Chapter 12 Quality Control 493
the possibility of making errors exists, just as errors can occur in standard
hypothesis testing. In other words, occasionally a point that lies outside the
control limits does not have any special cause but occurs because of normal
process variation. On the other hand, there could exist a special cause that
is not big enough to move the point outside of the control limits. Statistical
analysis can never be 100% certain.
Variable and Attribute Charts
There are two categories of control charts: those which monitor variables
and those which monitor attributes. Variable charts display continuous
measures, such as weight, diameter, thickness, purity, and temperature. As
you have probably already noticed, much statistical analysis focuses on the
mean values of such measures. In a process that is in control, you expect the
mean output of the process to be stable over time.
Attribute charts differ from variable charts in that they describe a feature
of the process rather than a continuous variable such as a weight or volume.
Attributes can be either discrete quantities, such as the number of defects in
a sample, or proportions, such as the percentage of defects per lot. Accident
and safety rates are also typical examples of attributes.
Using Subgroups
In order to compare process levels at various points in time, we usually
group individual observations together into subgroups. The purpose of the
subgroup is to create a set of observations in which the process is relatively
stable with controlled variation. Thus the subgroup should represent a set of
homogeneous conditions. For example, if we were measuring the results of a
manufacturing process, we might create a subgroup consisting of values from
the same machine closely spaced in time. Once we create the subgroups, we
can calculate the subgroup averages and calculate the variance of the values.
The variation of the process values within the subgroups is then used to cal-
culate the control limits for the entire set of process values. A control chart
might then answer the question Do the averages between the subgroups vary
more than expected, given the variation within the subgroups?
The x
2
Chart
One of the most common variable control charts is the x chart (the “x bar
chart”). Each point in the x chart displays the subgroup average against the
subgroup number. Because observations usually are taken at regular time
intervals, the subgroup number is typically a variable that measures time,
