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 4 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: 2.07,2.08,2.07,2.08,2.05
Sample Mean: 2.07