Period Cycle Time
1 45
2 33
3 44
4 30
5 51
6 47
7 39
8 34
9 69
10 43
11 29
12 38
13 45
14 49
15 73
16 38
17 50
18 40
19 57
20 36
21 31
22 46
23 40
24 51
25 48
26 37
27 42
28 50
Calculated R-Bar:
Upper control limit for the range:
Upper control limit for the individuals:
Lower control limit for the individuals:
Based upon what the control chart is telling you what would you do?
Is there adaquate discrimination?
To calculate the R-Bar (average range) and control limits, we need to first determine the range for each sample. The range is calculated by subtracting the smallest value from the largest value within each sample. Let's calculate the ranges for each sample:
Sample 1 range = 45 - 45 = 0
Sample 2 range = 33 - 33 = 0
Sample 3 range = 44 - 44 = 0
Sample 4 range = 30 - 30 = 0
Sample 5 range = 51 - 51 = 0
Sample 6 range = 47 - 47 = 0
Sample 7 range = 39 - 39 = 0
Sample 8 range = 34 - 34 = 0
Sample 9 range = 69 - 69 = 0
Sample 10 range = 43 - 43 = 0
Sample 11 range = 29 - 29 = 0
Sample 12 range = 38 - 38 = 0
Sample 13 range = 45 - 45 = 0
Sample 14 range = 49 - 49 = 0
Sample 15 range = 73 - 73 = 0
Sample 16 range = 38 - 38 = 0
Sample 17 range = 50 - 50 = 0
Sample 18 range = 40 - 40 = 0
Sample 19 range = 57 - 57 = 0
Sample 20 range = 36 - 36 = 0
Sample 21 range = 31 - 31 = 0
Sample 22 range = 46 - 46 = 0
Sample 23 range = 40 - 40 = 0
Sample 24 range = 51 - 51 = 0
Sample 25 range = 48 - 48 = 0
Sample 26 range = 37 - 37 = 0
Sample 27 range = 42 - 42 = 0
Sample 28 range = 50 - 50 = 0
Since all the ranges are zero, the calculated R-Bar will also be zero.
To determine the control limits for the range, we can use the following formula:
Upper Control Limit (UCL) for the range = R-Bar * D4
Lower Control Limit (LCL) for the range = R-Bar * D3
D3 and D4 are constants based on the sample size. For a sample size of 4, D3 = 0 and D4 = 2.282.
For the individuals control chart, we can calculate the control limits using the following formulas:
Upper Control Limit (UCL) for the individuals = R-Bar * A2
Lower Control Limit (LCL) for the individuals = R-Bar * A1
A1 and A2 are constants based on the sample size. For a sample size of 4, A1 = 0 and A2 = 2.659.
However, since all the ranges are zero in this data, it appears that there is some error in the data itself or in recording the ranges. Without meaningful range values, we cannot accurately calculate the R-Bar and control limits.
Based on the control chart, if the data were valid, we usually look for patterns or points that fall outside the control limits to identify special causes of variation. These special causes can indicate issues that need to be addressed in order to improve the process.
Regarding the question of "adequate discrimination," it is not clear what is meant by that term in this context. In statistical process control, discrimination usually refers to the ability to distinguish between different levels or classes of a variable. In this case, we don't have enough information about the specific variable or the goal of the analysis to determine if there is adequate discrimination.