Understanding Variation in Your Charts
Module 5
What is the state of
Statistical Control?
• A stable mean over time with only random
variation about that mean so that it is
possible to predict how the system will
behave in the near future. – a paraphrase
of Shewhart’s 1931 definition.
– No trends
– No spikes
– No steps
– No cyclical patterns
Does this chart show data in statistical control?
How about this one?
Statistical Process Control vs.
Stationary Time Series
• Here SPC and Time Series Analysis
agree.
– A Time series is stationary if “there is no systematic
change in the mean (no trend), if there is no
systematic change in the variation, and if strictly
periodic variations have been removed.” (Source:
Chatfield (2004) The Analysis of Time Series: An
Introduction.)
What is common cause variation?
• The “faults” of the system that cause the
random variation around the mean of a
series that is in statistical control.
• The causes that are common- they belong
to the system.
– “The natural variation inherent in a process on
a regular basis.”*
– “The variation expected to occur according to
an underlying statistical distribution if
parameters remain constant.”*
Special Causes of Variation
• Causes that are assignable, foreign to the
system, and special to a particular time period,
group of workers, etc.
• Special Causes create variation that is NOT
random. They cause a process to be out of
statistical control.
• “Unnatural variation due to events, changes, or
circumstances that have not previously been
typical or inherent in the regular process.”*
*Benneyan et al. Statistical process control as a tool for research and
Healthcare improvement. Qual Saf Health Care 2003; 12:458-464
Can you tell whether IPC I had an effect?
SPC vs. Epi
• Common Cause
Variation
• Special Cause
Variation
• Endemic
• Epidemic
What is process capacity?
• Not often used in health care.
• The range a population distribution is able to
stick within for 999 out of 1000 observations.
• In a normally distributed process, this
corresponds to plus or minus 3 sigma.
• It is also the .00135 and .99865 quantiles of the
probability plot, even if skewed and not normal.
Consider this:
• If the process capability is between 10 and 50,
but the specifications for the product are
between 20 and 40, do we have a problem?
• Related problem: If the GPRA measures goal is
that 75 percent of the population needs to have
a blood pressure below 130/80, what does the
average blood pressure have to be?
• Related problem: If the process capability is
between 10 and 50, how far down does the
value have to get following an intervention to
detect change with a single point?
Conclusion regarding process
capability
• Background noise (process capability)
determines whether your upper and lower
specifications can be met.
• With too much background noise, meeting a
specification or goal where only the upper limit is
specified may require the whole process to shift
more than you want. Remember BP!
• With too much background noise, can you see
change in the process? When the standard error
is 15, can you detect a change of 5?
If your current average systolic BP among persons
w/diabetes is 140 and you want to meet a goal of 75%
of patients with a systolic BP of 130 or less, what happens?
110 120 130 140
If you can do that without improving your process
capability, the whole curve shifts.
110 120 130 140
And now your average blood pressure is 120, with half of your population less
than 120. If you medicated people to that extent, is it safe?
Is Process Capability Important in
Quality Measurement?
How do we detect
special cause variation?
Rules based on
probability
theory
Two Normal Distributions
This curve is
the probability
distribution when
there is a difference.
This curve is
the probability
distribution when
there is no
difference.
Probability of
Saying there
isn’t a difference
where there is—
Type II Error = β risk
-30
Probability of saying
there is a difference
when there isn’t—
Type I Error = α risk
50
100
x
180
Statistical significance is defined here.
Rules for Interpreting Charts
• Based on minimizing Type I error.
– “Producer’s Risk”
– “Provider’s Short Term Risk”
• Based on minimizing Type II error.
– “Consumer’s Risk”
– “Patient’s Risk”
Rules for Run Charts
(Run Charts with Median Centerline)
• Too many or too few runs. See Test 1 on page
57 and the table on page 58 of Carey and Lloyd.
• Run Length: A run with too many data points.
– If < 20 observations, 7+ points in a run.
– If 20+ observations, 8+ points in a run.
• Trend: Consecutive increases or decreases.
– If 5-8 obs, then 5 or more
– If 9 to 20 obs, then 6 or more
– If 20+, then 7 or more.
Note: Rules preferred by Carey and Lloyd.
Rules for Control Charts
First, divide your control chart into
zones.
From Amin, 2001
Indian Health Service, DHHS
Rules for Control Charts
(Nelson Rules)
1. One point beyond zone A.
2. 9 points in a row in zone C or beyond.*
3. Six points in a row (including endpoints)
steadily increasing or decreasing.
4. 14 points in a row alternating up and
down.
5. 2/3 points in Zone A or beyond.
*Western Electric/AT&T rules require only 8.
Rules for Control Charts (Continued)
(Nelson Rules)
6. 4/5 point in a row in zone A or beyond.
7. 15 points in a row in zone C.
8. 8 points in a row on both sides of the
centerline with one in zone C.
Caution
• Most of these rules assume a normal
distribution.
• With p, np, c, and u charts use only:
–
–
–
–
Test 1. One point beyond zone A.
Test 2. 9 points in a row in zone C and beyond*
Test 3. Six points in a row increase/decreasing.
Test 4. 14 points in a row alternating up and down.
• The more tests you use, the greater the alpha risk, the
risk of a Type I Error, which is? 
• The more observations you have, the greater the alpha
risk.
*Only use this test if the distribution is symmetrical.
Your Turn
Your Turn
Can you find another test met several times?