1

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

2021-S-0004

Standard Practices for 

Evaluating Measurement 

Uncertainty of Quantitative 

Measurements in Forensic 

Toxicology

Forensic Toxicology Subcommittee

Toxicology Scientific Area Committee

Organization of Scientific Area Committees (OSAC) for Forensic Science
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

Draft OSAC Proposed Standard

2021-S-0004

Standard Practices for Evaluating 

Measurement Uncertainty of 

Quantitative Measurements in 

Forensic Toxicology

Prepared by 

Forensic Toxicology Subcommittee

Version: 1.0

2020

Disclaimer:

This OSAC Proposed Standard was written by the Forensic Toxicology Subcommittee/ 

Toxicology Scientific Area Committee of the Organization of Scientific Area Committees 

(OSAC) for Forensic Science following a process that includes an open comment period. This 

Proposed Standard will be submitted to a standards developing organization and is subject to 

change. 

There may be references in an OSAC Proposed Standard to other publications under 

development by OSAC. The information in the Proposed Standard, and underlying concepts and 

methodologies, may be used by the forensic-science community before the completion of such 

companion publications.

Any identification of commercial equipment, instruments, or materials in the Proposed Standard 

is not a recommendation or endorsement by the U.S. Government and does not imply that the 

equipment, instruments, or materials are necessarily the best available for the purpose.

To be placed on the OSAC Registry, certain types of standards first must be reviewed by a 

Scientific and Technical Review Panel (STRP). The STRP process is vital to OSAC’s mission of

generating and recognizing scientifically sound standards for producing and interpreting forensic
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

science results. The STRP shall provide critical and knowledgeable reviews of draft standards or 

of proposed revisions of standards previously published by standards developing organizations 

(SDOs) to ensure that the published methods that practitioners employ are scientifically valid, 

and the resulting claims are trustworthy.

The STRP panel will consist of an independent and diverse panel, including subject matter 

experts, human factors scientists, quality assurance personnel, and legal experts, which will be 

tasked with evaluating the proposed standard based on a comprehensive list of science-based 

criteria.

For more information about this important process, please visit our website 

at: https://www.nist.gov/topics/organization-scientific-area-committees-forensicscience/scientific-technical-review-panels
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

Standard Practices for Evaluating Measurement Uncertainty of Quantitative 

Measurements in Forensic Toxicology
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1 Foreward 

2

3 This document was developed to provide the minimum requirements for evaluating 

4 measurement uncertainty for quantitative measurements in forensic toxicology 

5 laboratories. Measurement uncertainty is required to ensure confidence, reliability, and 

6 proper interpretation of test or calibration results. It is also one of the components used to 

7 establish measurement traceability. This standard was developed by the Toxicology 

8 Subcommittee of the Organizational Scientific Area Committee. 

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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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45 Table of Contents

46

47 Forward 5

48 1 Scope 7

49 2 Normative References 7

50 3 Terms and Definitions 8

51 4 Measurement Uncertainty 10

52 ANNEX A 22

53 ANNEX B 34

54 ANNEX C 46

55 ANNEX D 53

56 ANNEX E 60

57

58
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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59 1 Scope 

60

61 This document provides minimum requirements for evaluating measurement uncertainty 

62 for quantitative results in forensic toxicology. The document is for testing activities and 

63 calibration of breath alcohol measuring instruments and provides direction on evaluation 

64 of components, bias, calculations, and reporting. It does not address evaluating 

65 measurement uncertainty for breath alcohol testing, this topic will be covered in a different 

66 document.

67

68 2 Normative References

69

70 National Institute of Standards and Technology, SOP 29-Standard Operating Procedure for 

71 the Assignment of Uncertainty (February 2018). Available for download at 

72 https://www.nist.gov/pml/weights-and-measures/laboratory-metrology/standard73 operating-procedures

74

75 Joint Committee for Guides in Metrology (JCGM) Evaluation of Measurement Data-Guide to 

76 the Expression of Uncertainty in Measurement (GUM) (GUM 1995 with minor corrections) 

77 (Sevres, France: International Bureau of Weights and Measures [BIPM]-JCGM 100], 

78 September, 2008. Available at https://www.bipm.org/en/publications/guides/gum.html 

79

80 SLR Ellison and A Williams (Eds). Eurachem/CITAC Guide: Quantifying Uncertainty in 

81 Analytical Measurement, Third edition, (QUAM: 2012 P1) Available for download at 

82 http://www.eurachem.org/index.php/publications/guides

83

84 Joint Committee for Guides in Metrology (JCGM), International vocabulary of metrology –

85 Basic and general concepts and associated terms (VIM), 3rd ed. (Sèvres, France: 

86 International Bureau of Weights and Measures [BIPM]-JCGM 200, 2012) (2008 with minor 

87 corrections). Available for download at 

88 http://www.bipm.org/en/publications/guides/vim.html

89

90 ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in Forensic 

91 Toxicology, First Edition, 2018. Available for download at https://asb.aafs.org/wp92 content/uploads/2018/06/017_Std_e1.pdf

93

94
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95 3 Terms and Definitions

96

97 For purposes of this document, the following definitions and acronyms apply.

98

99 3.1 

100 accuracy

101 Closeness of agreement between a measured quantity value and a true quantity value of a 

102 measurement. 

103

104 3.2 

105 analytical run (batch)

106 A set of standards, controls, and/or case samples that are contemporaneously prepared 

107 and/or

108 analyzed in a particular sequence.

109

110 3.3 

111 bias, statistical

112 A systematic tendency for estimates or measurements to be above or below their true 

113 values. 

114

115 Note 1: Statistical bias arises from systematic as opposed to random error. 

116

117 Note 2: Statistical bias can occur in the absence of prejudice, partiality, or discriminatory 

118 intent.

119

120 3.4 

121 calibration

122 Operation that, under specified conditions, establishes a relationship between the quantity 

123 value and corresponding indications.

