Category: Basic QC Concepts | Estimated reading time: 11 minutes
Two Numbers That Secretly Control Everything
The lines on a Levey-Jennings chart are not arbitrary drawings. They are all calculated from two numbers: the Target Value (TV) as the center line, and the SD as the distance between lines. Change either one, and the exact same QC data can look calm or riddled with alarms.
In the field, this gives rise to two frequently asked questions:
- "The manufacturer's SD is huge. Can I use it?"
- "Can I change the SD to match my data spread?"
The Preliminary Testing article explains how to establish the TV and SD. This article answers the next question: what are the consequences if those numbers are incorrect, and when is it acceptable to change a number.
The Role of TV and SD in Charts and Westgard Rules
- TV is the center line. All rules that evaluate position relative to the mean (4₁s, 10x, trends) depend on it.
- SD determines all other distances: ±1SD, ±2SD, ±3SD. Every Westgard rule (1₂s, 1₃s, 2₂s, R₄s, 4₁s) is defined in units of SD, so SD determines at what value a rule is triggered.
This means TV and SD are not just "initial settings." They determine what value is considered acceptable and what value triggers a reject.
Manufacturer Ranges: What They Are, and What They Are Not
Control material inserts contain a mean and a range, often called bottle limits. According to Westgard QC (2011), this range is not intended to be used as a laboratory's routine control limits. Its function is to provide an indication of the range where the laboratory mean is expected to fall. Because it is designed to estimate the mean's position, not to describe the daily variation of a single instrument, it is normal for this range to be much wider than the actual variation in your laboratory.
Some findings reported in Westgard QC literature:
- Ranges labeled "2 SD" by manufacturers are often much wider when measured against the laboratory's own SD.
- One cited hematology study reported that the manufacturer-recommended range was actually equivalent to about 6 SD, not 2 SD. The authors have even encountered laboratories with ranges equivalent to up to 10 SD, which makes the control chart look like a straight line.
- A 2017 global QC survey found that some laboratories use manufacturer or peer group ranges for SD, and such ranges tend to be wider than what the laboratory's actual SD would produce.
A practical tip: check the insert to see if the range is stated as ±2SD, ±3SD, or otherwise. If a ±2SD range is treated as if it were ±3SD, the SD you derive is off by a third.
Real-World Example: "String of Pearls"
Westgard QC (2013) documented a case. An assayed control material came with a mean of 127 and an SD of 5. The laboratory's actual data produced a mean of 129 and an SD of 2.2. The manufacturer's SD was 2.3 times larger than the laboratory's actual performance.
Consequently, the chart looked like a "string of pearls": all points comfortably resided within ±1SD. Yet when calculated with the correct mean and SD, the same chart clearly showed problems. In that case, even dramatic changes only reached slightly below −2SD according to the manufacturer's SD, which only triggered a warning, not a reject. A cited comment from the laboratory in question revealed the human factor: the technicians did not look at the LJ chart unless a "Failure" flag appeared.
This is precisely the trap discussed in the "Always Green QC" article: a chart that is always calm does not necessarily mean the process is performing well.
How Big is the Impact? Numbers from Simulation
To feel the scale, I ran a simple Monte Carlo simulation with the same logic as the Monte Carlo calculator in the previous article: N = 2 control levels per run, up to 20 runs, with two sets of rules:
- Set A: 1₃s + 2₂s
- Set B: full multirule (1₃s, 2₂s, R₄s, 4₁s, 10x)
All error magnitudes are expressed in actual process SD, and the reject number is the probability of having at least one reject in 20 runs.
If the Used SD is Too Wide
Imagine an additional systematic error of 2 actual SD occurs. This is a problem that should be easily detected.
- Correct SD: set A detects it on the first run with a 41% probability, and within 3 runs with an 83% probability. Median detection time is about 2 runs.
- SD used is 2 times larger (similar to the Westgard example above): set A only detects 0.3% within 3 runs, and only about 2% even after 20 runs. Practically blind.
- With multirule (set B), the 10x rule still catches it because this rule does not depend on the SD scale, but it takes time: median is about 5 runs (10 points), and only about 13% detected within 3 runs. The fast rules (1₃s, 2₂s, 4₁s) are practically useless when the SD is too wide.
- SD 3 times larger: set A does not detect anything in 20 runs, and multirule relies entirely on 10x.
For smaller errors, 1.5 actual SD, this pattern is the same: with an SD 2 times larger, set A only detects about 0.2% in 20 runs.
If the Used SD is Too Narrow
For example, if the SD is calculated from one short session so that it is about 1.5 times smaller than the true long-term SD (Westgard QC notes that a period that is too short gives an SD that is too small).
- The process is actually normal, but the probability of having at least one reject in 20 runs reaches about 90% (set A) and about 97% (set B).
- By comparison, with the correct SD, the numbers are about 14% (set A) and 28% (set B) for 20 runs. This number is cumulative over 20 runs, not per run.
The result is a "forest of alarms": rejects keep appearing without any real problems, and this is the gateway to the "repeat until it passes" culture discussed in the QC Reject article.
If the TV is Off (Correct SD)
Suppose the reference mean is lower than the actual process mean:
- Difference of 0.5 SD: probability of reject in 20 runs increases from about 13% to 33% (set A), and from about 29% to 62% (set B).
- Difference of 1 SD: about 80% (set A) and 98% (set B).
- Difference of 1.5 SD: above 99% for both sets.
