1. If 
= 90.60, 
= 0.95, and the sample size is 3, determine the control limits
for averages and for ranges. Use the control chart formulas on the previous page.
= ______________ 
= ______________
= ______________ 
= ______________
2. A filling process has the grand average 10.3 kg, the average
range 1.6 kg, and
sample size n = 5. Calculate the upper and lower control limits
for 
and R.
= ______________ = ______________
= ______________ = ______________
#32 Use the spreadsheet data below to answer the following questions:
1. What is the number of observations (individual x's)?
2. What is the subgroup size or the number of observations per sample (n)?
3. How many samples in all were taken ?
4. How much is ? What is the value of ?
5. What is a problem with putting day shift data together consecutively?
6. What other features of the data do you see?
| Day | Time | Obs.1 (left) | Obs.2 (ctr.) | Obs.3 (rt.) | Average | Range |
| 1/2 | 10:00 | 31 | 33 | 29 | 31.0 | 4 |
| 11:15 | 28 | 28 | 27 | 27.7 | 1 | |
| 1:30 | 28 | 28 | 27 | 27.7 | 1 | |
| 3:00 | 26 | 29 | 27 | 27.3 | 3 | |
| 3:45 | 30 | 35 | 31 | 32.0 | 5 | |
| 1/3 | 8:30 | 26 | 29 | 27 | 27.3 | 3 |
| 10:30 | 26 | 28 | 27 | 27.0 | 2 | |
| 1:30 | 29 | 28 | 27 | 28.0 | 2 | |
| 3:30 | 26 | 27 | 26 | 26.3 | 1 | |
| 1/4 | 8:30 | 27 | 27 | 26 | 26.7 | 1 |
| 11:20 | 27 | 28 | 26 | 27.0 | 2 | |
| 1:00 | 27 | 28 | 27 | 27.3 | 1 | |
| 3:45 | no data | |||||
| 1/5 | 9:00 | 26 | 28 | 29 | 27.7 | 3 |
| 11:00 | 27 | 29 | 26 | 27.3 | 3 | |
| 2:00 | 27 | 28 | 26 | 27.0 | 2 | |
| 3:30 | 25 | 29 | 25 | 26.3 | 4 | |
| 1/6 | 8:30 | 27 | 29 | 27 | 27.7 | 2 |
| 11:00 | 27 | 29 | 27 | 27.7 | 2 | |
| 1:45 | 27 | 28 | 28 | 27.7 | 1 | |
| 3:45 | 28 | 34 | 39 | 30.3 | 6 | |
| 1/7 | 8:30 | 27 | 29 | 26 | 27.3 | 3 |
| 11:00 | 27 | 29 | 26 | 27.3 | 3 | |
| 2:00 | 27 | 29 | 26 | 27.3 | 3 | |
| 3:45 | 29 | 30 | 28 | 29.0 | 2 | |
| mean | 27.29 | 29.13 | 27.08 | 27.8 | 2.5 | |
| st. dev. | 1.34 | 1.99 | 1.32 | grand ave. | ave. range | |
| range | 6 | 8 | 6 | |||
| count | 24 | 24 | 24 | 72 |