124

125 3.5 

126 calibrator

127 Measurement standard used in calibration.

128

129 3.6 

130 certified reference material

131 CRM

132 Reference material (RM) characterized by a metrologically valid procedure for one or more 

133 specified properties, accompanied by a certificate that provides the value of the specified 

134 property, its associated uncertainty, and a statement of metrological traceability.

135

136 3.7 

137 control

138 Material of known composition that is analyzed along with unknown samples(s) in order to 

139 evaluate the performance of an analytical procedure. 
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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140

141 3.8 

142 limit of detection

143 LOD

144 An estimate of the lowest concentration of an analyte in a sample that can be reliably 

145 differentiated from blank matrix and identified by the analytical method.

146

147 3.9 

148 lower limit of quantitation

149 LLOQ

150 An estimate of the lowest concentration of an analyte in a sample that can be reliably 

151 measured with acceptable bias and precision.

152

153 3.10

154 measurand

155 The quantity intended to be measured.

156

157 3.11

158 measurement traceability

159 (metrological traceability)

160 Property of a measurement result whereby the result can be related to a reference through 

161 a documented unbroken chain of calibrations, each contributing to the measurement 

162 uncertainty. 

163

164 3.12 

165 precision

166 The measure of the closeness of agreement between a series of measurements obtained by 

167 replicate measurements on the same or similar samples. 

168

169 3.13

170 repeatability

171 Measurement precision under a set of conditions that includes the same measurement 

172 procedure, same operators, same measuring system, same operating conditions, same 

173 conditions and same location, and replicate measurements on the same or similar objects 

174 over a short period of time.

175

176 3.14 

177 reproducibility

178 Measurement precision under a set of conditions that includes different locations, 

179 operators, measuring system, and replicate measurements on the same or similar objects.

180

181

182

183
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184 4 Measurement Uncertainty

185

186 4.1 Background

187

188 Quantitative values obtained from measurement processes have an expected variability. 

189 Repeated measurements will result in different values each time a measurement is made 

190 provided the measuring system has sufficient resolution to allow those differences to be 

191 seen. Each time a measurement is made, the measured value depends on numerous factors 

192 including setup and capability of the measuring system, the exact measurement method 

193 (procedure), and the person performing the measurement. 

194

195 Measurement Uncertainty (MU) is an estimate of the potential variability of a measurement 

196 based on the information known about the measurand and the measurement method. The 

197 measurement may be part of the test, a calibration method, or the final reported test or 

198 calibration result. “Measurement uncertainty does not imply doubt about the validity of a 

199 measurement; on the contrary, knowledge of the uncertainty implies increased confidence 

in the validity of the measurement result1 200 ” 

201

202 Laboratory stakeholders require tests and calibrations performed to be reliable, accurate, 

203 and comparable. MU is an important parameter describing the confidence, as well as 

204 limitations, of measurement results. Comparison of quantitative test or calibration results 

205 between laboratories or evaluation of quantitative results in relation to a legal specification 

206 or requirement necessitates knowledge of the MU. 

207

208 The National Institute for Standards and Technology (NIST) has developed an 8-step 

process for evaluating and reporting MU (Figure 1). 209 2 This framework established by NIST 

210 conforms to the principles set forth in the Joint Committee for Guides in Metrology (JCGM) 

211 Evaluation of Measurement Data-Guide to the Expression of Uncertainty in Measurement 

(GUM3 212 ) and is a helpful reference.

213

214

215

216

1 SLR Ellison and A Williams (Eds). Eurachem/CITAC Guide: Quantifying Uncertainty in Analytical 

Measurement, Third edition, (QUAM: 2012 P1) Available for download at 

http://www.eurachem.org/index.php/publications/guides

2 National Institute of Standards and Technology, SOP 29-Standard Operating Procedure for the Assignment 

of Uncertainty (April 2021). Available for download at

https://www.nist.gov/system/files/documents/2019/05/13/sop-29-assignment-of-uncertainty20190506.pdf

3 Joint Committee For Guides in Metrology (JCGM) Evaluation of Measurement Data-Guide to the Expression 

of Uncertainty in Measurement (GUM) (GUM 1995 with minor corrections) (Sevres, France: International 

Bureau of Weights and Measures [BIPM]-JCGM 100], September, 2008. Available at 

http://bipm.org/en/publications/guides/gum.html
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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217 Figure 1: The NIST 8-Step Process for Evaluating and Reporting Measurement Uncertainty4

218

219

220

221 4.2 Requirements for Measurement Uncertainty for Quantitative Determinations 

222

223 4.2.1 General Requirements

224

225 4.2.1.1 Laboratories shall have and apply procedures for evaluating MU for methods used 

226 to calibrate breath alcohol instruments and for test methods that produce a quantitative 

227 test result. 

228

229 4.2.1.2 MU is specific to each measurement process and shall be evaluated separately for 

230 each analyte in each testing or calibration method. 

231

232 In testing, this requires that each combination of analyte, extraction and analytical 

233 technique be evaluated separately. Multiple matrices may have to be evaluated separately 

234 based on results of method validation.

235

236 4.2.1.3 Using the largest evaluated MU for more than one analyte within a method or one 

237 analyte across methods is not acceptable. 

238

239 4.2.1.4 Test and Calibration Methods for which the MU is evaluated shall meet the 

240 minimum requirements set forth in:

241

4 Adapted from ASCLD/LAB Guidance on the Estimation of Measurement Uncertainty-Annex D

 Note: Document can be obtained from anab@anab.org

Step Specify the measurement process

Step Identify uncertainty components

Step Quantify uncertainty components

Step Convert quantities to standard uncertainties

Step Calculate combined standard uncertainty

Step Expand the combined standard uncertainty by coverage factor (k)

Step Evaluate the expanded uncertainty

Step Report the uncertainty
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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242 a. ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in Forensic 

243 Toxicology. 

244 b. ANSI/ASB Standard 036, Standard Practices for Method Validation in Forensic 

245 Toxicology

246

247 4.2.2 Step 1: Specify the Measurement Process

248

249 The measurandshall be defined and documented. This can be in the form of a written 

250 statement, a visual diagram, and/or a mathematical expression. 

