Bill Farrell, Ph.D.
Senior Analyst
Sutter Health
Sutter Health is a family of not-for-profit
hospitals and physician organizations that share
resources and expertise to advance health care
quality. Serving more than 100 communities in
Northern California, Sutter Health is a regional
leader in cardiac care, cancer treatment, orthopedics,
obstetrics, and newborn intensive care, and
is a pioneer in advanced patient safety technology.
Authors writing about (and people teaching)
statistical process control often tend to show
SPC charts in pairs: If there’s an Individual
(or Item) chart on top, they show a moving range
chart on the bottom; if there’s an xBar chart
on top, they add an S chart (standard deviation
or sigma) on the bottom. Software for SPC abets
this tendency: in addition to buttons on the
menu bar for I and xBar charts, there will be
buttons for I/mR and xBar/S charts; one click
and you’ve got your paired charts.
Does the second chart aid in the interpretation
of the main chart? The answer is No. Is it necessary
for the second chart to be in control before
we can accept the main chart? Again, the answer
is No. Here is a quote from a respected author
on the topic (Donald Wheeler, Advanced Topics
in Statistical Process Control, p. 110):
The ultimate argument in favor of the mR
chart is not that it improves the ability
of the I chart to detect signals, but that
it serves as a reminder of the correct way
of computing limits for the I chart. When
the mR chart is used with the I chart it serves
both as a reminder of the correct method,
and as a signal to others that the user knows
the correct method.
Because there are, in theory, several methods
for computing SPC limits (median deviations,
root mean square deviations, moving ranges),
Wheeler and his academic/industrial colleagues
may believe they have to demonstrate that they
“know the correct method.” But the correct method
is built into modern SPC software, making these
secondary charts distracting at best and misleading
at worst. To further complicate the issue, rule
violations are defined differently for these
secondary charts. There is only one way an mR
or S chart can be out of control: a single point
above 3 sigma. For xBar and I charts, on the
other hand, rule violations include two out
of three points beyond 2 sigma, six points ascending
or descending, etc.
To reiterate: an out-of-control point on an
S or mR chart says nothing about how (or whether)
we can interpret the main xBar or I chart. The
fact that the range went from 5 in Quarter 1
to 10 in Quarter 2 has already been factored
into the limits for the I chart. The fact that
the standard deviation (actually, the bias-corrected
standard error) went from 3.6 in Quarter 1 to
7.5 in Quarter 2 has already been factored into
the limits for the xBar chart.
I and xBar charts track the variability of
a process. S and mR charts track the variability
of the variability of a process. Why would anyone
be interested in this? Donald Wheeler might
want to show us that he knows what he’s doing
and remind us of how SPC limits are calculated,
which is fine. Someone on a factory floor might
be interested in maintaining a narrow range
of output on the fender-stamping machine, which
is also fine. In healthcare, though, these secondary
charts would seem to raise many more questions
than they answer.
