An intermediate course for future biochemists, biological technicians, medical laboratory technologists, chemists and materials scientists, about the data and quality systems that make lab results trustworthy. The first module covers records and integrity: writing ALCOA+ notebook entries, how a sample moves through a LIMS or LIS, and querying sample results by batch and date in SQL. The second module covers quality control: Levey-Jennings charts and Westgard rules, calibration curves with LOD and LOQ, and propagating measurement uncertainty. The third module covers quality systems: SOPs, deviations and CAPA, audits and accreditation (ISO/IEC 17025, ISO 15189, CLIA, CAP, GMP and GLP), and deciding when a result may be rejected or repeated. Python and SQL activities are fill-in-the-blank and use only the standard library and SQLite, so no programming background is needed. Every activity is a paper or data exercise. Real lab quality work also depends on supervised training and formal credentials, such as a NAACLS-accredited program and ASCP certification for medical laboratory scientists, and on-the-job GMP training in regulated manufacturing.

Keep trustworthy lab records, query LIMS data, run QC with Westgard rules, build calibration curves, estimate uncertainty, and work within SOPs, CAPA and accreditation.

Lab Data & Quality

Choose a measurement: for example, checking whether your kitchen measuring cup really holds 250 mL by weighing the water it holds on a kitchen scale (water is close to 1.00 g per mL).

Start a new page. Write the date, a title, the objective and a page number.

Write a short procedure in numbered steps before you begin, as if it were an SOP (give it a made-up number and version, such as SOP-HOME-001 v1).

List your materials and equipment with identifiers: for example, "scale: brand and model, readability 1 g" and "cup: marked 250 mL".

Do the measurement three times. Record every reading in ink as you take it, with units.

Deliberately make one recording error, then correct it properly: a single line through the wrong value, the right value, your initials, the date and a reason.

Show your calculation of the mean and of the difference from 250 g.

Write a one-line result and conclusion, and note any deviation from your written procedure (or write "Deviation: none").

Sign and date the entry, then cross out any unused space on the page.

Swap with a friend or classmate if you can: can they repeat your measurement from your entry alone?

## Why it matters

In a lab, if it was not written down, it did not happen. Your notebook is the legal and scientific record of what you did, when, with what, and what you saw. Patent disputes have been decided on notebook entries. Regulators reject results that cannot be reconstructed from records. And on a practical level, six months from now you, or a colleague, will need to repeat or troubleshoot your work from what you wrote today.

## ALCOA+: the data integrity standard

Regulators and quality systems describe good records with the acronym **ALCOA**, extended to **ALCOA+**:

| Letter | Meaning | In practice |
|---|---|---|
| **A**ttributable | You can tell who recorded it and who did the work | Initials or signature, user login in an ELN |
| **L**egible | Anyone can read it, now and later | Permanent ink, clear handwriting |
| **C**ontemporaneous | Recorded at the time it happened | Write as you go, not at the end of the day |
| **O**riginal | The first record, or a certified true copy | Raw instrument printouts kept, not retyped |
| **A**ccurate | Correct and complete, with no undocumented edits | Real values, every digit, errors corrected properly |
| **+** Complete, Consistent, Enduring, Available | Nothing missing, in order, lasting, retrievable | Numbered pages, dated entries, backed up |

The US FDA's data integrity guidance for drug manufacturing uses these principles: https://www.fda.gov/regulatory-information/search-fda-guidance-documents/data-integrity-and-compliance-drug-cgmp-questions-and-answers (Checked on 2026-10-23.)

## Rules for a paper notebook

- Use a **bound notebook with numbered pages**. Do not tear out pages.
- Write in **permanent ink**, never pencil.
- **Date every entry** and sign or initial it. Many regulated labs also require a witness or reviewer signature.
- **Never erase, use correction fluid or overwrite.** Correct an error with a **single line** through it, so the original is still readable, then write the correct value with your initials, the date and a short reason.
- Do not leave blank spaces that someone could fill in later. Cross out unused space on a page.
- Attach printouts permanently and sign across the edge of the attachment and the page.
- Record what actually happened, including mistakes and failed runs.

### A correction done right

```text
Mass of standard: 0.2514 g  0.2541 g  AB 2026-10-23 transcription error, value re-read from balance printout
```

(In a notebook, the first value has a single line through it.)

## What a complete entry contains

1. **Date, title and objective.** What are you trying to do?
2. **Reference to the method.** SOP number and version, or a full procedure if it is new.
3. **Materials.** Reagents with **lot numbers and expiry dates**, sample IDs, standards with certificate numbers.
4. **Equipment.** Instrument IDs, and confirmation that calibration was current.
5. **Procedure as performed.** Especially any change from the written method.
6. **Raw data and observations.** Every reading with units, colours, times, anything unexpected.
7. **Calculations.** Show the formula and the numbers, not just the answer.
8. **Results and conclusion.** What the data show, and whether acceptance criteria were met.
9. **Deviations.** Anything that did not go to plan, and the deviation number if one was raised.
10. **Signature** (and reviewer or witness, if required).

### Worked example (short)

```text
2026-10-23  Prep of 0.10 M phosphate buffer, pH 7.40, 1 L   p. 47
Objective: buffer for enzyme assay EA-12 (SOP-BUF-004 v3)
Materials: Na2HPO4 anhydrous, lot K2291, exp 2028-02; NaH2PO4 anhydrous, lot J1170, exp 2027-11
Equipment: balance BAL-02 (daily check pass 08:05), pH meter PH-03 (cal 08:12, slope 96.1 percent)
Weighed: Na2HPO4 8.6283 g; NaH2PO4 4.7069 g
Dissolved in ~800 mL DI water, 22.4 C. pH read 7.36; adjusted with 0.5 mL 1 M NaOH to 7.40.
Made up to 1000 mL in flask VF-1000-03. Labelled BUF-1023-01, exp 2026-11-23, stored 4 C.
Deviation: none.  AB 2026-10-23
```

## Electronic lab notebooks (ELNs)

Many labs now use an **ELN**. It brings templates, search, links to instrument files and sample records, and automatic time stamps. In regulated work, US rules for electronic records and signatures are in **21 CFR Part 11** (https://www.ecfr.gov/current/title-21/chapter-I/subchapter-A/part-11, checked on 2026-10-23). Key features you should expect:

- **Unique user logins**, never shared accounts.
- An **audit trail** that records who changed what, when, and why, and cannot be switched off by users.
- **Electronic signatures** linked to the person.
- Backups and controlled access.