251

252 NOTE: To be clear about the measurement process for which the MU evaluation is for, it is 

253 important to be as specific as possible when defining the measurand. To distinguish one 

254 measurement process from another within a laboratory, it may be necessary to include a 

255 reference to a specific type of equipment used or a specific procedure in the statement 

256 defining the measurand.

257

258 EXAMPLES: 

259 

260 Testing of biological samples

261 Concentration of ethanol (g/100mL) in ante-mortem whole blood

262 Concentration of oxycodone (mg/kg) in a sample of liver homogenate

263

264 Calibration of breath alcohol measuring instruments

265 Calibration of XYZ model breath alcohol measuring instrument using dry gas certified 

266 reference material

267

268 4.2.3 Step 2: Identify Uncertainty Components

269

270 Minimum method components that shall be considered, as applicable, in an evaluation

271 of MU include:

272

273 a. Certified reference material(s) and calibrations of equipment used to establish 

274 measurement traceability;

275

276 b. Data from the measurement process (i.e. repeatability, reproducibility or from 

277 intermediate measurement conditions)

278

279 c. Human factors (e.g., multiple analysts performing the same measurement method, 

280 experience, training , etc.);

281

282 d. Sampling conducted during the measurement method;

283

284 e. Sample preparation; and

285

286 f. Environmental conditions during the measurement process.
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287

288

289 4.2.4 Step 3: Quantify Uncertainty Components

290

291 Uncertainty components shall be quantified. All digits shall be carried through calculations 

292 until final expanded measurement uncertainty is determined. Only then should rounding 

293 and significant figure rules be applied.

294

295 The GUM (2.3.2) refers to the method of evaluation of one or more uncertainty components 

296 as: 

297 Type A evaluation (of uncertainty): method of evaluation of uncertainty by the 

298 statistical analysis of series of observations (e.g., relative standard deviation of a 

299 historical data set of quality control results)

300

301 Type B evaluation (of uncertainty): method of evaluation of uncertainty by means 

302 other than the statistical analysis of series of observations (e.g., obtaining the 

303 uncertainty associated with a CRM from its certificate of analysis)

304

305 The method of evaluation, Type A or Type B, will be determined for each component 

306 identified. It is most common to have a mixture of the two methods where some identified 

307 uncertainty components are quantified using a Type A method of evaluation and some 

308 identified uncertainty components are quantified using a Type B method of evaluation.

309

310 Any double-counting of a component will result in an overestimation of the measurement 

311 uncertainty and should be avoided, when possible. However, overestimation is generally 

312 more desirable than underestimation.

313

314 A record shall be maintained for Type A and Type B evaluations.

315

316 4.2.4.1 Minimum requirement(s) for data used in Type A evaluations:

317

318 4.2.4.1.1 Shall come from method validation and/or ongoing quality control 

319 (measurement assurance program) for the measurement method.

320

321 a. Method validation may include the evaluation of one or more specific uncertainty 

322 components.

323

324 b. Data from proficiency tests may only be used if the proficiency test has established 

325 metrological traceability for the quantitative value of the proficiency test. A consensus 

326 value does not establish metrological traceability.

327

328 4.2.4.1.2 Shall be representative of the measurand that will be tested or calibrated.

329 

330 4.2.4.1.3 Shall be representative of the range (e.g., matrix, or detector response over the 

331 expected concentration range, etc.) of the measurements made.
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332

333 4.2.4.1.4 Shall be evaluated according to the size and distribution of the statistical sample.

334

335 4.2.4.2 Establishing a quantity value for Type A evaluations

336

337 To appropriately evaluate the magnitude of uncertainty for the measurement process using 

338 Type A evaluation, calculate a standard deviation or a relative standard deviation using 

339 historical data for each identified Type A uncertainty component. Typically, method 

340 performance is best represented by measurements of quality control (QC) samples taken 

341 over multiple instrumental batches, each with different instrument calibrations (cf. 

342 ANSI/ASB Standard 036, 2019). A graphical representation of all QC measurements used 

343 for the Type A uncertainty component that demonstrates statistical control of the 

344 measurements used shall be maintained. Additional methods may also be used to ensure 

345 statistical control.

346

347 If multiple QC measurements are available in each instrumental batch, all QC 

348 measurements can be included when computing the standard deviation or relative 

349 standard deviation. Inclusion of multiple QC measurements in the computation of the 

350 standard deviation will bias the standard uncertainty estimate slightly if the QC data 

351 exhibits any batch-to-batch variation but mitigates the need for more complex standard 

352 deviation computations. If needed, other statistical methods, such as the ANOVA method 

353 outlined in section 8.2.2.3.4 of ANSI/ASB Standard 036 or random subsampling of the QC 

354 data to select a single representative QC measurement from each batch, can be used to 

355 correct for this bias.

356

357 If the result to be reported for a specimen will be either an individual measured value or 

358 the average of multiple measured values from a single instrumental batch, the standard 

359 deviation or the relative standard deviation shall be used as the Type A standard 

360 uncertainty for the reported specimen value. Setting aside the slight bias produced if the 

361 standard deviation is computed from data containing multiple QC measurements in each 

362 batch, this standard uncertainty should provide an assessment of the Type A uncertainty 

363 that is either on target or conservative (i.e., larger than necessary) for the reported 

364 specimen value. 

