Details of Assignment (W4): Complete problems 6.12, S6.11, S6.20, S6.23, S6.27, and S6.35 in the textbook.Submit one Excel file. Put each problem result on a separate sheet in your file. (also uploaded problems)

 

S6.11Twelve 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 were:

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?

 

S6.12Eagletrons are all-electric automobiles produced by

Mogul Motors, Inc. One of the concerns of Mogul Motors is that the

Eagletrons be capable of achieving appropriate maximum speeds.

To monitor this, Mogul executives take samples of eight Eagletrons

at a time. For each sample, they determine the average maximum

speed and the range of the maximum speeds within the sample.

They repeat this with 35 samples to obtain 35 sample means and

35 ranges. They find that the average sample mean is 88.50 miles

per hour, and the average range is 3.25 miles per hour. Using these

results, the executives decide to establish an R chart. They would

like this chart to be established so that when it shows that the range

of a sample is not within the control limits, there is only approximately

a 0.0027 probability that this is due to natural variation.

What will be the upper control limit (UCL) and the lower control

limit (LCL) in this chart?

 

S6.20Jamison 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:

 

SAMPLES	1	2	3	4	5	6	7	8	9	10
DEFECTIVES	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?

S6.23The 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	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?

 

S6.27Meena 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.

 

S6.35One 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”:

SAMPLE  (WEEK)	LATE FLIGHTS	SAMPLE  (WEEK)	LATE FLIGHTS
11	2	16	2
221	4	17	3
13	10	18	7
44	4	19	3
15	1	20	2
6666666	1	21	3
1 7	13	22	7
8	9	23	4
1 9	11	24	3
110	0	25	2
111	3	26	2
112	4	27	0
113	2	28	1
1144	2	29	3
1155	8	30	4

 (WEEK)

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?