The ALCOA+ principles apply exactly the same way. An ELN that lets anyone edit an entry without a trace is not meeting them.

## Common mistakes

- Writing results on a glove, paper towel or sticky note and copying them later. That breaks "original" and "contemporaneous".
- Recording only the final answer, not the raw readings.
- Omitting lot numbers, so a bad reagent lot cannot be traced.
- Scribbling out an error until it is unreadable.
- Sharing an ELN login with a colleague.

## Quick recap

- Follow ALCOA+: attributable, legible, contemporaneous, original, accurate, plus complete, consistent, enduring, available.
- Bound notebook, permanent ink, dated and signed, single-line corrections with initials, date and reason.
- A complete entry lets someone else repeat your work: method, lots, instrument IDs, raw data, calculations, deviations.
- ELNs add audit trails and e-signatures; in regulated labs they fall under 21 CFR Part 11.

## Try it

Open the **Do** tab to write a complete notebook entry for a simple kitchen measurement.


Write a complete, ALCOA+-compliant notebook entry and know what an electronic lab notebook adds.

Lab notebooks and ELNs

Ten Tips For Keeping a Better Lab Notebook

Chemistry Lab Skills: Maintaining a Lab Notebook

## Why it matters

A busy lab handles thousands of samples a day. Each one must be matched to the right patient or batch, tested by the right method on a calibrated instrument, reviewed, reported to the right person and stored or discarded on time. Paper cannot keep up. Laboratory information systems do this work, and almost every lab job involves using one. Understanding how they track a sample makes you faster, and it helps you spot when something has gone wrong.

## LIMS, LIS and ELN

| System | Typical setting | Centred on |
|---|---|---|
| **LIMS** (laboratory information management system) | Research, pharmaceutical QC, environmental, food, contract testing labs | Samples, batches, tests, specifications, instruments |
| **LIS** (laboratory information system) | Hospital and clinical labs | Patients, orders from clinicians, results reported to the medical record |
| **ELN** (electronic lab notebook) | Research and development | Experiments and the scientist's narrative |

The lines blur: many products combine features. The key difference is focus. A LIS lives inside the healthcare system and exchanges orders and results with the electronic health record, often using the **HL7** messaging standard. A LIMS is built around samples, specifications and batch release.

## The life of a sample

Whatever the system, a sample follows the same broad path.

1. **Order or request.** A clinician orders tests (LIS), or a production step triggers QC testing (LIMS).
2. **Collection and labelling.** The sample gets a unique ID, usually a **barcode**. Clinical labs require at least **two patient identifiers** (such as full name and date of birth) on the tube.
3. **Receipt and accessioning (login).** The lab checks the sample against the request: right container, right volume, labelled correctly, received in time and at the right temperature. Samples that fail are **rejected** with a reason, and the requester is told.
4. **Chain of custody.** Every handover is recorded. For forensic, drug testing and some environmental work, the chain of custody is a legal requirement.
5. **Test assignment and worklists.** The system assigns tests and builds worklists or instrument run lists.
6. **Analysis.** Instruments receive the run list and send results back through an **instrument interface**, avoiding retyping.
7. **Review and approval.** QC must pass for the run. Results are checked against specifications or reference ranges. Many clinical labs use **autoverification**: rules that release normal results automatically and hold unusual ones for a person to review.
8. **Reporting.** Results go to the clinician, the medical record, or a certificate of analysis for a batch. **Critical values** (results that suggest immediate danger to a patient) are phoned to a responsible person and the call is documented.
9. **Storage and disposal.** The sample is kept for its retention period, then discarded, and the system records where it is and when it went.

## What the system remembers

A LIMS or LIS keeps far more than results:

- **Specifications and reference ranges**, so out-of-range values are flagged.
- **QC results** for each run, linked to the patient or sample results they cover.
- **Instrument status**, including calibration and maintenance due dates. Many systems block a run on an instrument that is overdue.
- **Reagent lots** used in each run.
- **Analyst training records**, so only qualified people can enter or approve certain tests.
- **An audit trail** of every change.

Because all of this is linked, the lab can answer questions like "which results used reagent lot K2291?" or "which samples ran on HPLC-02 after its last good calibration?" in seconds. In the next lesson you will write those queries yourself in SQL.

## Worked example: tracing a sample

A QC sample from tablet batch B-102 has ID S-2051.

- Logged in at 09:14 by AB; condition acceptable; stored at room temperature, shelf R3.
- Assigned: assay (HPLC) and dissolution.
- Assay run on HPLC-02, run R-778, system suitability passed, result 99.1 percent of label claim (specification 95.0 to 105.0).
- Reviewed by CD at 15:02; approved.
- Certificate of analysis generated for batch B-102 after all tests passed.

If an auditor asks how 99.1 percent was obtained, every link (sample, run, instrument, analyst, reviewer) is in the system.

## Common mistakes

- Relabelling a tube by hand instead of reprinting through the system.
- Accepting a sample that does not match its request "to save time".
- Entering results by hand when an instrument interface exists, which introduces transcription errors.
- Sharing logins, which destroys attribution.
- Ignoring a system warning about an overdue calibration.