365

366 If the the result to be reported for a specimen will be the average of measured values from 

367 multiple instrumental batches, the standard deviation or the relative standard deviation 

368 divided by the square root of the number of instrumental batches used when averaging the

369 specimen data shall be used as the Type A standard uncertainty for the reported specimen 

370 values. Division by the square root of the number of batches converts the standard 

371 deviation for single-batch results into the standard deviation of the mean of multiple-batch 

372 results. As above, setting aside the slight bias produced if the standard deviation is 

373 computed from data containing multiple QC measurements in each batch, this standard 

374 uncertainty should provide an assessment of the Type A uncertainty that is either on target 

375 or conservative for the reported specimen value.

376
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377

378 4.2.4.2.1 Testing Laboratories

379

380 4.2.4.2.1.1 Use of Validation Data

381

382 Validation data may initially be used for the Type A uncertainty component. Continued use 

383 of validation data for this uncertainty component requires that laboratories demonstrate 

384 the data is representative of the data generated during day-to-day analysis by analysts who 

385 have demonstrated competence.

386

387 4.2.4.2.1.2 Multiple controls within the same method

388

389 For methods where validation has demonstrated constant variance across the entire 

390 calibration range (homoscedasticity) as shown through the use of residual plots for the 

391 calibration curve or other statistical means, laboratories shall use either:

392

393 a. Combined data from all controls analyzed; or

394

395 b. Select data from one specified control (e.g., a control at or near a legal specification).

396

397 For methods where validation has demonstrated that variance is not constant across the 

398 entire calibration range (heteroscedasticity), laboratories shall establish a procedure for 

399 how MU will be calculated. Procedures may include:

400

401 a. Utilize the Type A data from the control producing the largest variance; or

402

403 b. Perform an in-depth evaluation to determine where the variation changes occur across 

404 the calibration range and establish an appropriate uncertainty to report based on 

405 where these variation changes occur; or

406

407 c. Utilize the Type A data from the control at the concentration closest to the sample 

408 concentration. This is acceptable only when an evaluation of the difference in the 

409 standard deviation between the two applicable control levels does not impact the 

410 evaluation of conformance with a legal specification.

411

412 4.2.4.2.1.3 Multiple Analysts/Instruments/Laboratories

413

414 For a method that has been validated on multiple instruments or in multiple laboratories 

415 by analysts who have demonstrated competence, provided that quality control criteria for 

416 acceptance and reporting criteria are the same across all instruments and laboratories, 

417 calculate MU using control data in accordance with Section 4.2.4.2.1.4..

418

419

420

421
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422 4.2.4.2.1.4 Quality Control Data

423

424 Appropriate methods for calculating MU using quality control data include, but are not 

425 limited to:

426

427 a. Calculation of MU using control data generated since validation or first day-to-day use 

428 of the method;

429

430 b. Calculation of a rolling MU where the laboratory chooses to include a set number of 

431 data points from the most recent analyses. The data shall be representative of the 

432 performance of the method; or

433

434 c. Calculation of a batch-specific MU based on use of data from only the current analytical 

435 batch. This method is more commonly used for non-routine analysis where limited data 

436 points are available.

437

438 4.2.4.2.2 Calibration of Breath Alcohol Measuring Instruments

439

440 4.2.4.2.2.1 Use of Validation Data

441

442 Validation data may initially be used for the Type A uncertainty component. Continued use 

443 of validation data for this uncertainty component requires that laboratories demonstrate 

444 that the data is representative of the data generated during day-to-day calibration of breath 

445 alcohol measuring instruments by personnel who have demonstrated competence.

446

447 4.2.4.2.2.2 Multiple measurement standards within the same method

448

449 For methods that have demonstrated constant variance across the entire calibration range 

450 as shown through the use of residual plots for the calibration curve or other statistical 

451 means, laboratories may either:

452

453 a. Combine data from all measurement standards analyzed to estimate a single MU; or

454

455 b. Calculate the measurement uncertainty at each measurement standard concentration.

456

457 For methods where validation has demonstrated that variance is not constant across the 

458 entire calibration range, laboratories may either:

459

460 a. Perform an in-depth evaluation to determine where the variance changes occur across 

461 the calibration range and establish an appropriate uncertainty to report based on 

462 where these variance changes occur; or

463

464 b. Calculate the MU at each measurement standard concentration across a population of 

465 instruments or for an individual breath alcohol measuring instrument.

466
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467 4.2.4.2.2.3 Use of Measurement Standard Data or Quality Control Data

468

469 Appropriate methods of selecting measurement standard data or quality control data 

470 include, but are not limited to, the following across a population of instruments or for an 

471 individual instrument:

472

473 a. Calculation of MU using measurement standard data generated since validation or first 

474 day-to-day use of the instrument; or

475

476 b. Calculation of a rolling MU where the laboratory chooses to include a set number of

477 data points. The data shall be representative of the performance of the instrument. 

478

479 4.2.4.3 Minimum requirements for Type B evaluations:

480

481 Components requiring a Type B evaluation may include: uncertainty associated with a 

482 certified reference material, uncertainty of a reference material, and/or uncertainty from 

483 equipment calibration (e.g., balance, volumetric flask, pipette, barometer, or thermometer).

484

485 4.2.4.3.1 Shall consider all components that are not accounted for in a Type A evaluation.

486

487 4.2.4.3.2 Shall account for all identified and significant systematic bias (see 4.2.6.1).

488

489 4.2.4.3.3 Shall be handled according to the assumed distribution of the quantity value.

490

491 4.2.4.4 Establishing a quantity value for Type B evaluations

492

493 4.2.4.4.1 For component(s) used in the preparation of a calibrator, the components can be 

494 quantified individually or as a group for the calibrator.

495

496 a. If estimating uncertainty over the full calibration range, use the largest standard 

497 deviation calculated above;

498

499 b. If estimating the uncertainty for multiple concentration ranges, use the largest standard 

500 deviation calculated above for each concentration range, respectively;

501

502 c. If estimating the uncertainty at each calibrator or measurement standard concentration 

503 separately, use the value for the applicable calibrator.

