Chapter 12 Quality Control 495
n is the number of observations in the subgroup. Note that in this control
chart and the charts that follow, n need not be the same for all subgroups.
Control charts are easier to interpret if this is the case, though.
The value for μ might also be known from past values. Alternatively, μ
might represent the target mean of the process rather than the actual mean
attained. In practice, though, μ might also be unknown. In that case, the
mean of all of the subgroup averages x replaces μ as follows:
LCL 5 x 2
3 s
!n
UCL 5 x 1
3 s
!n
The interpretation of the mean chart is the same whether the true process
mean is known or unknown.
Here is an example to help you understand the basic mean chart. Stu-
dents are often concerned about getting into courses with “good” profes-
sors and staying out of courses taught by “bad” ones. In order to provide
students with information about the quality of instruction provided by
different instructors, many universities use end-of-semester surveys in
which students rate various professors on a numeric scale. At some schools,
such results are even posted and used by students to help them decide in
which section of a course to enroll. Many faculty members object to such
rankings on the grounds that although there is always some apparent varia-
tion among faculty members, there are seldom any signifi cant differences.
However, students often believe that variations in scores refl ect the profes-
sors’ relative aptitudes for teaching and are not simply random variations
due to chance effects.
x Chart Example: Teaching Scores
One way to shed some light on the value of student evaluations of teaching
is to examine the scores for one instructor over time. The Teacher work-
book provides data ratings of one professor who has taught principles of
economics at the same university for 20 consecutive semesters. The in-
struction in this course can be considered a process, because the instructor
has used the same teaching methods and covered the same material over
the entire period. Five student evaluation scores were recorded for each
of the 20 courses. The fi ve scores for each semester constitute a subgroup.
Possible teacher scores run from 0 (terrible) to 100 (outstanding). The range
names have been defi ned in Table 12-2 for the workbook.
