Statistical Process Control | Complete Solution

Statistical Process Control

A canning company packages canned soup for a major soup manufacturer for distribution to regional wholesalers.  The company processes 5,000 cans of soup each day using an automated packaging machine that is programmed to fill each can with 14.0 ± 0.1 ounces net weight of soup.  The company's quality assurance process consists of randomly selecting five cans from the production line each hour and carefully weighing them.  Each hour's sample group is considered acceptable if no less than four out of the five cans examined weigh 14.0 ± 0.1 ounces.  Sample observations for a 24-hour production run are reflected in the table below. 

Hour

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

1

13.98

13.93

14.01

14.06

14.05

2

14.08

13.89

13.98

14.05

13.94

3

13.96

13.91

13.9

13.95

13.96

4

13.89

13.97

13.97

14.00

13.98

5

13.98

13.98

14.06

13.99

13.99

6

13.97

14.09

14.04

14.11

13.96

7

14.08

13.91

14.02

14.04

14.09

8

13.99

13.97

14.03

13.98

14.03

9

13.92

13.95

13.92

13.98

13.99

10

14.00

13.98

14.1

13.91

13.96

11

13.87

14.07

13.93

13.96

14.03

12

14.02

14.04

14.02

13.93

13.94

13

14.03

14.01

13.95

13.98

14.00

14

14.02

14.00

13.95

14.09

14.02

15

14.00

14.04

14.04

13.96

13.95

16

14.05

13.93

13.92

14.03

14.03

17

14.11

14.07

14.06

14.00

14.00

18

14.02

13.99

13.94

13.91

14.04

19

14.02

14.03

14.01

13.94

14.06

20

13.98

13.95

13.95

13.97

13.97

21

13.97

14.04

14.02

13.96

14.06

22

13.91

14.02

13.99

14.00

13.96

23

13.97

14.04

14.04

14.02

14.03

24

14.08

14.01

14.02

14.09

13.98

Prepare an x-bar chart and R-chart that reflect a 99.7% confidence level in order to answer questions 15 through 20:

1. What is the x-bar UCL?
   • 13.65
   • 14.78
   • 14.06
   • 13.25

1. What is the x-bar LCL?
   • 13.23
   • 13.93
   • 14.07
   • 13.56

1. What is the range UCL?
   • 0.24
   • 0.39
   • 0.49
   • 0.67

1. What is the range LCL?
   • 0.00
   • -0.12
   • 0.12
   • -0.20

1. Does x-bar chart indicate that the process was operating within statistical control during the 24-hour period?
   • Yes
   • No

1. Does the R-chart indicate that the process was operating within statistical control during the 24-hour period?
   • Yes
   • No

The manager of the customer service hotline for an internet service provider has been approached by the President of the company regarding a perceived increase in the number of customer complaints regarding the lack of timely technical assistance being provided by hotline technicians.  In order to evaluate the validity of the President’s concerns he decided to survey customers regarding their satisfaction with the timeliness of the technical assistance they received.  Surveys were conducted during a thirty-day period with twenty-five randomly selected customers participating in the survey each day.  The number of customers surveyed who expressed dissatisfaction with the timeliness of the technical assistance they received is summarized in the following table.

Day

No. Complaints

1

0

2

5

3

6

4

0

5

0

6

1

7

3

8

0

9

1

10

2

11

2

12

0

13

0

14

3

15

5

16

1

17

6

18

2

19

0

20

1

21

4

22

3

23

0

24

2

25

1

26

0

27

8

28

9

29

2

30

1

Using the preceding data set, prepare a c-chart and p-chart that reflects a 99.7% confidence level in order to answer questions 21 through 25:

1. What is the UCL for the number of complaints?
   • 5.83
   • 6.78
   • 6.24
   • 4.99

1. What is the LCL for the number of complaints?
   • 0.00
   • 0.13
   • 0.25
   • -0.16

1. What is the UCL for the proportion of complaints?
   • 0.45
   • 0.39
   • 0.26
   • 0.15

1. What is the LCL for the proportion of complaints? 
   • -0.18
   • -0.07
   • 0.00
   • 0.08

1. Do the c-chart and p-chart indicate that the process was operating within statistical control at all points during the thirty day period?
   • Yes
   • No