An I-MR Chart is a control chart which is used when data is in continuous category and is collected once at a time. It consists of two charts placed one over above, I Chart which is individual chart and MR chart is plotted for moving range which is absolute value of the difference between two consecutive points.
Data following normal distribution is an assumption while drawing I-MR chart however in practical or real-world problem data doesn’t follow normal distribution all the time hence Process stability follows major role. I-MR charts are very sensitive to Normality of the data. Non-Normal data if considered as normal data can cause unexpected behaviors including false alarm rates and difficulty in identifying the special cause variation.
If data is not normal, it is always advisable to do transformation using Box-Cox or Johnsons transformation to avoid the false alarm and get the right behavior of data for stability and control.
A normal distribution may have the value from minus to plus infinity. In the real-world example this doesn’t occur physically very often. For example, Cycle time cannot be in negative numbers.
Following is the Example for drawn I-MR charts when data is considered as normal however data is not normal and respective I-MR charts using data transformation: -
Cycle time in Minutes: -
Sl.No
Cycle Time (In Minutes)
S.No
Cycle Time (In Minutes)
S.No
Cycle Time (In Minutes)
1
3196
11
267
21
322
2
241
12
302
22
147
3
372
13
518
23
774
4
42
14
554
24
185
5
481
15
566
25
556
6
6081
16
900
26
555
7
131
17
158
27
361
8
26
18
109
28
556
9
1445
19
167
29
898
10
363
20
51
30
170
Table 1
Probability Plot of dats Using Mini-tab Normality test for data in Table 1: -
Normality test is done to illustrate whether data is normal or non-normal.
I-MR Charts drawn in Minitab for Table 1 mentioned assuming data following Normal distribution: -
The chart clearly illustrates that process is out of control, however out of control points are trigged due to false alarms
I-MR Chart drawn in Minitab for Table 1 mentioned after transforming days using Box-Cox transformation: -
The Chart clearly illustrates that process is in control, our of control data points mentioned earlier were due to false alarm in wrong assumption of data being normal.