Homework Sourse1 At Quickie Car Wash the wash process is advertised to take
1. At Quickie Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 10 seconds. Use Table A in the lecture note # 8 to establish control limits for sample means and ranges for the car wash process. (20 points)
2. Garcia’s Garage desires to create some colorful charts and graphs to illustrate how reliably its mechanics “get under the hood and fix the problem”. The historical average for the proportion of customers that return for the same repair within the 30-day warranty period is 0.10. Each month, Garcia tracks 100 customers to see whether they return for warranty repairs. The results are plotted as a proportion to report progress toward the goal. Determine the control limits for this chart. In March, 8 of the 100 customers in the sample group returned for warranty repairs. Is the repair process in control? (20 points)
3. The Canine gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 45 grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of 10 packets and weights each packet. When the process is in control, the range in the weight of each sample has averaged 6 grams.
a. Design an R and an X-bar chart for this process by determining control limits. (10 points)
b. The results from the last 5 samples of 10 packets are shown in the following table. Is the process in control? (Here, you can use the control limits and center lines from the above, part a) If not, what would you do? (10 points)
Sample
X-bar
R
1
44
9
2
40
2
3
46
5
4
39
8
5
48
3
4. Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. Several samples of eight tubes were taken, each tube was weighted, and the weights in the following table were obtained.
Tube Number
Sample
1
2
3
4
5
6
7
8
1
7.98
8.34
8.02
7.94
8.44
7.68
7.81
8.11
2
8.33
8.22
8.08
8.51
8.41
8.28
8.09
8.16
3
7.89
7.77
7.91
8.04
8.00
7.89
7.93
8.09
4
8.24
8.18
7.83
8.05
7.90
8.16
7.97
8.07
5
7.87
8.13
7.92
7.99
8.10
7.81
8.14
7.88
6
8.13
8.14
8.11
8.13
8.14
8.12
8.13
8.14
a. Assume that only six samples are sufficient and develop the control charts for the mean and the range. (10 points)
b. Plot the observations on the control chart and comment on your findings. (10 points)
5. Janice Sanders, CEO of Pine Crest Medical Clinic, is concerned over the number of times patients must wait more than 30 minutes beyond their scheduled appointments. She asked her assistant to take random samples of 64 patients to see how many in each sample had to wait more than 30 minutes. Each instance is considered a defect in the clinic process. The table below contains the date from 15 samples.
Sample
# of defects
1
5
2
2
3
1
4
3
5
1
6
5
7
2
8
3
9
6
10
3
11
9
12
9
13
5
14
2
15
3
a. Assuming Janice Sanders is willing to use three-sigma control limits, construct a p-chart. (10 points)
b. Based on your p-chart and the data in the table, what can you conclude about the waiting time of the patients? (10 points)
| Sample | X-bar | R |
| 1 | 44 | 9 |
| 2 | 40 | 2 |
| 3 | 46 | 5 |
| 4 | 39 | 8 |
| 5 | 48 | 3 |
Solution