## Quick recap

- LIMS focuses on samples and batches; LIS on patients and clinical orders; ELN on experiments.
- A sample moves through request, labelling, accessioning, testing, review, reporting and storage, with each step recorded.
- Specifications, QC, instruments, reagents, training and audit trails are linked, which makes tracing possible.

## Try it

This lesson is quiz-only. Open the **Do** tab to check your understanding.


Trace a sample through a LIMS or LIS, from request and accessioning to review, reporting and storage.

LIMS and LIS

Introduction to Laboratory Informatics: Life of a Specimen – What is a LIMS?

What is the difference between an LIS and a LIMS?

## Why it matters

A LIMS stores its records in a relational database, and the questions a lab asks every day are database queries. Which samples from this batch are still untested? What did HPLC-02 measure after its last good calibration? Which results used reagent lot K2291? Most LIMS screens are built on queries like these, and many labs let analysts and QC reviewers run read-only reports in **SQL** (Structured Query Language). You do not need to be a programmer to read and adapt a simple query. This lesson shows the handful of SQL pieces that cover most lab questions.

## Tables and keys

A lab database splits information into tables so each fact is stored once:

- `samples`: one row per sample, with `sample_id`, `batch_id`, `sample_type` and `received_date`.
- `results`: one row per result, with `result_id`, `sample_id`, `analyte`, `value`, `units`, `run_date` and `instrument_id`.

`sample_id` is the **primary key** of `samples` (unique for each sample) and appears in `results` as a **foreign key**, linking each result to its sample. One sample can have many results: an assay, a water content, a dissolution test.

## SELECT, FROM, WHERE, ORDER BY

```sql
SELECT sample_id, value, run_date
FROM results
WHERE analyte = 'assay'
ORDER BY run_date;
```

- `SELECT` lists the columns you want.
- `FROM` names the table.
- `WHERE` keeps only rows that meet a condition. Text values go in single quotes.
- `ORDER BY` sorts the output (add `DESC` for newest first).

Combine conditions with `AND` and `OR`, and use parentheses when you mix them:

```sql
WHERE analyte = 'assay' AND (instrument_id = 'HPLC-01' OR instrument_id = 'HPLC-02')
```

### Dates

Many systems store dates as `YYYY-MM-DD` text, which sorts correctly. A date range uses `BETWEEN`, which includes both ends:

```sql
WHERE run_date BETWEEN '2026-10-01' AND '2026-10-07'
```

If a column stores a full timestamp (`2026-10-07 14:30`), `BETWEEN '2026-10-01' AND '2026-10-07'` misses results from later on the 7th. Use `run_date < '2026-10-08'` for the upper end in that case.

## Joining tables

The batch is stored on the sample, not on the result. To see results by batch, **join** the tables on the shared key:

```sql
SELECT r.sample_id, s.batch_id, r.analyte, r.value
FROM results AS r
JOIN samples AS s ON s.sample_id = r.sample_id
WHERE s.batch_id = 'B-102';
```

`AS r` and `AS s` are short aliases, so `r.value` means the `value` column of `results`. `JOIN ... ON` pairs each result with its sample row.

## Counting and summarising

```sql
SELECT s.batch_id, COUNT(*) AS n_results, ROUND(AVG(r.value), 2) AS mean_assay
FROM results AS r
JOIN samples AS s ON s.sample_id = r.sample_id
WHERE r.analyte = 'assay'
GROUP BY s.batch_id;
```

`GROUP BY` makes one output row per batch, and `COUNT`, `AVG`, `MIN` and `MAX` summarise each group.

## Worked example: an instrument question

HPLC-02 failed its calibration check on 2026-10-09. The last good calibration was 2026-10-04. Which results need review?

```sql
SELECT sample_id, analyte, value, run_date
FROM results
WHERE instrument_id = 'HPLC-02'
  AND run_date >= '2026-10-04'
ORDER BY run_date, sample_id;
```

This is the kind of query a QC reviewer runs during an investigation. The output is the list of results to assess.

## Good habits

- **Read-only.** Reporting queries use `SELECT` only. Changing records (`UPDATE`, `DELETE`) in a regulated system happens only through the application, with an audit trail, never by hand in the database.
- **Check the row count.** If you expected 3 rows and got 300, a condition is missing.
- **Be exact with text.** `'B-102'` and `'b-102'` may not match, and stray spaces matter.
- **Name your columns** in `SELECT` instead of using `SELECT *`, so reports stay stable when the table changes.

## Common mistakes

- Forgetting the join condition, which pairs every result with every sample.
- Using double quotes for text values (in many databases double quotes mean a column name).
- Mixing `AND` and `OR` without parentheses.
- Forgetting that `BETWEEN` includes both ends.

## Quick recap

- `SELECT` columns, `FROM` a table, `WHERE` conditions, `ORDER BY` for sorting.
- `JOIN ... ON` links results to samples through `sample_id`.
- `GROUP BY` with `COUNT` and `AVG` summarises by batch or instrument.
- Reporting queries are read-only; changes go through the application and its audit trail.

## Try it

Open the **Do** tab. The query already joins the tables and sorts the rows: you add one `WHERE` clause to pull one batch's assay results for one week.


Query lab results by sample, batch and date with SELECT, WHERE, JOIN and GROUP BY.

Querying sample data

Learn Basic SQL in 15 Minutes | Business Intelligence For Beginners | SQL Tutorial For Beginners 1/3

Write ALCOA+ notebook entries, trace samples through a LIMS or LIS, and query sample results in SQL.

Records and Integrity

## Why it matters

How do you know today's results are right? Every analytical run in a clinical, pharmaceutical or environmental lab includes **quality control (QC) samples**: materials with a known, stable expected value that are tested exactly like real samples. If the QC results behave, the run is accepted. If they do not, the patient or batch results from that run are held. Medical laboratory technologists make this call many times a shift, and getting it wrong in either direction is costly: releasing bad results harms patients, and rejecting good runs wastes time and samples.

