Moving Range (MR)

Introduction: Moving Range (MR)

The Moving Range (MR) is a statistical measure used in control charts to monitor short-term variability in a process. It is calculated as the absolute difference between consecutive data points and is an essential component of Individuals and Moving Range (I-MR) charts in Statistical Process Control (SPC).

Background

In quality management, it is often necessary to monitor processes where only single observations are available rather than subgroups of data. The Moving Range provides a simple yet effective way to quantify variation in such cases, making it especially valuable for processes with low production volumes or one-off measurements.

Key Elements / Features

Purpose:

• Measures short-term variation in a process.
• Detects inconsistencies or shifts in variability.
• Enables monitoring when subgrouping is not possible.

Formula:

For a sequence of observations X1, X2, …,Xn:

\(
MR_i = |X_i – X_{i-1}|
\)

The average moving range is calculated as:

\(
\overline{MR} = \dfrac{\sum MR_i}{n – 1}
\)

Where:

• MRi = moving range at time i
• Xi = current observation
• Xi−1 = previous observation

Applications / Examples

• I-Chart (Individuals Chart): Plots individual data values over time.
• MR-Chart (Moving Range Chart): Displays moving ranges to visualise short-term variability.
• Control Limits: The average MR is used to calculate control limits for I-Charts.

Example:

A machine produces parts with diameters (mm): 10.2, 10.3, 10.5, 10.4

MR(2)=∣10.3−10.2∣=0.1

MR(3)=∣10.5−10.3∣=0.2

MR(4)=∣10.4−10.5∣=0.1

The average moving range is:

\(
\overline{MR} = \dfrac{0.1 + 0.2 + 0.1}{3} = 0.133
\)

This value (\(\overline{MR} = 0.133\)) is then used to determine control limits for the process.

Relevance / Impact

Benefits:

• Simple to calculate and interpret.
• Useful where subgrouping is not feasible.
• Sensitive for detecting short-term variation.

Limitations:

• Less stable with very small datasets.
• Can be influenced by outliers or sudden shifts.

See also

• Statistical Process Control (SPC)
• Special Cause Variation
• Control Limits
• Variation