504

505 If the test or calibration method includes the preparation of multiple calibrators or 

506 measurement standards, the individual components can be quantified individually across 

507 all calibrator concentrations (e.g. a single component quantity value can be used for the 

508 pipette uncertainty that adequately covers the pipettes used to prepare all calibrator 

509 concentrations) and then a or b below can be applied. Alternatively, the components can be 

510 quantified as a group for each calibrator concentration and then a - c applied.

511
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512 Depending on the measurement process, these components related to calibrator 

513 preparation, typically requiring a Type B evaluation, may be accounted for by on-going 

514 quality control data (Type A).

515

516 4.2.5 Step 4: Convert Quantities to Standard Uncertainties

517 Quantify all uncertainty components as a standard uncertainty of the quantity values and in 

518 the same measurement unit or in a measurement unit relative to the quantity values. 

519

520 4.2.5.1 Type A evaluations

521

522 Typically, an assessment of Type A uncertainty is calculated to be a standard uncertainty. If 

523 not already presented as a standard uncertainty, divide by the appropriate factor (e.g., 2 or 

524 3) to convert to a standard uncertainty.

525

526 4.2.5.2 Type B evaluations

527

528 If not reported by the manufacturer as a standard uncertainty, the appropriate probability 

529 density function for the component needs to be used to compute one standard deviation or 

530 relative standard deviation associated with the specified distribution.

531

532 If reported by the manufacturer as an expanded uncertainty, divide by the appropriate 

533 coverage factor (e.g., 2 or 3), to arrive at a standard uncertainty.

534

535 4.2.6 Step 5: Calculate the combined standard uncertainty

536

537 Calculate the combined standard uncertainty using each uncertainty contributor quantity 

538 value. Acceptable methods to do so include the root sum of the squares formula and the 

539 Monte Carlo5 method.

540

541 After the combined standard uncertainty is calculated, components may be individually 

542 evaluated for significance. A component is deemed significant if it impacts the least 

significant digit in the reported value for MU. 543 6 Components determined to be insignificant 

544 may be removed from the uncertainty calculations.

545

546 Note: If multiple individual components are removed from the uncertainty combination, 

547 then the aggregate impact of the removed components should be evaluated.

5 Joint Committee For Guides in Metrology (JCGM) Evaluation of Measurement Data-Guide to the Expression 

of Uncertainty in Measurement (GUM)-Supplement 1-Propagation of distributions using a Monte Carlo 

Method (Sevres, France: International Bureau of Weights and Measures [BIPM]-JCGM 101:2008], September, 

2008. Available at https://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf

6 National Institute of Standards and Technology, SOP 29-Standard Operating Procedure for the Assignment 

of Uncertainty (February 2018). Available for download at https://www.nist.gov/pml/weights-andmeasures/laboratory-metrology/standard-operating-procedures
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548

4.2.6.1 Evaluation of bias 549 7

550

551 Measurement accuracy encompasses both precision and bias. A measurement is more 

552 accurate when it has less bias and greater precision. The GUM states “it is assumed that the 

553 result of a measurement has been corrected for all recognized significant systematic effects 

554 and that every effort has been made to identify such effects.”

555

556 An evaluation of bias may not always be possible. An evaluation of bias requires one or 

557 more controls prepared with metrological traceability, having a known reference value and 

558 uncertainty.

559

560 4.2.6.1.1 The general approach to bias evaluation shall:

561

562 a. Determine if bias is present by comparing measurement standard or control data to

563 reference values with established metrological traceability.

564

565 b. Estimate the combined uncertainty without considering the relevant bias.

566

567 c. Compare the bias with the combined standard uncertainty.

568

i. Where the bias is less than the combined standard uncertainty, bbbbbbbb < uucc 569 , the bias is 

570 viewed as not significant and may be neglected or included as a component in the 

571 estimation of uncertainty.

572

ii. Where the bias is greater than the combined standard uncertainty, bbbbbbbb > uucc 573 , it is 

574 viewed as significant and additional action is required, see 4.2.6.1.1.1 and 4.2.6.1.1.2. 

575

576 4.2.6.1.1.1 Testing

577

578 a. Eliminate or reduce the bias until it is not significant; or

579

580 b. Correct the measurement result for the bias, including the uncertainty of the correction 

581 in the evaluation of uncertainty. Both the observed measurement result and the 

582 corrected measurement result with the estimation of MU shall be reported; or

583

584 c. Report the measurement result and the expanded MU with bias included. The method 

585 used to include the bias in the expanded uncertainty shall be a statistically valid 

method7 586 and in compliance with the GUM; or

587

588 d. Report the observed measurement result, the MU, and the bias. 

589

590

7 Section 3.2.5 of NIST SOP 29 (2019)
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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591 4.2.6.1.1.2 Calibration of Breath Alcohol Instruments

592

593 Eliminate or reduce bias until it is not significant by repeating the adjustment process 

594 and/or performing the appropriate repair.

595

596 4.2.7 Step 6: Calculate the expanded uncertainty

597

598 4.2.7.1 A coverage factor (k) shall be determined using a Student’s t-distribution8 based 

599 on the degrees of freedom to provide the desired level of confidence.

600

601 4.2.7.2 The minimum coverage probability for all quantitative test results and calibration 

602 results shall be 95.45 % (often referred to as approximately 95 %).

603

604 4.2.8 Step 7: Evaluate the expanded uncertainty 

605

606 4.2.8.1 A determination whether the evaluated measurement uncertainty is acceptable 

607 shall be made by the laboratory. The laboratory is responsible for supporting their 

608 decision. As applicable, minimum aspects to consider include:

609

610 a. Stakeholder interests;

611

612 b. Legal requirements;

613

614 c. The relationship between the reported test or calibration quantitative value and the 

615 expanded MU; particular consideration shall be taken around the LLOQ/LOD (e.g., an 

616 expanded MU of 0.01 ng/mL for a method with an LLOQ of 0.01 ng/mL should prompt 

617 the laboratory to reevaluate the LLOQ.); and

618

619 d. The relationship between the quality control limits for the method and the expanded 

620 measurement uncertainty (e.g., ± 20 % quality control limits for a method with 

621 expanded MU of 10 %. For any single analytical batch, this QC limit would allow a 

622 variation of up to 20% which exceeds the stated expanded MU for the method. This 

623 should prompt the laboratory to reevaluate the quality control limits to ensure the MU 

624 statement will always be correct). 