## The Levey-Jennings chart

A **Levey-Jennings chart** plots each QC result over time against lines for the expected mean and for ±1, ±2 and ±3 standard deviations (SD). The mean and SD come from the lab's own repeated measurements of that QC lot (often at least 20 results over several days), not just the manufacturer's insert.

To compare results on the same scale, convert each one to a **z-score**:

```text
z = (result - mean) / SD
```

**Worked example.** A glucose control has mean 100 mg/dL and SD 2.5 mg/dL. A result of 106 mg/dL has z = (106 - 100) / 2.5 = 2.4: between 2 and 3 SD above the mean.

If results follow a normal distribution, about 95 percent fall within ±2 SD and about 99.7 percent within ±3 SD. So one result beyond 2 SD happens by chance about 1 time in 20, which is why a single 2 SD result is treated only as a warning.

## Westgard rules

James Westgard's **multirule QC** combines several rules, each sensitive to a different kind of error. The names read as "number of results, and limit": 2_2s means two results beyond 2 SD.

| Rule | Violated when | Usually points to |
|---|---|---|
| **1_2s** (warning) | One result beyond ±2 SD | Triggers inspection with the other rules |
| **1_3s** (reject) | One result beyond ±3 SD | Random error or a large systematic error |
| **2_2s** (reject) | Two consecutive results beyond 2 SD **on the same side** | Systematic error (shift) |
| **R_4s** (reject) | One result above +2 SD and the other below -2 SD (range over 4 SD) | Random error |
| **4_1s** (reject) | Four consecutive results beyond 1 SD on the same side | Systematic error (gradual shift) |
| **10_x** (reject) | Ten consecutive results on the same side of the mean | Systematic error (bias, drift) |

Strictly, R_4s is applied to two control levels within the same run, while 2_2s, 4_1s and 10_x can be applied within a run and across consecutive runs. In this lesson's activity we apply every rule to a single control's sequence of results, to keep it simple.

Rules for your lab are chosen when the method is validated, based on how good the method is compared with its allowed error. Some labs use fewer rules for very precise methods. Westgard's site explains the full approach: https://www.westgard.com/mltirule.htm (Checked on 2026-10-23.)

## Worked example: judging a run

The last five results (as z-scores, oldest first) for a control are:

```text
0.4, 1.1, -0.3, 2.3, 2.6
```

- The last result (2.6) is beyond 2 SD: **1_2s warning**, so check the other rules.
- 1_3s? No, 2.6 is below 3.
- 2_2s? The last two results, 2.3 and 2.6, are both above +2 SD. **Yes: reject.**
- This pattern suggests a systematic shift: perhaps a new reagent lot, a calibration problem or a deteriorating control.

## What to do when a rule fails

1. **Do not report** patient or batch results from the run.
2. **Do not simply repeat the control** until it passes. That hides real problems.
3. Investigate: reagents and lots, calibration, instrument maintenance, the control material itself (stored correctly, in date), recent changes.
4. Fix the cause, recalibrate if needed, rerun controls, then rerun the affected samples.
5. **Document** the failure, the investigation and the corrective action.

In clinical labs, QC rules and records are required under CLIA (42 CFR Part 493: https://www.ecfr.gov/current/title-42/chapter-IV/subchapter-G/part-493, checked on 2026-10-23) and checked by accrediting bodies such as CAP.

## Common mistakes

- Treating a 1_2s warning alone as a rejection, or ignoring it entirely.
- Rerunning a failed control until it passes.
- Using the manufacturer's range instead of the lab's own mean and SD.
- Ignoring slow trends because no single result looks bad (the 4_1s and 10_x rules catch these).

## Quick recap

- z = (result - mean) / SD puts every QC result on the same scale.
- 1_2s warns; 1_3s, 2_2s, R_4s, 4_1s and 10_x reject.
- Random-error rules: 1_3s, R_4s. Systematic-error rules: 2_2s, 4_1s, 10_x.
- On rejection: hold results, investigate, fix, rerun, document.

## Try it

Open the **Do** tab. A Python Westgard checker already handles most rules; you write the 2_2s rule.


Plot QC on a Levey-Jennings chart and flag runs that break Westgard rules.

QC charts and Westgard rules

Chapter 3 Levey-Jennings Charts & Westgard Rules

Bio-Rad Blackboard - Levey-Jennings Charts

## Why it matters

Most quantitative lab methods do not measure concentration directly. An HPLC measures peak area, a spectrophotometer measures absorbance, an ICP measures emission intensity. A **calibration curve** turns that signal into a concentration. How well you build it decides how accurate your results are, and its statistics tell you the smallest amounts you can reliably detect and report. Method validation guidelines (such as ICH Q2 for pharmaceuticals) require labs to show both.

## Building a calibration curve

1. Prepare a **blank** and at least five standards that span the expected range of samples.
2. Measure each standard (often in replicate).
3. Fit a straight line by **least-squares linear regression**: signal = slope x concentration + intercept.
4. Check the fit: look at the **residuals** (measured signal minus the line's predicted signal). They should scatter randomly around zero. A curved pattern means the response is not linear over that range.
5. Use the line to calculate sample concentrations: c = (signal - intercept) / slope.

**Correlation coefficient r (or r squared)** is often reported, and many methods require, for example, r squared of at least 0.99. But a high r squared does not prove linearity: a slightly curved response can still give r squared of 0.995. Always look at the residuals.

## Limit of detection and limit of quantitation

- **Limit of detection (LOD):** the lowest concentration that can be reliably distinguished from zero. Below it, you report "not detected".
- **Limit of quantitation (LOQ):** the lowest concentration that can be measured with acceptable precision and accuracy. Between LOD and LOQ, you can say the analyte is present but cannot give a reliable number.