A mean that is off by 1 SD is almost certain to trigger a reject in a short time, and the pattern that appears on the chart is "points always on one side of the mean" as discussed in the Levey-Jennings Chart Patterns article.
Methodology note: this simulation uses independent normally distributed data and combines all control levels into one sequential data stream, the same as the Monte Carlo calculator. This is a simplification for relative comparison, not a substitute for formal SQC design calculations. What is important from these numbers is the direction and magnitude of the difference, not the exact figures.
Two Failures in Opposite Directions
- SD too wide makes QC blind: looks calm, false sense of security, real errors slip through.
- SD too narrow makes QC noisy: endless alarms, alarm fatigue, and eventually the rules are ignored.
Both equally damage the QC function, just with different faces.
When to Use Manufacturer Values, When to Use In-House SD?
The CLSI C24 guidelines referenced by Westgard QC direct laboratories to establish their own mean and SD. In practice:
Manufacturer values are used for:
- Estimating a reasonable mean range before you have data.
- Reasonableness checks. Compare the mean from your preliminary testing with the manufacturer's range. If your mean is outside the range, the control material can still be used, provided subsequent measurements are evaluated against the mean and SD that you established yourself, not against the manufacturer's target mean. However, a large difference from the manufacturer's target can indicate a systematic error or bias. Verify with assayed material or PT/EQA samples to see if that bias is consistent across various materials or only appears in one control material.
In-house SD is used for:
- Routine control limits and Westgard rules.
- General guidelines cited by Westgard QC for C24: at least 20 measurements over approximately 20 days to establish a new mean and SD. The 30-measurement preliminary test in the previous article is a good starting point, not an endpoint.
Beware of SD from short periods. 20–30 measurements in one session only capture short-term (within-day) variation. Inter-day variation due to calibration, operator, and reagents has not yet been accounted for. That is why Westgard teaches cumulative (or lot-to-date) calculations: the mean and SD are updated as data increases during the life of the lot. Regarding the Repeatability & Reproducibility article: the SD for routine control limits should reflect long-term variation within the laboratory, not just variation within one session.
A practical suggestion: every time you establish an SD for a new lot, compare it with the cumulative SD of the previous lot. If it is significantly different, find the cause before accepting the new number.
"Can I Change SD to Match Data Spread?" The Dividing Line Between Improvement and Chasing Data
The answer: you can, but only for the right reasons.
Legitimate changes:
- Updating the SD based on cumulative data from a stable process, for example after a certain period or when changing lots.
- Excluding points that have an identified and documented cause (as discussed in the Preliminary Testing article).
- Establishing a new mean per reagent or control material lot, rather than widening the SD. Westgard QC notes that different reagent lots can shift all values, and the temptation is to widen the range so that inter-lot differences no longer trigger flags. The correct resolution is to adjust the mean for that lot, not to dull the detection capability.
Illegitimate changes (often called "chasing data"):
- Widening the SD after a flag appears, so that rejects stop.
- Changing the SD after a shift occurs, so that new points "look normal."
- Using manufacturer ranges to avoid inter-lot flags.
Westgard QC describes the outcome: a quality system that is compliant on paper but completely ineffective.
A simple test before changing any number: does the reason for this change stem from stable data or from a desire for the flags to stop? If the actual SD is indeed increasing because the process is deteriorating, the answer is to fix the process (flow in the QC Reject article), not to widen the limits.
Finally, every change to the TV or SD should be recorded: date, reason, data basis, who decided, and who approved.
A Quick Way to Check if Your SD is Correct
In a stable process with the correct SD, a normal distribution estimates that about 68% of points fall within ±1SD, about 95% within ±2SD, and about 99.7% within ±3SD. As a rough check:
- Almost all points over months fall within ±1SD: suspect the SD is too wide ("string of pearls"). This aligns with the Nelson rule of 15 points within ±1SD discussed in the Levey-Jennings Chart Patterns article.
- Quite a few points outside ±2SD without an identified cause: suspect the SD is too narrow, or the process is indeed unstable.
- CV from in-house SD compared with target imprecision or TEa (see the Accuracy, Precision & Monthly Evaluation article).
With few samples, these percentages are only rough indications, and they become more meaningful as more data is added.
Impact on Other Metrics
SD is not just about control limits. If a bloated SD is used to calculate the CV, it also misleads other evaluations. Because Sigma = (TEa − |Bias|) / CV, a CV that is too large makes Sigma look lower than reality, while an SD that is too small makes Sigma look too good. One incorrect number can propagate into several decisions at once.
Summary
- TV and SD determine the chart appearance and the result of Westgard rules. Both are not administrative settings.
- Manufacturer ranges are estimates of where the mean is expected to fall, not routine control limits.
- An SD that is too wide makes QC blind (even a 2 SD error is barely detected), an SD that is too narrow makes QC noisy, and a TV that is off causes constant rejects.
- Establish your own mean and SD: at least about 20 measurements over about 20 days, then update with cumulative data.
- Change the SD only based on stable data and documented reasons. Never change it to stop flags.
- If changing lots, reset the mean, do not widen the SD.
Closing
Levey-Jennings charts are only as good as the numbers that comprise them. Two seemingly trivial numbers, TV and SD, determine whether your QC is sensitive, blind, or noisy. Establishing them correctly, updating them with discipline, and resisting the temptation to "adjust" when flags become bothersome is invisible work that supports the entire QC system above it.