625

626 4.2.9 Step 8: Report the expanded uncertainty

627

628 4.2.9.1 The estimated MU shall be included in the test/calibration report or an attachment 

629 to the report for all quantitative test results in accordance with the ANSI/ASB Standard 053 

630 Standard for Reporting in Forensic Toxicology and for all calibrations.

631

632 a. The MU shall be reported as an expanded uncertainty and include the coverage 

633 probability for testing laboratories 

8 Table G2 of the GUM, another reference table, or appropriate statistical software
21

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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634

635 b. The MU shall be reported as an expanded uncertainty and include the coverage factor, 

636 k, and the coverage probability for calibration laboratories. 

637

638 c. The measurement result shall include the measured quantity value, y, along with the 

639 associated expanded uncertainty, U, and the measurement result should be reported as 

640 y ± U where U is consistent with the units of y. Specific applications may warrant use of 

641 a different format than y ± U.

642

643 d. The expanded uncertainty should be reported to at most 2 significant figures unless the 

644 laboratory has a documented rationale to report beyond 2 significant figures.

645

646 e. Rules for rounding the expanded uncertainty shall be defined by the laboratory.

647

648 f. The measurement result shall be reported using the same number of decimal places as 

649 the rounded expanded uncertainty unless a legal specification specifies how the 

650 measurement result is to be reported. Rules for rounding or truncating the 

651 measurement result shall be defined by the laboratory.

652

653 g. Laboratories shall not report the single largest measurement uncertainty for a group of 

654 analytes within a method or the largest measurement uncertainty for a single analyte 

655 across multiple methods.

656

657 h. For testing laboratories, if a significant bias is identified and the action taken is 

658 4.2.6.1.1.1 b or c, this shall be clearly communicated.

659

660 4.3 Periodic evaluation of measurement uncertainty

661

662 The interval for review and recalculation of a method’s MU shall be set by the laboratory.

663 The interval and re-evaluation of measurement uncertainty will depend on, but not be 

664 limited to, the following factors:

665

666 a. Both Type A and Type B uncertainty components included in the calculation;

667

668 b. The frequency with which one of the components change;

669

670 c. The frequency with which the testing or calibration method is performed;

671

672 d. The magnitude of a change in a component in relationship to the calculated MU;

673

674 e. A change in the measurement process; and

675

676 f. Any laboratory administrative decision such as a set time interval.

677
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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678 Any recalculation of the measurement uncertainty shall meet all requirements of this 

679 standard.
23

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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680 ANNEX A

681 (Informative)

682

683 Concentration of ethanol in an ante-mortem blood specimen9

684

685 Test Method Information

686

687 Multiple analysts were trained and qualified to use the laboratory’s method to determine 

688 the concentration of ethanol in ante-mortem blood specimens. All analysts use the same 

689 equipment for this test method. This includes a pipette diluter that delivers the specified 

690 sample volume together with a specified volume of aqueous internal standard. 

691

692 The test method relies on gas chromatography with a flame ionization detector. Samples 

693 are introduced to the gas chromatograph via a headspace autosampler. 

694

695 Calibrators are used to generate a calibration curve with each analytical batch. The 

696 calibrators are certified reference materials (CRMs) and span the reportable concentration 

697 range (e.g. 0.020 g/dL to 0.400 g/dL). The CRMs are not altered prior to use (i.e., not 

698 diluted). Constant variance (homoscedasticity) was observed across the concentration 

699 range. Method validation indicated that the proper calibration model was unweighted 

700 linear regression.

701

702 Measurement assurance is achieved through the use of Quality Control (QC) samples. These 

703 include a quantitative blood matrix control prepared by the laboratory at approximately 

704 0.080 g/dL and unaltered CRMs at low, medium, and high concentrations (obtained from a 

705 different supplier than the CRMs used as calibrators). As with the CRMs used as calibrators, 

706 those used as QC samples are not altered prior to use.

707

708 Test specimens are analyzed in two separate batches. The average of the two measurement 

709 results is reported; however, the procedure requires that the individual measurements be 

710 no more than 5 % from the average or the analyses are repeated.

711

712 Calibrators, QC samples, and test samples are aliquoted in one instance using the same 

713 equipment.

714

715 Measurement Traceability

716

717 The traceability for this measurement process is established through the calibrators used 

718 to generate the calibration curve on the measuring system, as well as through the 

719 calibration of other equipment used in the measurement process. 

720

9 An evaluation of measurement uncertainty is specific to the measurement traceability that has been 

established for the measurement, the measurement assurance processes that are in place, the laboratory test 

method, the laboratory facility, etc. Therefore, the example that follows shall be evaluated and revised by 

each laboratory to take into consideration the elements that are specific to that laboratory.
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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721 All CRMs have been purchased from a Reference Material Producer that meets the 

722 ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in Forensic 

723 Toxicology.

724

725 All external calibrations of measuring equipment are performed by calibration laboratories 

726 that meet the ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in 

727 Forensic Toxicology. The pipette diluter has been and is routinely calibrated. 

728

729 Measurement Assurance 

730

731 The quantitative blood matrix control is prepared by the laboratory to a concentration of 

732 approximately 0.080 g/dL. It is made in a large batch, packaged, and stored in a manner to 

733 provide a long shelf-life for the control. The expected concentration is determined in-house 

734 through repeat measurements. Pre-defined criteria for acceptable performance are based 

735 on historical data across multiple lots from the last 2 years. To date, the laboratory has 

736 greater than 100 measurements made using this control since the method was validated.