One approach in ICH Q2 uses the standard deviation of the response (sigma) and the slope (S) of the calibration curve:

```text
LOD = 3.3 x sigma / S
LOQ = 10 x sigma / S
```

Sigma can be the **residual standard deviation** of the regression line, the standard deviation of the y-intercept, or the standard deviation of blank measurements. The residual standard deviation for n points is:

```text
s_res = sqrt( sum of squared residuals / (n - 2) )
```

The n - 2 is because the line used up two parameters (slope and intercept).

### Worked example

Lead standards (µg/L) and instrument signals:

| Concentration | 0 | 1 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|---|
| Signal | 0.010 | 0.122 | 0.228 | 0.452 | 0.668 | 0.889 |

A least-squares fit gives a slope of about 0.1098 per µg/L and an intercept of about 0.0106. The residuals are small, and the residual standard deviation is about 0.0019. So:

```text
LOD = 3.3 x 0.0019 / 0.1098 = about 0.057 µg/L
LOQ = 10  x 0.0019 / 0.1098 = about 0.17 µg/L
```

A sample with a calculated concentration of 0.12 µg/L would be reported as detected but below the LOQ; one at 3.2 µg/L is reported as a number. (Your activity will compute these values exactly.)

Calculated LOD and LOQ are estimates. Validation guidelines expect them to be **confirmed** by analysing samples near those levels.

## Good practice

- **Bracket your samples.** Do not report results above the highest standard; dilute and rerun.
- **Do not force the line through zero** unless the method was validated that way.
- **Run check standards** during the run (for example every 10 samples) to show the calibration still holds.
- **Use independent standards** for QC: prepared from a different stock or lot than the calibration standards, so a stock error does not hide itself.
- **Record everything:** standard preparation, lot numbers, the fitted equation, r squared and residuals.

## Common mistakes

- Trusting r squared without looking at residuals.
- Extrapolating below the lowest or above the highest standard.
- Using the same stock solution for calibration standards and QC.
- Reporting numeric results below the LOQ as if they were reliable.
- Dropping an inconvenient standard from the curve without a documented reason.

## Quick recap

- Fit signal against concentration with least squares; check residuals, not just r squared.
- c = (signal - intercept) / slope, within the calibrated range only.
- LOD = 3.3 x sigma / S and LOQ = 10 x sigma / S (ICH Q2 approach), with sigma often the residual SD.
- Confirm LOD and LOQ experimentally, and use independent QC standards.

ICH quality guidelines (Q2 covers analytical validation): https://www.ich.org/page/quality-guidelines (Checked on 2026-10-23.)

## Try it

Open the **Do** tab. The Python code fits the curve with `statistics.linear_regression` and computes the residual SD; you add the LOD and LOQ formulas.


Fit a calibration curve, check its residuals, and compute the limit of detection and limit of quantitation.

Calibration curves

Spectrophotometers, calibration curves and Beer's Law

Chapter 5: Limit of Detection and Limit of Quantitation | CHM 214 | 040

## Why it matters

No measurement is exact. A result of "0.995 mg/mL" really means "somewhere close to 0.995, within some range". **Measurement uncertainty** quantifies that range. It tells a client whether a result is clearly inside a specification, or close enough to the limit that the difference may not be real. Accredited testing and calibration labs (ISO/IEC 17025) must estimate it for their methods, and medical labs accredited to ISO 15189 must too.

## Key terms

- **Standard uncertainty (u):** the uncertainty of one input expressed as a standard deviation.
- **Relative standard uncertainty:** u divided by the value, for example u(m) / m.
- **Combined standard uncertainty (u_c):** the uncertainty of the final result, combining all inputs.
- **Expanded uncertainty (U):** u_c multiplied by a **coverage factor k**, usually k = 2, which gives a range expected to contain the true value with about 95 percent confidence.

Results are reported as value ± U, with k stated: "0.9950 ± 0.0024 mg/mL (k = 2)".

## Where the input uncertainties come from

**Type A** evaluations use statistics on repeated measurements: the standard deviation of replicates (or of the mean, s / sqrt(n)).

**Type B** evaluations use other information: certificates, manufacturer specifications, tolerances. A tolerance written as ±a is converted to a standard uncertainty by assuming a distribution:

| Information | Assumed distribution | Standard uncertainty |
|---|---|---|
| Certificate gives U with k = 2 | Normal | U / 2 |
| Tolerance ±a, any value equally likely | Rectangular | a / sqrt(3) |
| Tolerance ±a, values near the centre more likely (often glassware) | Triangular | a / sqrt(6) |

## Combining uncertainties

For a result calculated by **adding or subtracting** inputs, combine the **standard uncertainties** in quadrature (square, add, square root):

```text
y = a + b - c      u(y) = sqrt( u(a)^2 + u(b)^2 + u(c)^2 )
```

For a result calculated by **multiplying or dividing**, combine the **relative** uncertainties in quadrature:

```text
y = a x b / c      u(y) / y = sqrt( (u(a)/a)^2 + (u(b)/b)^2 + (u(c)/c)^2 )
```

Quadrature works because independent errors partly cancel: it is unlikely that every input is at its worst in the same direction at once. This assumes the inputs are independent.

