Page 199 - The Handbook for Quality Management a Complete Guide to Operational Excellence

186 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 187

The reader may note that the data used to construct the u chart were
the same as those used for the p chart, except that we considered the
counts as being counts of occurrences (bruises) instead of counts of phys-
ical items (bruised peaches). The practical implications of using a u chart
when a p chart should have been used, or vice versa, are usually not seri-
ous. The decisions based on the control charts will be quite similar in most
cases regardless of whether a u or a p chart is used.
One way of helping determine whether or not a particular set of
data is suitable for a u chart or a p chart is to examine the equation used
to compute the centerline for the control chart. If the unit of measure is
the same in both the numerator and the denominator, then a p chart is
indicated; otherwise, a u chart is indicated. For example, if
bruises per crate
Centerline =
number of crates
t
then the numerator is in terms of bruises while the denominator is in
terms of crates, indicating a u chart.
The unit size is arbitrary but once determined it cannot be changed
without recomputing all subgroup occurrences-per-unit and control
limits. For example, if the occurrences were accidents and a unit was
100,000 hours worked, then a month with 250,000 hours worked would
be 2.5 units and a month with 50,000 hours worked would be 0.5 units.
If the unit size were 200,000 hours, then the two months would have
1.25 and 0.25 units respectively. The equations for the centerline and
control limits would “automatically” take into account the unit size, so
the control charts would give identical results regardless of which unit
size is used.
As with all control charts, a special cause is probably present if there
are any points beyond either the upper or lower control limit. Analysis of
u chart patterns between the control limits is extremely complicated
when the sample size varies and is usually not done.

Control Charts for Counts of Occurrences-per-Unit (c Charts)
c charts are statistical tools used to evaluate the number of occurrences-
per-unit produced by a process. c charts can be applied to any variable
where the appropriate performance measure is a count of how often a
particular event occurs and samples of constant size are used. c charts
answer the question: “Has a special cause of variation caused the central
tendency of this process to produce an abnormally large or small number
of occurrences over the time period observed?” Note that, unlike p or np
charts, c charts do not involve counting physical items. Rather, they
involve counting of events. For example, when using an np chart one
would count bruised peaches. When using a c chart one would count the
bruises.

09_Pyzdek_Ch09_p151-208.indd 186 11/21/12 1:42 AM