737

738 The CRMs used for QC samples at low, medium, and high concentrations were purchased 

739 from a different supplier than the CRMs used as calibrators. 

740

741 The QC samples are used to ensure validity of the test method across the concentration 

742 range. The CRM QC samples are also used to verify the calibration curve and to evaluate the 

743 method’s bias on an ongoing basis.

744

745 Step 1 Specify the measurement process

746

747 As a written statement:

748

749 “The Concentration of Ethanol in Ante-Mortem Blood using [the validated laboratory 

750 procedure]”

751

752 Step 2 Identify uncertainty components

753

754 The following list of possible contributors to the uncertainty in this method were identified 

755 by the laboratory:

756

757 Analyst

758 ● Inter-analyst variation in sample preparation and measurements

759 ● Training

760 ● Experience

761

762 Calibrators

763 ● CRM –uncertainty in the stated reference value

764 ● Matrices of calibrators and test specimens

765
25

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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766 Quality Control Samples

767 ● CRM – second source; uncertainty in the stated reference value

768 ● Matrix control – stability

769

770 Internal Standard Preparation

771 ● Components:

772 ● NaCl – reagent grade

773 ● n-propanol – reagent grade

774 ● Concentration – equipment used to prepare (balance, volumetric flask)

775

776 Preparation of aliquots of Calibrators, Quality Control Samples and Measurand

777 ● Homogenization

778 ● Test Specimens – mixing 

779 ● Matrix control – mixing

780

781 ● Temperature

782 ● All calibrators, quality control samples and the test specimens are brought to room 

783 temperature

784 ● Variation in the time allowed to reach room temperature

785 ● Variation in room temperature at different times of year

786

787 ● Pipette diluter

788 ● Volume of sample and volume of internal standard

789 ● Calibration uncertainty or laboratory specification to verify calibration status 

790

791 ● Headspace vials

792 ● Crimping action

793 ● Material of vial and stopper

794

795 ● Time between replicate sampling of test specimens

796

797 Analysis

798 ● Instrument parameter settings (e.g., oven temperature(s), gas flow, split ratio, aging of 

799 chromatographic column, autosampler syringe, autosampler precision, headspace 

800 equilibration time, headspace equilibration temperature, etc.)

801 ● Interference from the matrix

802 ● Interference from reagents

803 ● Interference from other compounds

804 ● Stability of sample(s) from preparation through analysis

805 ● Instrument precision

806 ● Systematic instrumental variation within an analytical batch

807

808 Data Processing

809 ● Calibration model

810 ● Integration parameters 
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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811 ● Processing algorithms

812

813 NOTE: This list of uncertainty components to be considered could also be compiled into a 

814 fishbone diagram or into any other format of the laboratory’s choosing. 

815

816 NOTE: A laboratory may identify different uncertainty components when an evaluation of 

817 their specific measurement process is performed.

818

819 Step 3 Quantify uncertainty components

820

821 The laboratory has existing data from the measurement process: 

822

823 ● The calibration model was determined during method validation and was shown 

824 through the use of residual plots to have constant variance across the linear range. 

825 Therefore, the laboratory is going to evaluate a single measurement uncertainty to 

826 represent the entire reportable concentration range.

827

828 ● Each analytical batch does include one or more independently-prepared samples of the 

829 blood matrix quality control sample. This blood matrix QC sample is prepared to have 

830 an ethanol concentration of approximately 0.080 g/dL. All analysts have made 

831 measurements using this blood matrix QC sample (across multiple lots). To date, the 

832 laboratory has greater than 100 measurements of the blood matrix QC sample since 

833 validation. 

834

835 ● The laboratory also has data from three certified reference materials that were used as 

836 quality control samples. The ethanol concentration of the CRM QC samples spans the 

837 reportable concentration range. The primary use of the CRM QC samples is to evaluate 

838 bias in the measurement method, but these samples also provide additional evaluation 

839 of a number of uncertainty components.

840

841 Table 1 shows the individual uncertainty components and how they will be evaluated:

842

843 Table 1: Method of Evaluation of Uncertainty Components (Example 1)

Uncertainty Component Method of Evaluation

Analysts

Inter-analyst variation

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Training

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Experience

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Calibrators
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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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CRM – uncertainty in the stated 

reference value Type B Evaluation

Matrices of calibrators and test 

specimens

Initially evaluated during method validation and 

determined to be insignificant, therefore not 

included in the uncertainty evaluation.

Quality Control Samples

CRM – second source; uncertainty 

in the stated reference value

Primary use is to evaluate bias.

The evaluation of bias will be done after the 

calculation of combined standard uncertainty.

Matrix control - stability

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Internal Standard Preparation

Components:

 NaCl – reagent grade

 n-propanol – reagent grade

The measurement result will only be impacted by 

the volume of the internal standard added to each 

sample (i.e. variation due to pipette diluter).

Concentration- equipment used to 

prepare (balance, volumetric 

flask)

Procedural requirement to use the same lot of 

Internal Standard for all samples in an analytical 

batch.

The measurement result will only be impacted by 

variation in the volume of the internal standard 

added to each sample (i.e. variation due to pipette 

diluter).

Preparation of aliquots of Calibrators, Quality Control Samples and Test 

Specimens

Homogenization – mixing 

Initially evaluated during method validation and 

determined to be significant, therefore

controlled through the procedure administrative 

requirement for agreement of replicates (Type B 

Evaluation ).

Temperature – all calibrators, 

quality control samples and the 

measurand are brought to room 

temperature

Variation in the time allowed to 

reach room temperature

Variation in room 

temperature at different times 

of year

Partially quantified in Type A Evaluation of 

process reproducibility data - blood matrix QC 

sample and partially through the procedure 

administrative requirement for agreement of 

replicates (Type B Evaluation).

