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) | \(x\) |
| 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 | \(\overline{MR} = \frac{\sum{MR_i}}{i-1}\) Note that the first data point does not have a \(MR\) \(\sigma = S_{mr} = \frac{\overline{MR}}{d_2(w)}\) 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 | \(UCL = \mu + 3 \sigma\) \(LCL = \mu - 3 \sigma\) |
| Moving Range (Indicator 2) Centerline | \(\overline{MR} = \sigma\cdot d_2(w)\) |
| Moving Range (Indicator 2) Control Limits | \(UCL = \overline{MR} + 3\sigma \cdot d_3(w)\) \(LCL = max(\overline{R}_i + 3\sigma \cdot d_3(w);0)\) Where \(w=2\) |
Table: Individuals and Moving Range chart properties