Calculating range control limits involves determining the upper and lower bounds within which the ranges of subgroups in your data are expected to fall, assuming the process is in statistical control. This helps monitor process variability. Here's a step-by-step guide:
1. Calculate the Average Range (R̄)
First, collect data and divide it into subgroups (samples). Then, for each subgroup, calculate the range (R) by subtracting the smallest value from the largest value. Finally, determine the average range (R̄) by summing all the individual ranges and dividing by the number of subgroups (k).
R̄ = (R₁ + R₂ + ... + Rₖ) / k
Where:
- R̄ = Average Range
- R₁, R₂, ... Rₖ = Range of each subgroup
- k = Number of subgroups
2. Determine the Control Chart Factors
You'll need to use control chart factors, specifically D₃ and D₄, which depend on the subgroup size (n). These factors are typically found in control chart factor tables. These factors are derived from statistical calculations related to the expected distribution of ranges.
| Subgroup Size (n) | D₃ | D₄ |
|---|---|---|
| 2 | 0 | 3.267 |
| 3 | 0 | 2.574 |
| 4 | 0 | 2.282 |
| 5 | 0 | 2.114 |
| 6 | 0 | 2.004 |
Note: These are just a few examples. You will need a more comprehensive table based on your subgroup size.
3. Calculate the Upper and Lower Control Limits
Now, calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) for the Range chart:
- Upper Control Limit (UCL): UCL = D₄ * R̄
- Lower Control Limit (LCL): LCL = D₃ * R̄
4. Plot the Range Control Chart
Create a chart with the subgroup number on the x-axis and the range on the y-axis. Plot the individual ranges of each subgroup. Draw a horizontal line representing the average range (R̄), the UCL, and the LCL.
5. Analyze the Control Chart
Examine the chart for any points falling outside the control limits (UCL and LCL). Also, look for patterns or trends that indicate a lack of statistical control, such as:
- Points consistently above or below the center line.
- A run of several points on one side of the center line.
- Trends of increasing or decreasing ranges.
Example
Let's say you have 5 subgroups (k=5) with a subgroup size of 4 (n=4). The ranges for each subgroup are: R₁=5, R₂=7, R₃=3, R₄=6, R₅=4.
- Calculate R̄: R̄ = (5 + 7 + 3 + 6 + 4) / 5 = 5
- Find D₃ and D₄: For n=4, D₃ = 0 and D₄ = 2.282 (from a control chart factor table).
- Calculate UCL and LCL:
- UCL = 2.282 * 5 = 11.41
- LCL = 0 * 5 = 0
Therefore, in this example the UCL is 11.41 and the LCL is 0. Plot these values along with the individual ranges on your control chart.
