3.3 Control Chart Types and Uses
Key Takeaways
- A control chart (Shewhart chart) adds Upper and Lower Control Limits (usually set at +/- 3 standard deviations from the mean) to a run chart to mathematically define the boundaries of common cause variation.
- Variables data (continuous data like weight, blood pressure, or processing time) is analyzed using X-bar and R charts, while attributes data (count/discrete data like number of infections or compliance rates) is analyzed using p-charts or u-charts.
- A p-chart is used for classification data (yes/no, conform/non-conform) when the sample size varies, whereas a u-chart is used for counting the number of defects per unit when the area of opportunity varies.
- The presence of any point outside the +/- 3 sigma control limits on a control chart is a definitive signal of special cause variation requiring immediate investigation.
3.3 Control Chart Types and Uses
While run charts are excellent for detecting basic trends, control charts (also known as Shewhart charts) offer a more mathematically robust method for monitoring process variation. A control chart is essentially a run chart that replaces the median line with a mean line (average) and adds two statistically calculated lines: the Upper Control Limit (UCL) and the Lower Control Limit (LCL). These control limits are typically set at three standard deviations (+/- 3 sigma) from the mean. The area between the UCL and LCL represents the boundaries of common cause variation. Any data point that falls outside these limits is a definitive signal of special cause variation.
Selecting the Right Control Chart
A critical task for the patient safety professional is choosing the appropriate control chart type based on the nature of the data. Data is broadly classified into two categories: variables data (continuous data that is measured on a scale) and attributes data (count or discrete data that is categorized).
1. Charts for Variables Data (Continuous Data)
Variables data includes measures like patient wait times, length of stay, or lab turnaround times. Because these measures represent continuous values, they are analyzed using two charts plotted together:
- X-bar Chart: Monitors the process average over time.
- R Chart (Range Chart): Monitors the variation (dispersion) within subgroups over time.
2. Charts for Attributes Data (Count / Classification Data)
Attributes data involves counting events, defects, or classifications. Choosing the right attributes chart depends on the type of count and whether the sample size (denominator) is constant or variable:
- p-chart (Proportion): Used for classification data (e.g., compliant vs. non-compliant, yes vs. no) where the subgroup size varies. Example: tracking the percentage of surgical patients who received prophylactic antibiotics within 1 hour prior to incision each month, where the total number of surgeries changes monthly.
- np-chart: Used for classification data when the subgroup size is constant.
- u-chart (Rate): Used for count data (where an individual item can have multiple defects) and the subgroup size (area of opportunity) varies. Example: tracking the number of patient falls per 1,000 patient-days, or CLABSI rates per 1,000 line-days.
- c-chart: Used for count data when the subgroup size is constant.
- g-chart: Used for tracking the "number of days between" rare events. This is particularly useful in high-reliability organizations where events like ventilator-associated pneumonia or wrong-site surgery are extremely rare, making standard rate charts ineffective.
- t-chart: Used for tracking the "time between" extremely rare events, similar to the g-chart but using continuous time (e.g., hours or minutes) rather than discrete days.
| Control Chart Type | Data Type | Subgroup Size | Clinical Example |
|---|---|---|---|
| X-bar and R | Variables (Continuous) | Constant or Variable | Average emergency department throughput time in minutes |
| p-chart | Attributes (Classification) | Variable | Monthly rate of compliance with medication reconciliation (%) |
| np-chart | Attributes (Classification) | Constant | Number of incomplete charts out of exactly 50 audited daily |
| u-chart | Attributes (Counting Events) | Variable | Number of pressure injuries per 1,000 patient-days |
| c-chart | Attributes (Counting Events) | Constant | Number of medication errors on a specific unit with a constant volume |
| g-chart | Time/Days Between Events | N/A (Rare events) | Number of days between central line-associated bloodstream infections |
| t-chart | Time Between Events | N/A (Rare events) | Hours elapsed between clinical alarms in a neonatal ICU |
Control Chart Rules for Special Cause Variation
Control charts utilize standard statistical rules to detect special cause variation. These rules are divided into zones based on standard deviations from the mean: Zone C (+/- 1 sigma), Zone B (+/- 2 sigma), and Zone A (+/- 3 sigma). The five primary rules for identifying a process change include:
- Rule 1: Single Point Outside Control Limits: Any single data point that plots outside either the UCL or LCL (beyond +/- 3 standard deviations from the mean). This is a strong signal of an immediate, non-random process change.
- Rule 2: Shift in the Mean: 8 or more consecutive data points that plot entirely on one side of the mean line. (Note: Run charts require 6 points for a shift; control charts require 8 points due to higher statistical sensitivity).
- Rule 3: Linear Trend: 6 or more consecutive data points that are steadily increasing or steadily decreasing. (Note: Run charts require 5 points for a trend; control charts require 6).
- Rule 4: Zone A Test: 2 out of 3 consecutive data points that plot in Zone A (between 2 and 3 standard deviations from the mean) on the same side of the center line.
- Rule 5: Zone B Test: 4 out of 5 consecutive data points that plot in Zone B or beyond (between 1 and 2 standard deviations from the mean) on the same side of the center line.
When a safety team identifies any of these rules being met on a control chart, they must investigate the system. If the change represents an improvement (e.g., a shift below the mean for infection rates), the team should recalculate the control limits to reflect the new, improved level of process performance.
A patient safety officer is tracking the monthly rate of central line-associated bloodstream infections (CLABSI) per 1,000 central line-days. The denominator (line-days) varies each month. Which control chart is most appropriate?
When interpreting a control chart, which of the following scenarios mathematically indicates a signal of special cause variation?