## Worked example: a standard solution

You dissolve 100.0 mg of a reference material with purity 0.995 and make it up to 100.00 mL in a Class A volumetric flask.

```text
c = m x P / V = 100.0 x 0.995 / 100.00 = 0.9950 mg/mL
```

Input uncertainties:

| Input | Value | Standard uncertainty | Relative |
|---|---|---|---|
| Mass m | 100.0 mg | 0.05 mg (from the balance calibration) | 0.00050 |
| Purity P | 0.995 | 0.001 (certificate) | 0.00101 |
| Volume V | 100.00 mL | 0.08 / sqrt(3) = 0.046 mL (rectangular) | 0.00046 |

```text
relative u_c = sqrt(0.00050^2 + 0.00101^2 + 0.00046^2) = sqrt(1.47e-6) = 0.00121
u_c = 0.00121 x 0.9950 = 0.00121 mg/mL
U = 2 x 0.00121 = 0.0024 mg/mL (k = 2)
```

Result: **0.9950 ± 0.0024 mg/mL (k = 2)**. The purity contributes most, so a higher-grade reference material would help more than a better balance. An **uncertainty budget** table like the one above shows exactly where to improve.

## Using uncertainty in decisions

A specification is 0.990 to 1.010 mg/mL. A result of 0.9950 ± 0.0024 is clearly inside. A result of 0.9915 ± 0.0024 straddles the lower limit: the true value might be below it. Labs agree a **decision rule** in advance (often with the client) for these cases, as ISO/IEC 17025 requires.

## Common mistakes

- Adding uncertainties directly instead of in quadrature (overestimates).
- Mixing absolute and relative uncertainties in one formula.
- Using a tolerance as if it were a standard uncertainty (forgetting / sqrt(3) or / sqrt(6)).
- Reporting U without saying k.
- Quoting far more digits than the uncertainty justifies. Round U to one or two significant figures and the result to match.

## Quick recap

- Standard uncertainty is a standard deviation; expanded U = k x u_c, usually k = 2.
- Type A from repeats; Type B from certificates and tolerances (a / sqrt(3) rectangular).
- Sums: combine absolute uncertainties in quadrature. Products and quotients: combine relative uncertainties in quadrature.
- An uncertainty budget shows the biggest contributor.

NIST's guide to expressing uncertainty: https://www.nist.gov/pml/nist-technical-note-1297 (Checked on 2026-10-23.)

## Try it

Open the **Do** tab and finish a Python uncertainty calculator: you write the quadrature sum of relative uncertainties.


Estimate standard uncertainties and propagate them through a calculation to an expanded uncertainty.

Measurement uncertainty

Measurement Uncertainty | Metrology Matters

Error propagation formulas + error propagation examples with addition, multiplication, exponents.

Flag runs with Westgard rules, fit calibration curves with LOD and LOQ, and propagate measurement uncertainty.

Quality Control

Write a factual description of what happened: what, where, when, who found it and how. Avoid blame and guesses.

List the immediate (containment) actions you would take for the fridge, the kits, the calibrators and the 24-sample run.

Write an impact assessment: which materials, results and customers or patients could be affected, and what information you need to decide (for example, the kit manufacturer's stability data).

Draw a fishbone diagram with at least one possible cause under each of Methods, Machines, Materials, People, Measurement and Environment.

Use 5 Whys on the most likely cause and write the root cause in one sentence.

Write a correction, at least one corrective action and at least one preventive action, each with an owner (a role, not a name) and a due date.

Write an effectiveness check: what you will measure, for how long, and what counts as success.

Read your report as if you were an auditor: could someone who was not there understand what happened and why your actions fix it?

## Why it matters

In a regulated lab, work is done the same way every time because it follows a written, approved procedure. When something does not go to plan, the lab does not quietly fix it and move on. It records what happened, works out why, judges the impact on results and products, and changes something so it does not happen again. This loop (SOP, deviation, investigation, CAPA) is the heart of quality systems under GMP, GLP, ISO/IEC 17025 and clinical accreditation. Technicians are usually the ones who spot and first document a deviation, so you need to know how to write one well.

## Standard operating procedures (SOPs)

An **SOP** is a controlled document describing exactly how to do a task. A typical SOP has:

1. **Title, document number and version**, for example SOP-QC-017 v4.
2. **Purpose and scope:** what it covers and what it does not.
3. **Responsibilities:** who does what (analyst, reviewer, supervisor).
4. **Definitions and safety notes.**
5. **Materials and equipment.**
6. **Procedure:** numbered, unambiguous steps, with acceptance criteria.
7. **Records:** which forms or LIMS entries to complete.
8. **References** and **revision history.**

**Document control** keeps SOPs trustworthy: only the current approved version is in use, old versions are withdrawn, changes go through review and approval, and staff are **trained and signed off** on the new version before they use it. Using a printed copy of an old version is itself a deviation.

## Deviations

A **deviation** is any departure from an approved procedure, specification or expected condition.

- **Planned deviation:** approved in advance for a specific, justified reason (for example, using an alternative qualified instrument while the usual one is serviced).
- **Unplanned deviation:** something that happened: a missed step, an equipment failure, an environmental excursion, a mislabelled sample.

Labs also have specific procedures for **out-of-specification (OOS)** results: a test result outside the product's specification. FDA's OOS guidance describes a phased investigation: first check for an obvious laboratory error, then a full investigation if none is found. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/investigating-out-specification-oos-test-results-pharmaceutical-production-level-2-revision (Checked on 2026-10-23.)

### What a good deviation report contains

- **What happened**, factually: what, where, when, who found it. No blame, no speculation.
- **Immediate actions** (containment): what was done to stop the impact, such as quarantining reagents or holding results.
- **Impact assessment:** which samples, batches, results or patients could be affected.
- **Investigation and root cause.**
- **CAPA** and its owner and due date.
- **Approval** by quality assurance.

## Finding the root cause

The first explanation ("human error") is rarely the root cause. Two simple tools help:

- **5 Whys:** keep asking why until you reach something the organisation can change.
- **Fishbone (Ishikawa) diagram:** list possible causes under headings such as Methods, Machines, Materials, People, Measurement and Environment.

