6.3 Statistical Control Charts & Corrective Action Limits

6.3 Statistical Control Charts & Corrective Action Limits

Quality Control (QC) measurements yield quantitative data that must be systematically tracked over time to verify that measurement systems remain in a state of statistical control. ANSI/AARST MS-QA-2023 mandates the construction and routine evaluation of Statistical Control Charts (Shewhart charts) to detect operational drift, equipment failure, or procedural errors before compromised data reach clients.

---

Constructing Statistical Control Charts

A statistical control chart is a graphical representation of QC measurement performance plotted sequentially over time. The X-axis represents chronological sample numbers or deployment dates, while the Y-axis represents the evaluation metric. Three primary control charts are maintained under MS-QA-2023:

1. Duplicate Precision Control Chart: Plots Relative Percent Difference (RPD) or absolute difference for sequential duplicate pairs.
2. Blank Control Chart: Plots measured concentrations (pCi/L) for field and office blanks to monitor background contamination trends.
3. Spike Bias Control Chart: Plots Relative Percentage Error (RPE) or Percent Recovery for calibration chamber spikes to track systematic calibration accuracy.

Each control chart features three established horizontal reference lines:

• Central Line (CL): The expected baseline mean (e.g., 0% RPE for spikes, historic mean RPD for duplicates).
• Upper Warning Limit (UWL): Set at 2 standard deviations ($2\sigma$) from the Central Line.
• Upper Control Limit (UCL) / Action Limit: Set at 3 standard deviations ($3\sigma$) from the Central Line.

---

Understanding Warning Limits vs. Control Limits

MS-QA-2023 establishes distinct statistical boundaries and required responses for Warning Limits and Control Limits:

Warning Limits ($2\sigma$)

• Threshold: For duplicate measurements at concentrations $\ge 4.0 \text{ pCi/L}$, the Warning Limit corresponds to an RPD of 28% (the in-control target average is 14%). For spikes, it represents an RPE exceeding ±20%.
• Operational Meaning: A single data point breaching the Warning Limit indicates increased process variability or early calibration drift. It signals that the measurement system is experiencing elevated random noise or minor bias.
• Required Response: Breaching a Warning Limit does not automatically invalidate client measurement data. However, it requires the Radon Measurement Professional (RMP) to conduct an immediate operational review, inspect handling protocols, check instrument battery and background parameters, and increase monitoring on subsequent deployments.

Control Limits / Action Limits ($3\sigma$)

• Threshold: For duplicate measurements at concentrations $\ge 4.0 \text{ pCi/L}$, the Upper Control Limit corresponds to an RPD of 36%. For spikes, it represents an RPE exceeding ±30%. For blanks, it corresponds to readings exceeding 1.0 pCi/L.
• Operational Meaning: A data point breaching the Control Limit represents an out-of-control condition. Statistically, there is a less than 0.3% probability that a 3-sigma breach is due to normal random variation. It indicates an assignable-cause error, such as instrument failure, damaged detectors, severe storage contamination, or laboratory calculation errors.
• Required Response: Breaching a Control Limit immediately invalidates all measurement results generated within the affected device batch or time frame. Client reports must be held, and a mandatory corrective action workflow must be initiated.

---

Out-of-Control Decision Rules

Under MS-QA-2023, an out-of-control condition requiring formal corrective action is triggered by any of the following statistical rules:

1. Single 3-Sigma Breach: Any single QC measurement point breaching the Upper Control Limit ($3\sigma$).
2. Two Consecutive 2-Sigma Breaches: Two consecutive QC measurement points breaching the Warning Limit ($2\sigma$) in the same direction.
3. Seven-Point Shift / Run: Seven consecutive QC measurement points falling on one side of the Central Line, indicating a systematic calibration shift or background elevation.

---

Step-by-Step Corrective Action Workflow

When a control chart signals an out-of-control condition, MS-QA-2023 requires the RMP to execute a standardized five-step corrective action process:

Step 1: Immediate Halt and Isolation

Immediately suspend client report issuance for all measurements associated with the affected instrument, batch, or time period. Quarantine remaining unexposed detectors from the compromised batch.

Step 2: Root-Cause Investigation

Systematically investigate potential error sources across three operational domains:

• Field Handling: Inspect deployment logs for protocol violations, physical damage, extreme moisture exposure, or improper detector sealing.
• Storage & Transit: Test office storage background levels, inspect transit containers for radon leakage, and review temperature logs.
• Instrument / Laboratory: Check CRM battery voltage, photomultiplier tube status, optical chamber cleanliness, electret reader reference voltages, or laboratory calibration constants.

Step 3: Implementation of Corrective Solution

Execute specific corrective measures based on root-cause findings: repair or recalibrate instruments at an approved facility, re-train field technicians on SOPs, or discard compromised detector inventory.

Step 4: Verification of Re-Established Control

Deploy verification QC samples (e.g., immediate intercomparison checks or chamber spikes) to prove that the measurement system has returned to statistical control. Offer affected clients complimentary re-tests where original data were invalidated.

Step 5: Formal Documentation

Record the complete incident in the firm's official Corrective Action Log, detailing the failure date, affected serial numbers, root cause analysis, corrective actions taken, and formal sign-off by the QA Manager and RMP.

---

Summary of Control Chart Limits & Required Responses