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 Spring9(3)1-27
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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.

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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 1920s, Walter Shewhart, a
  statistician at the ATT Bell Laboratories,
  developed the control chart and its associated
  rules of interpretation.

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Components of Control Chart
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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

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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
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Freezing revising control limits
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Selecting Appropriate Chart

• XmR
• X-bar
• Tukey
• Time-in-between
• P-chart

• Risk adjusted P-chart
• Risk adjusted X-bar chart

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Examples of Measures
Continuous variables
Rates and discrete events

• 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 patients 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

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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
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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