Charts | I-MR / X-MR Theory
Binomial Poisson Normal Charts Histograms Hypothesis Testing
p Chart pn Chart u Chart c Chart X-Bar R X-Bar s I-MR / X-MR Out-of-Control
I-MR charts are the same as X-Bar R charts. However, I-MR charts work with a subgroup of 1. When calculating, though, we do so with a subgroup of 2. This is because, for each calculation, we compare the sample value with the next sample value. Thus, with 5 sets of samples, we take the range of 1 & 2 for the calculation of set 1, the range of 2 & 3 for the calculation of set 2 and so on. This is known as the Moving Range (MR).
Control Limits
Calculating control limits for continuous charts is a little more difficult than for discrete data such as Poisson or Binomial. Here, we calculate differently for each of the two charts.
I Chart
- Control Line (CL) = X =
ΣXi/n - Upper Control Limit (UCL) =
X + 3MR/d2 - Lower Control Limit (LCL) =
X - 3MR/d2
MR Chart
- Control Line (CL) = MR =
ΣMRi/n - Upper Control Limit (UCL) =
D4MR - Lower Control Limit (LCL) =
D3MR
Determinine d2, D4 and D3
Calculating the necessary values for d2, D4 and D3 is simply a matter of looking it up in the following table, provided you know the sample size n
| n | d2 | D4 | D3 |
| 2 | 1.128 | 3.267 | 0 |