimus (ROP) develops statistical analysis solutions that are positioned to accurately and objectively examine and interpret a business's most important data. With exceptional steps taken to provide results in a readable, customized format, ROP meets varied business needs for I-MR Control Chart applications. To know more about our offerings and discuss your projects directly with our experienced analysts,

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