Assignment (Statistical Process Control)
1) At Quickie Car Wash, the wash process is advertised totake less than 6 minutes. Consequently, management hasset a target average of 340 seconds for the wash process.Suppose the average range for a sample of 9 cars is 9 seconds.
2) Webster Chemical Company produces mastics andcaulking for the construction industry. The product isblended in large mixers and then pumped into tubes andcapped. Management is concerned about whether thefilling process for tubes of caulking is in statistical control.
The process should be centered on 8 ounces per tube.Several samples of eight tubes were taken, each tube wasweighed, and the weights in Table 5.3 were obtained.
a. Assume that only six samples are sufficient and developthe control charts for the mean and the range.
b. Plot the observations on the control chart and commenton your findings.
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
|
3) The Big Black Bird Company produces fiberglass campertops. The process for producing the tops must be controlledso as to keep the number of dimples low. Whenthe process was in control, the following defects werefound in 10 randomly selected camper tops over an extended period of time:
|
Top
|
Dimples
|
|
1
|
7
|
|
2
|
9
|
|
3
|
14
|
|
4
|
11
|
|
5
|
3
|
|
6
|
12
|
|
7
|
8
|
|
8
|
4
|
|
9
|
7
|
|
10
|
6
|
a. Assuming 10 observations are adequate for this purpose, determine the three-sigma control limits fordimples per camper top.
b. Suppose that the next camper top has 15 dimples.What can you say about the process now?
4) Janice Sanders, CEO of Pine Crest Medical Clinic, is concernedover the number of times patients must wait morethan 30 minutes beyond their scheduled appointments. Sheasked her assistant to take random samples of 64 patientsto see how many in each sample had to wait more than 30minutes. Each instance is considered a defect in the clinicprocess. The table below contains the data for 15 samples.
|
Sample
|
Number 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-sigmacontrol limits, construct a p-chart.
b. Based on your p-chart and the data in the table,what can you conclude about the waiting time of thepatients?