# 6603 Quality amp; Statistical Process Control Assignment Below are given five problems taken from your textbook.

6603 Quality & Statistical Process Control Assignment

Below are given five problems taken from your textbook. Data tables given with each

problem are actually embedded Excel spreadsheets which can be activated by doubleclicking on the table. Use the data and Excel to create control charts and answer

questions about the scenarios presented. Feel free to copy and paste the data from this

document into a separate spreadsheet for ease of handling.

1. Twelve samples, each containing five parts, were taken from a process that

produces steel rods. The length of each rod in the samples was determined. The

results were tabulated and sample means and ranges were computed. The results

are given below.

a. Determine the upper and lower control limits and overall means for Mean

and Range Charts

b. Create the charts in Excel with values from the 12 samples plotted on each

chart. Doe the data indicate the process is in control? Why or why not?

Sample Sample Mean (inches) Sample Range (inches)

1 10.002 0.011

2 10.002 0.014

3 9.991 0.007

4 10.006 0.022

5 9.997 0.013

6 9.999 0.012

7 10.001 0.008

8 10.005 0.013

9 9.995 0.004

2. Five data entry operators work at the data processing department of the

Birmingham Bank. Each day for 30 days, the number of defective records in a

sample of 250 records typed by these operators has been noted. That data is given

below.

a. Determine 3σ upper and lower control limits. Why can’t the lower control

limit be a negative number?

b. The industry standards for the upper and lower control limits are 0.10 and

0.01, respectively. What does this imply about Birmingham Bank’s

performance?

Sample # of Defectives Sample # of Defectives Sample # of Defectives

1 7 11 18 21 17

2 5 12 5 22 12

3 19 13 16 23 6

4 10 14 4 24 7

5 11 15 11 25 13

6 8 16 8 26 10

7 12 17 12 27 14

8 9 18 4 28 6

9 6 19 6 29 12

3. Houston North Hospital is trying to improve its image by providing a positive

experience for its patients and their relatives. Part of the “image” program

involves providing tasty, inviting patient meals that are also healthful. A

questionnaire accompanies each meal served, asking the patient, among other

things, whether he or she is satisfied or unsatisfied with the meal. A 100-patient

sample of the survey results over the past 7 days yielded the data below.

Construct a p-chart that plots the percentage of patients unsatisfied with their

meals. Set the control limits to include 99.73% of the random variation in meal

selection. How do you interpret the results?

Day Nbr of Unsatisfied Patients Sample Size

1 24 100

2 22 100

3 8 100

4 15 100

5 10 100

6 26 100

7 17 100

4. One of New England Air’s top competitive priorities is on-time arrivals. Quality

VP Claire Bond decided to personally monitor New England Air’s performance.

Each week for the past 30 weeks Bond checked a random sample of 100 flight

arrivals for on-time performance. The table below contains the number of flights

that did not meet New England Air’s definition of “on time”.

a. Use Excel to construct a p-chart with centerline and upper and lower

control limits. Also plot the New England Air data on the control chart.

b. Assuming the airline industry’s upper and lower control limit standards for

late flights are .1000 and .0400, respectively. Place these limits on your

control chart.

c. What can Claire Bond report about New England Air’s late flight arrivals?

Week Late Flights Week Late Flights Week Late Flights

1 2 11 3 21 3

2 4 12 4 22 7

3 10 13 2 23 4

4 4 14 2 24 3

5 1 15 8 25 2

6 1 16 2 26 2

7 13 17 3 27 0

8 9 18 7 28 1

9 11 19 3 29 3

5. West Battery Corp has recently been receiving complaints from retailers that its 9-

volt batteries are not lasting as long as other name brands. James West, head of

the Quality program at West’s Austin plant, believes there is no problem because

his batteries have had an average life of 50 hours, about 10% longer than

competitors’ models. To raise the lifetime above this level would require new

technology not available to West. Nevertheless, he is concerned enough to set up

hourly assembly line checks. Previously, after ensuring that the process was

running properly, West took size n = 5 samples of 9-volt batteries for each of 25

hours to establish the standards for control chart limits. Those samples are given

Hour Sample 1 Sample 2 Sample 3 Sample 4 Sample 5

1 51 50 49 50 50

2 45 47 70 46 36

3 50 35 48 39 47

4 55 70 50 30 51

5 49 38 64 36 47

6 59 62 40 54 64

7 36 33 49 48 56

8 50 67 53 43 40

9 44 52 46 47 44

10 70 45 50 47 41

11 57 54 62 45 36

12 56 54 47 42 62

13 40 70 58 45 44

14 52 58 40 52 46

15 57 42 52 58 59

16 62 49 42 33 55

17 40 39 49 59 48

18 64 50 42 57 50

19 58 53 52 48 50

20 60 50 41 41 50

21 52 47 48 58 40

22 55 40 56 49 45

23 47 48 50 50 48

24 50 50 49 51 51

25 51 50 51 51 62

Using the above data to establish Mean and Range control chart limits, West now takes 5

more hours of data shown on the next table.

Hour Sample 1 Sample 2 Sample 3 Sample 4 Sample 5

26 48 52 39 57 61

27 45 53 48 46 66

28 63 49 50 45 53

29 57 70 45 52 61

30 45 38 46 54 52

Use Excel to draw Mean and Range control charts, determining the center lines and upper

and lower control limits (using the first 25 hours only). Plotting results from Hours 26

through 30, determine and state whether the manufacturing process is in control.