---
alias: user-guide-individuals-and-moving-range
description: "This chart displays individual data points and moving ranges for process monitoring"
---

# Individuals And Moving Range (X Rm)

The following table lists the properties of the Individuals And Moving Range (X Rm) chart.

| Property                                            | Description                                                       |
|-----------------------------------------------------|--------------------------------------------------------------------|
| **Chart**                                     | Individuals and Moving Range *(I-MR)*                          |
| **Process observation types**                 | Variables                                                  |
| **Process observations relationships**        | Independent                                                |
| **Sample Size**                               | 1                                                          |
| **Distribution type**                         | Normal                                                     |
| **Size of shift to detect**                   | Large (≥ 1.5σ)                                             |
| **Individuals (Indicator 1)**               | $x$                                                          |U
| **Moving Range (Indicator 2)**              | $r_k = Abs(x_{k+1}-x_k)$         |
| **Mean**   | $\mu = \overline{\overline{x}} = \frac{\sum{x_i}}{n}$ |
| **Mean Range**   | $\overline{MR} = \frac{\sum{MR_i}}{i-1}$ |
| **Process Mean**   | $\mu$ |
| **Process Standard Deviation**   | $\overline{MR} = \frac{\sum{MR_i}}{i-1}$<br/>Note that the first data point does not have a $MR$<br/>$\sigma = S_{mr} = \frac{\overline{MR}}{d_2(w)}$<br/>Because we only support $w=2$, the $d_2(w)$ can be replaced by the constant `1,1284` |
| **Individuals (Indicator 1) Centerline**      | $\mu$ |
| **Individuals (Indicator 1) Control Limits**  | $UCL = \mu + 3 \sigma$<br/>$LCL = \mu - 3 \sigma$|
| **Moving Range (Indicator 2) Centerline**     | $\overline{MR} = \sigma\cdot d_2(w)$ |
| **Moving Range (Indicator 2) Control Limits** | $UCL = \overline{MR} + 3\sigma \cdot d_3(w)$<br/>$LCL = max(\overline{R}_i + 3\sigma \cdot d_3(w);0)$<br/>Where $w=2$|

Table: Individuals and Moving Range chart properties