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X-MR chart

What is it?

An individuals and moving range (X-MR) chart is a pair of control charts for processes with a subgroup size of one. Used to determine if a process is stable and predictable, it creates a picture of how the system changes over time. The individual (X) chart displays individual measurements. The moving range (MR) chart shows variability between one data point and the next. Individuals and moving range charts are also used to monitor the effects of process improvement theories.

What does it look like?

The individuals chart, on top, shows each reading. It is used to analyze central location. The moving range chart, on the bottom, shows the difference between consecutive readings. It is used to study system variability.

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When is it used?

Use an X-MR control chart when you can answer “yes” to all of the following questions:

  1. Do you need to assess the variability in the system?
    All control charts are used to assess whether the variation in a process is generated by special or common causes. Control charts are maintained on an ongoing basis in order to minimize the chance of reacting inappropriately to the variation by either overcontrolling or undercontrolling the system or process.

  2. Can the data be collected or does a collection of data already exist?
    The data must be generated on an ongoing basis. Control charts analyze a series of data points, not a single data point.

  3. Is the time order of the data preserved?
    Since control charts are designed to study the behavior of a system over time, it is critical that the data is recorded in the order it is collected and produced. Mixing the order of the data would be like editing a movie film with no attention given to the sequence of events.

  4. Is the data in variables format?
    Variables data is measurements, such as height, weight, length, pressure, time, or temperature. Other control charts are used for attributes data.

  5. Is the data collected in subgroups of one?
    This means single data points, not groups. Average and range charts (-R) are used to chart variables data with subgroups larger than one.

Getting the most

Collect as many points as possible before calculating control limits. The less data you have, the less likely it is that the chart represents the variability of the entire system. The more data points you use in control limit calculations, the more reliable the X-MR chart analysis will be. Typically, 20 to 25 data points will be used in control limit calculations.

Individuals charts are not as sensitive to shifts in data as other variables control charts. Therefore, this chart may not provide the quick process feedback that other control charts offer. For this reason you should also pay close attention to the MR chart, which shows variation between data points.

Effective use of X-MR charts depends heavily on good sampling techniques. Variation in chemical compounds and contamination levels in batch processes such as dip tanks and plating baths, for example, depends on the volume of product processes rather than time. In these cases, base sampling schedules on volume rather than time. Variation in temperature will often produce a cyclical chart of heating and cooling temperatures when samples are taken over time.