Finance problems

SAMPLE SAMPLE MEAN (in.) RANGE (in.)

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

10 10.001 0.011

11 10.001 0.014

12 10.006 0.009

a) Determine the upper and lower control limits and the overall

means for x-charts and R-charts.

b) Draw the charts and plot the values of the sample means and

ranges.

c) Do the data indicate a process that is in control?

d) Why or why not?

S6.20 Jamison Kovach Supply Company manufactures paper

clips and other office products. Although inexpensive, paper clips

have provided the firm with a high margin of profitability. Sample

size is 200. Results are given for the last 10 samples:

Sample: 1 2 3 4 5 6 7 8 9 10

Defective: 5 7 4 4 6 3 5 6 2 8

a) Establish upper and lower control limits for the control chart and

graph the data.

b) Is the process in control?

c) If the sample size were 100 instead, how would your limits and

conclusions change?

S6.23 The school board is trying to evaluate a new math

program introduced to second-graders in five elementary schools

across the county this year. A sample of the student scores on

standardized math tests in each elementary school yielded the following

data:

School #of errors

SCHOOL NO. OF TEST ERRORS

A 52

B 27

C 35

D 44

E 55

Construct a c-chart for test errors, and set the control limits

to contain 99.73% of the random variation in test scores.

What does the chart tell you? Has the new math program been

effective?

S6.27 Meena Chavan Corp.’s computer chip production process

yields DRAM chips with an average life of 1,800 hours and

s = 100 hours. The tolerance upper and lower specification limits

are 2,400 hours and 1,600 hours, respectively. Is this process capable

of producing DRAM chips to specification?

S6.35 One of New England Air’s top competitive priorities

is on-time arrivals. Quality VP Clair 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 that follows contains the number of

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

Week Late Week Late

Flights flights fl

IGHTS

1 2 16 2

2 4 17 3

3 10 18 7

4 4 19 3

5 1 20 2

6 1 21 3

7 13 22 7

8 9 23 4

9 11 24 3

10 0 25 2

11 3 26 2

12 4 27 0

13 2 28 1

14 2 29 3

15 8 30 4

a) Using a 95% confidence level, plot the overall percentage of late

flights (p) and the upper and lower control limits on a control

chart.

b) Assume that the airline industry’s upper and lower control limits

for flights that are not on time are .1000 and .0400, respectively.

Draw them on your control chart.

c) Plot the percentage of late flights in each sample. Do all samples

fall within New England Air’s control limits? When one falls outside

the control limits, what should be done?

d) What can Clair Bond report about the quality of service?