1. 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

2. User has a basic understanding of process variation
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.

3. 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.

4. Components of Control Chart
UCL
LCL
Observations

5. Points between control limits are due to random chance variation
Interpretation of Control Charts
Points between control limits are due to random chance variation
One or more data points above an UCL or below a LCL mark statistically significant changes in the process

6. More data points means more delay
Suggested Number of Data Points
More data points means more delay
Fewer data points means less precision, wider limits
A tradeoff needs to be made between more 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

7. Freezing & revising control limits

8. Risk adjusted X-bar chart
Selecting Appropriate Chart
XmR
X-bar
Tukey
Time-in-between
P-chart
Risk adjusted P-chart
Risk adjusted X-bar chart

9. Continuous variables Length of stay Average length of stay
Examples of Measures
Continuous variables
Length of stay
Average length of stay
Average age of a specific patient population
Process turn around time
Staff salaries
Severity of medication errors
Individual patient’s weights, blood sugars, cholesterol levels, temperatures, or blood pressures over time
Patient Satisfaction Average Scores
Infectious waste poundage generated
Electrical usage
Wait times
Accounts receivable balances
Time in restraints
Time before hanging up the phone
SF – 36 scores

10. Rates and discrete events
Examples of Measures
Rates and discrete events
Number of employee accidents
Number of patient falls
Nosocomial infection rates
Percent of patients in restraints
Medication error rate
Adverse event rate
C-Section rates
Number of dietary tray errors
Numbers of delinquent medical records
Percent of patients with insurance
Percent of patients who rated the facility as excellent
Telephone abandonment rates
Pressure ulcer rates
Employee injuries rates
Percent of records that contains appropriate documentation

11. If continuous variable
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

12. When case mix changes over time, use risk adjusted control charts
Risk Adjustment
When case mix changes over time, use risk adjusted control charts
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