1. The net weight of a soft drink is to be monitored by X‾ and R control charts using a sample size n = 5. Data for 20 preliminary samples are shown in Table below.
|
Sample Number
|
X1
|
x2
|
x3
|
X4
|
x5
|
|
|
15.8
|
16.3
|
16.2
|
16.1
|
16.6
|
|
2
|
16.3
|
15.9
|
15.9
|
16.2
|
16.4
|
|
3
|
16.1
|
16.2
|
16.5
|
16.4
|
16.3
|
|
4
|
16.3
|
16.2
|
15.9
|
16.4
|
16.2
|
|
5
|
16.1
|
16.1
|
16.4
|
16.5
|
16.0
|
|
6
|
16.1
|
15.8
|
16.7
|
16.6
|
16.4
|
|
7
|
16.1
|
16.3
|
16.5
|
16.1
|
16.5
|
|
8
|
16.2
|
16.1
|
16.2
|
16.1
|
16.3
|
|
9
|
16.3
|
16.2
|
16.4
|
16.3
|
16.5
|
|
10
|
16.6
|
16.3
|
16.4
|
16.1
|
16.5
|
|
11
|
16.2
|
16.4
|
15.9
|
16.3
|
16.4
|
|
12
|
15.9
|
16.6
|
16.7
|
16.2
|
16.5
|
|
13
|
16.4
|
16.1
|
16.6
|
16.4
|
16.1
|
|
14
|
16.5
|
16.3
|
16.2
|
16.3
|
16.4
|
|
15
|
16.4
|
16.1
|
16.3
|
16.2
|
16.2
|
|
16
|
16.0
|
16.2
|
16.3
|
16.3
|
16.2
|
|
17
|
16.4
|
16.2
|
16.4
|
16.3
|
16.2
|
|
18
|
16.0
|
16.2
|
16.4
|
16.5
|
16.1
|
|
19
|
16.4
|
16.0
|
16.3
|
16.4
|
16.4
|
|
20
|
16.4
|
16.4
|
16.5
|
16.0
|
15.8
|
a. Set up X‾ and R control charts using these data. Does the process exhibit statistical control?
b. Estimate the process mean and standard deviation.
c. Does fill weight seem to follow a normal distribution?
2. Rework Exercise 4 using an X‾-S chart.
a. Set up X‾ and S control charts. Is the process in statistical control?
b. Estimate the process mean and standard deviation. (σ^ = s‾/c4)
c. What are the limits that you would expect to contain nearly all the process measurements?