1. The Young Company produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimension (in.) from the last six samples are
|
|
Bottle
|
|
Sample
|
1
|
2
|
3
|
4
|
|
1
|
0.604
|
0.612
|
0.588
|
0.600
|
|
2
|
0.597
|
0.601
|
0.607
|
0.603
|
|
3
|
0.581
|
0.570
|
0.585
|
0.592
|
|
4
|
0.620
|
0.605
|
0.595
|
0.588
|
|
5
|
0.590
|
0.614
|
0.608
|
0.604
|
|
6
|
0.585
|
0.583
|
0.617
|
0.579
|
a) Assume that only these six samples are sufficient, and use the data to determine the necessary control limits.
b) Suppose the specification for the bottle neck diameter is 0.600 +/- 0.050 inches. If the population standard deviation is 0.013 inches, and the firm is seeking four-sigma quality, is the process capable of producing the bottle?
2. As a hospital administrator of a large hospital, you are concerned with the absenteeism among nurses' aides. The issue has been raised by registered nurses, who fell they often have to perform work normally done by their aides. To get the facts, absenteeism data was gathered for the last three weeks, which is considered a representative period for future conditions. After taking random samples of 64 personnel files each day, the following data were produced:
|
Day
|
Aides Absent
|
|
1
|
4
|
|
2
|
3
|
|
3
|
2
|
|
4
|
4
|
|
5
|
2
|
|
6
|
5
|
|
7
|
3
|
|
8
|
4
|
|
9
|
7
|
|
10
|
2
|
|
11
|
3
|
|
12
|
2
|
|
13
|
1
|
|
14
|
3
|
|
15
|
4
|
Because your assessment of absenteeism is likely to come under careful scrutiny, you would like a type 1 error of only 1 percent. You want to identify any instances of unusual absenteeism. If some is present, you will have to explore them on behalf of the registered nurses.
a) Design the appropriate control chart.
b) Based on your chart and the data from the last 3 weeks, what can you conclude about the absenteeism of nurses' aides?
3. A textile manufacturer wants to set up control charts for irregularities (e.g. oil stains, shop soil, loose threads, etc.) per 100 square yards of carpet. The following data were collected form a sample of 20 100-square-yard pieces of carpet
|
Sample
|
Irregularities
|
|
1
|
11
|
|
2
|
8
|
|
3
|
9
|
|
4
|
12
|
|
5
|
4
|
|
6
|
16
|
|
7
|
5
|
|
8
|
8
|
|
9
|
17
|
|
10
|
10
|
|
11
|
11
|
|
12
|
5
|
|
13
|
7
|
|
14
|
12
|
|
15
|
13
|
|
16
|
8
|
|
17
|
19
|
|
18
|
11
|
|
19
|
9
|
|
20
|
10
|
a) Using these data, set up a c-chart with z = 3.
b) Suppose that the next five samples had 15, 18, 12, 22 and 21 irregularities. What would you conclude?
4. A critical dimension of the service quality of a call center is the wait time of a caller to get a sales representative. Periodically, random samples of three customer calls are measured for time. The results of the last four samples are in the following table:
|
Sample
|
Time (sec)
|
|
1
|
495
|
501
|
498
|
|
2
|
512
|
508
|
504
|
|
3
|
505
|
497
|
501
|
|
4
|
496
|
503
|
492
|
a) Assuming that management is willing to use three-sigma control limits, and using only the historical information contained in the four samples, show that the call center access time is in statistical control.
b) Suppose that the standard deviation of the process distribution is 0.577. If the specifications for the access time are 500 +/- 18 seconds, is the process capable? Why or why not? Assume three-sigma quality.