Create the X-bar and R-charts for the following 25 samples. What conclusions can you draw?
First we calculate sample mean and range of Sample 23,24 and 25.
Sample | Item 1 | Item 2 | Item 3 | Item 4 | Item 5 | Sample Mean | Range |
23 | 10.20 | 9.50 | 9.60 | 9.80 | 10.30 | 9.88 | 0.80 |
24 | 10.30 | 10.60 | 10.30 | 9.90 | 9.80 | 10.18 | 0.80 |
25 | 9.90 | 10.30 | 10.60 | 9.90 | 10.10 | 10.16 | 0.70 |
Sample mean = Total of all items /5 , Range = Max observation - mIn observation
Sample | Sample Mean | Range |
1 | 10.28 | 0.70 |
2 | 10.17 | 0.35 |
3 | 10.07 | 0.40 |
4 | 10.09 | 0.40 |
5 | 10.31 | 0.30 |
6 | 10.16 | 0.40 |
7 | 10.12 | 0.50 |
8 | 10.27 | 0.30 |
9 | 10.34 | 0.50 |
10 | 10.30 | 0.40 |
11 | 10.05 | 0.85 |
12 | 10.14 | 0.70 |
13 | 10.28 | 0.80 |
14 | 10.40 | 0.40 |
15 | 10.36 | 0.55 |
16 | 10.29 | 0.60 |
17 | 10.42 | 0.70 |
18 | 9.96 | 1.00 |
19 | 10.22 | 0.80 |
20 | 10.38 | 0.40 |
21 | 10.14 | 1.00 |
22 | 10.23 | 0.55 |
23 | 9.88 | 0.80 |
24 | 10.18 | 0.80 |
25 | 10.16 | 0.70 |
Total | 255.20 | 14.90 |
Average | 10.208 | 0.596 |
X-double bar = 10.208
R-bar = 0.596
For sample size =5, Control chart constants:
A2 = 0.577
D3= 0
D4 =2.114
Using formulas above:
UCLx = 10.208 + 0.577*0.596 = 10.55
LCLx = 10.208-0.577*0.596= 9.86
UCLr = 2.114*0.596 = 1.26
LCLr = 0
Observations:
Create the X-bar and R-charts for the following 25 samples. What conclusions can you draw?