Quality Control in the Beef Industry
In this project, you will investigate quality control in industry.
You will construct and interpret a control chart to decide whether
to modify a manufacturing process. You will work with means,
standard deviations, ranges, upper and lower control limits, and
confidence intervals.
Background
Quality control is critical in a wide variety of industries. Most producers attempt to make the
dimensions of their product conform to certain limits. In many cases these limits are required for
safety reasons. One of the basic tools of statistical process control is the control chart, in which
the value of some aspect of the product is tracked over time.
For example, a meat packer might want the average fat content of ground beef to be 25%. It is not
possible to have exactly 25% fat in every package of ground beef, so the packer sets maximum
and minimum allowable limits on fat content. The beef packer collects random samples of ground
beef and measures the fat content. The mean and range of the values are recorded and tracked
over time using x and R control charts. The x-chart shows the means of random samples of the
product taken over some time period. The R-chart refers to the ranges of the samples. The control
chart shows the 2 measures concurrently. The measured fat content should fall well within the
specified limits, with the number of samples containing more than 25% fat being roughly the
same as those with less than 25%.
A) Bullet Questions
 Why is it important for products to be uniform or consistent? (1)

List some industries and their products that must be consistent or it could result in safety
problems. (1)

Are there any products where it might be beneficial for products to not be consistent? (1)
B) Getting Started
1. The heights of Canadian women approximate a normal distribution, with a mean of 162.6
cm and a standard deviation of 6.4 cm. What percent of the female population do you
expect to have heights between 154 cm and 172 cm? (3)
2. The masses of apples in a shipment are normally distributed, with a mean of 110 g and a
standard deviation of 16 g. Without using your calculator, state a range of masses that
includes 68% of the apples. (1)
C) Project Presentation
3. A meat packing plant operates 24 h per day. Over a period of 8 days, 5 random samples of
ground beef are chosen per 8-h shift. The fat
content of each sample is measured and the Shift
x
x
R
Shift
R
average fat content, x , and the range of fat
1
24.7 2.3
13 25.1 3.8
content, R, of the 5 samples are recorded. The
2
25.5 4.1
14 24.6 3.3
data are shown to the right. Follow these
x
instructions to construct an
and R control
3
25.0 5.2
15 24.2 3.6
chart for these data.
4
25.2 3.1
16 25.8 4.5
a) Enter the shift number in Ll, the means of
5
26.3 1.7
17 25.5 3.8
the samples, x , in L2, and the ranges of
the samples, R, in L3 on your TI-83
6
28.4 3.5
18 24.0 4.1
calculator, or computer. Note: Enter all
7
26.2 2.2
19 24.3 2.9
shifts 1 – 24 in L1 , and all means in L2,
8
24.7 4.1
20 26.1 4.2
and all ranges in L3
b) Calculate the mean and standard
deviation of the means ( x ) of the
samples. (L2)
9
24.5 3.7
21
23.8 3.0
10
24.5 6.3
22
25.4 5.3
11
23.4 1.4
23
26.0 5.2
12
22.9 2.5
24
25.3 5.0
c) This mean of means, the grand average, determines the centre line, CL, on the
control chart. The upper control limit, (UCL), is at 3 standard deviations above the
grand average. The lower control limit, (LCL) is at 3 standard deviations below the
grand average. Determine the values of UCL and LCL for these data. (2)
.
d) With shift number on the x - axis and average fat content on the y-axis, plot the
control chart lines, CL, UCL, LCL. Use graph paper or a spreadsheet. If you want
this data, download this file from the website http://cabennet.mvsd.ca. Plot the data
on this chart. It will end up looking similar to this. (You must make your own!!)
Do yours on graph paper or a spreadsheet. Label it #3d and staple it on. (4).
mean
x vs shift
30
28
26
24
22
20
0
5
10
15
20
25
shift
e) Explain what you think happened during shift #6. Use you chart to answer. (1)
f) Generate the R -chart using the same method. Show all work.
4. The UCL and the LCL are at 3 standard deviations from the mean.
a) How much of this data distribution is between them? (1)
b) What % of data should be outside these limits? (1)
5. Is the fat content of the ground beef within statistical control? In real life, x and R charts
have to be modified slightly because of the nature of data collection. Read below to find
our about interpreting control charts. (2)
Interpreting Control Charts
Patterns or trends within control charts may indicate that problems are
developing within the manufacturing process. Some rules of thumb
are:
 Points that fall outside the control limits can be attributed to
"assignable cause," which can be corrected by modifying
production.
 Seven or more points in a row either above or below the
centre line indicate that some aspect of the production
process is off target.
 Seven or more points in a row either increasing or decreasing
indicate a change in the production process.
 Points should not follow a repeating cycle.
When all points fall within the specified limits and none of the trends
described above are present, the process is said to be within statistical
control.