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 LCL Observations

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

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

Freezing & revising control limits

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

Examples of Measures  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  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 Continuous variablesRates and discrete events

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

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