In: Statistics and Probability
To determine if their 2.00 inch washers are properly adjusted, Duncan & Hall Inc. has decided to use an x‾-Chart which uses the range to estimate the variability in the sample.
Table:
Period |
obs1 |
obs2 |
obs3 |
obs4 |
obs5 |
Sample Mean |
Sample Range |
1 |
1.96 |
2.05 |
1.97 |
1.97 |
2 |
1.99 |
0.09 |
2 |
2 |
2.05 |
1.95 |
2 |
2.05 |
2.01 |
0.1 |
3 |
2.04 |
1.96 |
1.96 |
1.97 |
1.96 |
1.978 |
0.08 |
4 |
1.97 |
2 |
1.98 |
1.99 |
1.99 |
1.986 |
0.03 |
5 |
1.97 |
2.05 |
1.98 |
2.04 |
2.05 |
2.018 |
0.08 |
6 |
2.03 |
2.05 |
2.01 |
1.96 |
1.96 |
2.002 |
0.09 |
7 |
2.02 |
1.98 |
2.03 |
1.96 |
2.01 |
2 |
0.07 |
8 |
1.99 |
1.99 |
2.01 |
1.98 |
1.97 |
1.988 |
0.04 |
9 |
2 |
2.03 |
1.99 |
1.95 |
1.97 |
1.988 |
0.08 |
10 |
1.95 |
1.99 |
1.98 |
1.96 |
2 |
1.976 |
0.05 |
11 |
2.03 |
1.98 |
1.96 |
2.02 |
2.04 |
2.006 |
0.08 |
Step 5 of 7:
Use the following sample data, taken from the next time period,
to determine if the process is "In Control" or "Out of
Control".
Observations: 2,1.98,1.93,1.95,1.96
Sample Mean: 1.964
Period | obs1 | obs2 | obs3 | obs4 | obs5 | Sample Mean | Sample Range |
1 | 1.96 | 2.05 | 1.97 | 1.97 | 2 | 1.99 | 0.09 |
2 | 2 | 2.05 | 1.95 | 2 | 2.05 | 2.01 | 0.1 |
3 | 2.04 | 1.96 | 1.96 | 1.97 | 1.96 | 1.978 | 0.08 |
4 | 1.97 | 2 | 1.98 | 1.99 | 1.99 | 1.986 | 0.03 |
5 | 1.97 | 2.05 | 1.98 | 2.04 | 2.05 | 2.018 | 0.08 |
6 | 2.03 | 2.05 | 2.01 | 1.96 | 1.96 | 2.002 | 0.09 |
7 | 2.02 | 1.98 | 2.03 | 1.96 | 2.01 | 2 | 0.07 |
8 | 1.99 | 1.99 | 2.01 | 1.98 | 1.97 | 1.988 | 0.04 |
9 | 2 | 2.03 | 1.99 | 1.95 | 1.97 | 1.988 | 0.08 |
10 | 1.95 | 1.99 | 1.98 | 1.96 | 2 | 1.976 | 0.05 |
11 | 2.03 | 1.98 | 1.96 | 2.02 | 2.04 | 2.006 | 0.08 |
total | 21.942 | 0.79 | |||||
average | 1.995 | 0.072 |
from above :
sample mean x̅ = | 1.995 | ||||
average range R̅ = | 0.072 | ||||
sample size n = | 5 | ||||
for sample size n=5, criitcal value of constant A2= | 0.577 | ||||
control line (CL) = x̅= | 1.995 | ||||
upper control limit =x̅+3*A2R̅ = | 2.037 | ||||
lower control limit =x̅-3*A2R̅ = | 1.953 |
as 1.964 falls between upper and lower control limit ; therefore process is "In Control"