**Worked example, 5 Whys.** A reagent fridge reached 12 °C overnight (limit 2 to 8 °C).

1. Why? The compressor stopped.
2. Why? The fridge was unplugged.
3. Why? A cleaner unplugged it to use the socket.
4. Why? The plug looks like any other and is in a shared socket.
5. Why? The lab never labelled critical-equipment sockets or used locking plugs.

Root cause: critical equipment is on unprotected, unlabelled shared sockets. And a second question: why did nobody know until morning? The fridge had no alarm connected to anyone on call.

## CAPA

**CAPA** stands for **corrective and preventive action**.

- **Correction:** fixes the immediate problem (plug the fridge back in; quarantine and assess the reagents).
- **Corrective action:** removes the cause so it does not recur (locking plug, labelled dedicated socket, alarm to an on-call phone).
- **Preventive action:** stops a similar problem elsewhere before it happens (survey every critical fridge, freezer and incubator in the building for the same risk).
- **Effectiveness check:** after a set time, verify the action worked (for example, no further excursions and alarm tests passing over three months).

Each action has an **owner** and a **due date**, and QA tracks it to closure.

## Common mistakes

- Writing "analyst error, retrained" as the root cause without asking why the error was possible.
- Fixing the problem but not raising a deviation.
- Leaving out the impact assessment.
- Closing a CAPA without checking it worked.
- Editing an SOP copy by hand instead of going through change control.

## Quick recap

- SOPs are controlled documents; only the current, approved, trained version is used.
- A deviation records what happened, containment, impact, root cause and CAPA.
- Use 5 Whys or a fishbone to get past "human error".
- CAPA = correction, corrective action, preventive action, and an effectiveness check.

## Try it

Open the **Do** tab to write a deviation report and a CAPA plan for a realistic scenario, on paper.


Follow controlled SOPs, write a clear deviation report and plan corrective and preventive actions.

SOPs, deviations, CAPA

Deviation Investigation in the Pharmaceutical Industry

Corrective & Preventive Action (CAPA) Explained | Closing the Loop in Total Quality Management

## Why it matters

Clients, patients and regulators cannot check every result a lab produces. Instead they rely on **audits** and **accreditation**: independent checks that the lab's system produces reliable results. A lab that loses accreditation can lose its contracts or its legal right to report patient results. As a technician you will be interviewed by auditors, asked to show records, and expected to explain what you do and why. Knowing the main frameworks helps you understand why your lab's rules exist.

## Audits and inspections

- **Internal audits:** the lab's own quality staff (or trained colleagues) check compliance with its procedures, usually on a schedule.
- **External audits:** by an accreditation body, a client (a **supplier audit**) or a certification body.
- **Regulatory inspections:** by a government agency, such as the US FDA for drug manufacturing.

Auditors review documents and records, watch work being done, and interview staff. A common technique is **tracing**: pick one reported result and follow it back to the sample receipt, the analyst's training record, the instrument's calibration, the reagent lots, the raw data and the review signatures. Gaps become **findings** (also called **nonconformities**), often graded as major or minor. The lab responds with a CAPA plan.

## The main frameworks

| Framework | Applies to | What it is |
|---|---|---|
| **ISO/IEC 17025** | Testing and calibration labs (environmental, food, materials, forensic, calibration) | International standard for competence, impartiality and consistent operation |
| **ISO 15189** | Medical laboratories | International standard for quality and competence in medical labs |
| **CLIA** | US clinical labs testing human specimens | Federal regulations (42 CFR Part 493), administered by CMS |
| **CAP accreditation** | Clinical labs (US and international) | Peer-inspection programme using detailed checklists |
| **GMP (cGMP)** | Manufacturing of drugs, biologics and devices, including QC labs | Regulations such as 21 CFR Parts 210 and 211 (drugs), enforced by FDA |
| **GLP** | Non-clinical safety studies supporting regulatory submissions | Regulations such as 21 CFR Part 58 |

### ISO/IEC 17025

ISO/IEC 17025 sets requirements for impartiality and confidentiality, staff competence, equipment and **metrological traceability**, method validation, **measurement uncertainty**, handling of samples, quality control, reporting and a management system. Accreditation is granted by national accreditation bodies (for example, A2LA and ANAB in the US), which recognise each other's results through the **ILAC** arrangement (https://www.ilac.org/). See ISO's overview: https://www.iso.org/ISO-IEC-17025-testing-and-calibration-laboratories.html (Checked on 2026-10-23.)

### CLIA and CAP

Every US lab that tests human specimens for health assessment needs a **CLIA certificate**. CLIA sets requirements for personnel, QC, proficiency testing and quality systems based on test complexity: https://www.cms.gov/medicare/quality/clinical-laboratory-improvement-amendments (Checked on 2026-10-23.) **CAP accreditation** is a voluntary programme recognised by CMS as meeting CLIA requirements. CAP inspection teams, made up of practising lab professionals, use checklists and inspect accredited labs on a regular cycle: https://www.cap.org/laboratory-improvement/accreditation (Checked on 2026-10-23.)

### GMP and GLP

GMP covers how medicines and related products are made and tested, so that every batch meets its specifications. QC labs in a GMP plant follow strict rules on data integrity, OOS investigations, equipment qualification and batch release. FDA investigators record significant observations on a **Form 483** at the end of an inspection. FDA's CGMP page: https://www.fda.gov/drugs/pharmaceutical-quality-resources/current-good-manufacturing-practice-cgmp-regulations (Checked on 2026-10-23.) GLP is different: it covers how non-clinical safety studies are planned, performed, recorded and archived (21 CFR Part 58).

## Proficiency testing

In **proficiency testing (PT)**, an external provider sends the lab unknown samples, and the lab's results are compared with other labs or the known value. CLIA requires PT for many clinical tests, and ISO/IEC 17025 accreditation expects participation in PT or interlaboratory comparisons. PT samples must be tested like patient or routine samples, by the staff who normally do the test. Sending PT samples to another lab, or sharing results before the deadline, is a serious violation.

