# Introduction to Control Charts

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```					    Introduction to
Control Charts
By Farrokh Alemi Ph.D.
Sandy Amin

Based in part on Amin S. Control charts 101: a guide to health care
applications. Qual Manag Health Care 2001 Spring;9(3):1-27
Purpose

 Provide an overview of control chart
applications for common healthcare data.
 We assume:
 User has a basic understanding of process variation
 User has knowledge of simple statistics (i.e.
measures of central tendency).
 This lecture should help the user select the
appropriate type of chart and understand the
common rules of interpretation.
What is a control chart?

 A graphical display of data over time that
can differentiate common cause variation
from special cause variation
 In the late 1920’s, Walter Shewhart, a
statistician at the AT&T Bell Laboratories,
developed the control chart and its
associated rules of interpretation.
Components of Control
Chart

UCL
characteristics
Measured

Observations

LCL

Time period
Interpretation of Control
Charts
 Points between
control limits are due
to random chance

characteristics
Measured
variation
 One or more data
points above an UCL                        Time period
or below a LCL mark
statistically
significant changes
in the process
Suggested Number of
Data Points
 More data points means more delay
 Fewer data points means less precision, wider
limits
delay and less precision
 Generally 25 data points judged sufficient
 Use smaller time periods to have more data points
 Fewer cases may be used as approximation

The idea is to improve not to prove a point
Freezing & revising
control limits

Measured characteristic
Measured characteristic

1   3   5   7    9   11   13   15   17   19                             1   3   5   7    9    11   13   15   17   19

Time period                                                             Time periods
Selecting Appropriate
Chart
   XmR                Risk adjusted P-
   X-bar               chart
   Tukey              Risk adjusted X-
   Time-in-between     bar chart
   P-chart
Examples of Measures
Continuous variables                      Rates and discrete events

   Length of stay                           Number of employee accidents
   Average length of stay                   Number of patient falls
   Average age of a specific patient        Nosocomial infection rates
population                               Percent of patients in restraints
   Process turn around time                 Medication error rate
   Staff salaries                           Adverse event rate
   Severity of medication errors            C-Section rates
   Individual patient’s weights, blood      Number of dietary tray errors
sugars, cholesterol levels,              Numbers of delinquent medical
temperatures, or blood pressures          records
over time
   Patient Satisfaction Average             Percent of patients with insurance
Scores                                   Percent of patients who rated the
   Infectious waste poundage                 facility as excellent
generated                                Telephone abandonment rates
   Electrical usage                         Pressure ulcer rates
   Wait times                               Employee injuries rates
   Accounts receivable balances             Percent of records that contains
   Time in restraints                        appropriate documentation
   Time before hanging up the phone
   SF – 36 scores
Which Chart is Right?
 If continuous variable
 If one data point per time period
 If outliers likely: Tukey chart
 If outliers not likely: XmR chart
 If multiple data points per time period: Xbar chart
 If discrete event
 If event is rare: Time-in-between chart
 If event is not rare: P-chart

If case mix changes over time, use risk adjusted control charts

 When case mix changes over time, use
 Instead of comparing to historical patterns,
new observations are compared to
expectations
 Risk adjusted control charts are
calculated by applying the formulas for
control limits to the difference of
observed and expected values

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