Assignment:
Problem
A. R-chart and x-bar chart. Thermostats arc subjected to rigorous testing before they are shipped to air conditioning technicians around the world. The temperature of five thermostats (units) within a production lot arc randomly sampled and tested each hour. The table below displays the temperatures (in degrees Fahrenheit) of five thermostat units chosen each hour for five consecutive hours. Sample 1 was selected in the first hour, Sample 2 was selected in the second hour, and so on, and so forth. (Please note that a column of data is one sample. The exercise in class had a sample going across a row!)
a. Compute the upper and lower control limits for the sample means and ranges of the thermostat testing process.
b. Draw an R-chart and x-bar chart for this process. Examine both charts. Is this process in control? Explain.
|
Unit#
|
Sample 1
|
Sample 2
|
Sample 3
|
Sample 4
|
Sample 5
|
|
1
|
73.5
|
70.8
|
72.2
|
73.6
|
71.0
|
|
2
|
71.3
|
71.0
|
73.1
|
72.7
|
72.2
|
|
3
|
70.0
|
72.6
|
71.9
|
72.4
|
73.3
|
|
4
|
71.1
|
70.6
|
70.3
|
74.2
|
73.6
|
|
5
|
70.0
|
70.7
|
70.7
|
73.5
|
71.1
|
B. p-chart. A professor records the number of students who complain each week throughout the semester. This data is displayed in the table below. The number of complaints is out of a class size of forty students.
|
Week Number
|
Complaints
|
|
1
|
5
|
|
2
|
2
|
|
3
|
7
|
|
4
|
1
|
|
5
|
3
|
|
6
|
2
|
|
7
|
8
|
|
8
|
1
|
|
9
|
3
|
|
10
|
5
|
|
11
|
4
|
|
12
|
6
|
|
13
|
3
|
|
14
|
1
|
|
15
|
4
|
a. Compute the proportion of students who complain on a weekly basis and then design a p- chart (Calculate the three-sigma control limits for the p-chart.)
b. Plot the control limits and the proportion of complaints for the 15 samples. Based on your p-chart and the data collected, what can you conclude about the process? Explain.