## How to behave in an audit

- Answer the question asked, honestly and factually. "I don't know, but I can find out" or "That is in SOP-QC-017; I'll show you" is fine.
- Show records rather than describing them from memory.
- Never change, backdate or "tidy" records before or during an audit.
- If you notice a problem, say so: a self-identified issue with a CAPA is far better than one an auditor finds.

## Common mistakes

- Thinking audits are only the quality department's business.
- Preparing for audits instead of working to the standard every day.
- Treating PT samples specially.
- Confusing GMP (product manufacturing and testing) with GLP (non-clinical safety studies).

## Quick recap

- Audits are internal, external or regulatory; tracing a result end to end is a core technique.
- ISO/IEC 17025 for testing and calibration labs, ISO 15189 for medical labs.
- In the US, CLIA is the law for clinical labs; CAP accreditation is a recognised way to meet it.
- GMP governs manufacturing and QC; GLP governs non-clinical safety studies.
- Proficiency testing compares your lab with others; treat PT samples like routine work.

## Try it

This lesson is quiz-only. Open the **Do** tab to check your understanding.


Explain ISO/IEC 17025, ISO 15189, CLIA, CAP and GMP audits, and how proficiency testing works.

Audits and accreditation

Discover ISO/IEC 17025 | Standard for Testing and calibration laboratories

CAP Accreditation: 10 Steps on the Path to Laboratory Excellence

## Why it matters

Sooner or later a result looks wrong: one replicate far from the others, a patient value that does not fit their history, a batch result just outside specification. The temptation is to repeat the test, get a "better" number and report that. In regulated and clinical labs this is called **testing into compliance**, and it is one of the most serious data integrity failures there is. Labs need a disciplined way to decide when a result may be rejected, when a repeat is justified, and which result gets reported.

## Rule one: investigate before you reject

A result may be invalidated only for a **documented, assignable cause**: something you can show went wrong. Examples:

- A recorded instrument error or failed system suitability.
- A documented pipetting or dilution mistake noticed at the time.
- A sample problem: clotted, haemolysed, wrong container, short volume.
- A transcription error, proven by the raw data.

"It looks too high" is not an assignable cause. Without one, the original result stands and goes into the investigation.

## Statistical outlier tests

Statistics can tell you that a value is **unusual** compared with the others. It cannot tell you **why**. The **Grubbs test** checks whether the most extreme value in a small, normally distributed data set is an outlier:

```text
G = max |x - mean| / s
```

Compare G with a critical value for your n and confidence level. Commonly quoted two-sided 95 percent critical values:

| n | 3 | 4 | 5 | 6 | 7 | 8 | 10 |
|---|---|---|---|---|---|---|---|
| G critical | 1.155 | 1.481 | 1.715 | 1.887 | 2.020 | 2.126 | 2.290 |

**Worked example.** Six replicate results: 10.1, 10.3, 10.2, 10.0, 10.2, 11.0.

- Mean = 10.30, sample standard deviation s = 0.358.
- The most extreme value is 11.0: |11.0 - 10.30| = 0.70.
- G = 0.70 / 0.358 = 1.96, which is above 1.887.

So 11.0 is a statistical outlier at 95 percent. That is a reason to **investigate**, not by itself a reason to delete it. Limits on outlier tests:

- They assume normal data and usually test one outlier at a time.
- Small n gives them little power.
- FDA's OOS guidance says outlier tests are rarely appropriate for validated chemical assays and cannot by themselves invalidate a result in a GMP OOS investigation (they can have a role in highly variable biological assays). Follow your SOP.

## Repeat testing done right

- **Retest:** re-analyse the same sample (or preparation). **Resample:** take a new sample from the batch. Resampling needs stronger justification in GMP, because it can hide a real batch problem.
- The number of retests, and how results are combined or reported, must be **defined in the SOP before testing**, not decided after you see the numbers.
- Keep **all** results, including the original, in the record.

## Replicate acceptance

Many methods run samples in duplicate or triplicate and set an acceptance limit on agreement, for example "the range of replicates must not exceed 0.5 units" or "the CV must be 5 percent or less". If replicates fail, the SOP says what happens: usually the sample is repeated, and the failure is recorded. This is a predefined rule, so it is not testing into compliance.

## Clinical checks

Clinical labs use extra checks that trigger review or repeats:

- **Delta check:** compares a patient's result with their previous result. A large change may mean a sample mix-up.
- **Critical values:** results that suggest immediate danger are verified and phoned to a clinician.
- **Above the measuring range:** the sample is diluted and rerun, and the dilution factor applied.
- **Interferences:** haemolysis, lipaemia or icterus indices may flag results as unreliable.

## Common mistakes

- Repeating a test until the result passes and reporting only the passing one.
- Deleting a result because a Grubbs test flagged it, with no assignable cause.
- Deciding how many retests to do after seeing the first result.
- Averaging an OOS result with passing retests to "average into compliance".
- Not recording the original result.

## Quick recap

- Reject a result only for a documented, assignable cause.
- Outlier tests (Grubbs: G = max |x - mean| / s) flag unusual values; they do not explain them.
- Retest rules, replicate limits and reporting rules are set in the SOP in advance; keep every result.
- Clinical labs add delta checks, critical values and dilution of over-range samples.

## Try it

Open the **Do** tab. A SQL query groups replicate results by sample; you add the `HAVING` clause that finds samples whose replicates disagree by more than the acceptance limit and need repeat testing.


Decide when a result may be rejected, use the Grubbs test correctly, and apply predefined repeat-testing rules.

Outliers and repeat testing

Chapter 4: Grubbs Test for Outliers | CHM 214 | 031

Work within SOPs, write deviations and CAPA, understand audits and accreditation, and handle outliers and repeat testing.

Lab Data & Quality

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