Pipette diluter:

Volume of sample, volume of 

internal standard and dilution 

Calibration uncertainty or 

laboratory specification to verify 

calibration status

Type B Evaluation

Pipette diluter:

Variation in use by multiple 

staff

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Headspace vials:

 Crimping

 Material of stopper

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).
28

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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Time between replicate sampling 

of test item

Controlled through the procedure administrative 

requirement for agreement of replicates (Type B 

Evaluation).

Analysis

Instrument parameter settings 

(e.g. oven temperature(s), gas 

flow, split ratios, aging of 

chromatographic column, 

autosampler syringe, autosampler 

precision, headspace equilibration 

time, headspace equilibration 

temperature, etc)

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Interference from the matrix Duplicate listing of component – see Calibrators 

section above.

Interference from reagents

This component is not an uncertainty component 

but is a quality control concern. The laboratory 

analyzes a matrix blank that contains no analyte 

but does evaluate all reagents used in the 

analytical method. The laboratory procedure 

specifies acceptable criteria for this quality control 

sample.

Interference from other 

compounds

Initially evaluated during method validation and 

determined to be insignificant, therefore not 

included in the uncertainty evaluation.

Stability of sample(s) from 

preparation through analysis

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample) and through the procedure administrative 

requirement for agreement of replicates.

Instrument precision

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Systematic instrumental variation 

within an analytical batch

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample) and partially through the procedure 

administrative requirement for agreement of 

replicates (Type B Evaluation).

Data Processing

Calibration model

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample and CRMs used as QC).

Integration parameters 

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

Processing algorithms

Adequately represented by the Type A Evaluation

of process reproducibility data (Blood Matrix QC 

Sample).

844

845

846

847

848

849
 

29

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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850 Type A Evaluation of uncertainty components

851

852 Measurement Process Reproducibility - Blood Matrix quality control sample

853

854 The number of observations of the blood matrix QC sample in this example is greater than 

855 100. The statistic that will be calculated is the percent relative standard deviation.

856

857 To begin, the mean (average) and standard deviation of the blood matrix QC sample values 

will be calculated. 858 10

859

860 The mean is calculated as: 

861

xx = 1

nn�

nn

ii=1

xxii = (xx1 + xx2 + xx3 + ⋯ + xxnn)

nn

862

863

864 The mean of the reproducibility data in this example is 0.0798 g/dL.

865

866 The standard deviation is calculated as:

867

868

869

870 The standard deviation of the reproducibility data in this example is 0.0027 g/dL

871

872 Relative Standard Deviation (RSD) is calculated as:

873

RRRRRR = xx̅874

875

876 % RRRRRR = RRRRRR × 100 %

877

878 The %RSD of the reproducibility data in this example is:

879

RRRRRR = 

0.0027 gg/dddd

0.0798 gg/dddd 880 = 0.0341

881

882 % RRRRRR = 0.0341 × 100 = 3.41 %

883

884 Type B Evaluation of uncertainty components 

10 For the readability of the example, the display of digits used in all calculations was abbreviated. Best 

practice is to include and carry all digits through all calculations and only round the reported value and its 

uncertainty to the proper number of significant figures.
30

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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885

886 Interference from the matrix

887

888 The laboratory did evaluate matrix effects during method validation which resulted in the 

889 test method incorporating a dilution factor using the pipette diluter. Dilution of the sample, 

890 in combination with the procedural requirements to mix the test item minimizes matrix 

891 effects. The laboratory does acknowledge that it is impossible to evaluate all variations in 

892 test item matrix during method validation; therefore, the test method does include a blood 

893 matrix QC sample and a requirement for agreement between replicate samples to quantify 

894 the impact of matrix on the measurement.

895

896 NOTE: The laboratory procedural requirement for replicate agreement is an example of an 

897 administrative control that restricts variation in the measurement method. It is up to a 

898 laboratory to determine if such an administrative control will be used. The decision may be 

899 based on, but not limited to, knowledge of the measurement process, the impact of repeat 

900 analysis on cost and process efficiency, and the required expanded uncertainty. 

901 Measurement data may at times exceed the administrative limit, but may not be considered 

902 to be a statistical outlier, depending on its magnitude.

903

904 The laboratory procedure requires that two aliquots be taken from the homogenized test 

905 item and that the measured ethanol concentrations of the two aliquots must be within ±5 

906 % of the average or the analysis is repeated.

907

908 The two uncertainty components – process reproducibility and interference from matrix –

909 quantify a number of the same uncertainty components. The matrix control, over a longer 

910 period of time, holds the impact from the matrix constant while the effects from equipment, 

911 calibration, operators, and the laboratory environmental conditions vary. The replicate 

912 samples of the test item provide information on the test item matrix and a short–term 

913 evaluation of the effect from equipment, calibration, operators, and the laboratory 

914 environment. 

915

916 Calibrators: Uncertainty in the reference value

917

918 The laboratory reviewed the calibration certificates from all CRMs used for the calibration 

919 curve. The greatest uncertainty is 0.000233 g/dL for the 0.010 g/dL CRM.

920

RRRRRR RR RRRR uu uu uu uu = �

0.000233 gg/dddd

0.010 gg/dddd 921 � ∗ 100 = 2.33 %

922

923 Pipette Diluter

924

925 The laboratory has set internal criteria (±3 %) to ensure proper functioning of the pipette 

926 diluter. This is greater than the specifications for calibration used by the external 

927 calibration laboratory (±2 %). Additionally, the procedure to ensure proper functioning is 

928 performed quarterly compared to the external calibration which is performed annually. 
31

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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929 Therefore, the laboratory criteria of ±3 % will be used to quantify variability for this 

930 uncertainty component. 

931

932 Step 4 Convert quantities to standard uncertainties

933

934 The measurement unit

935

936 In this example, the estimated relative uncertainty is expressed as a percentage. 

937

938 Type A Evaluation of uncertainty components

939

940 Measurement Process Reproducibility data 

941

942 Test specimens are sampled in duplicate, analyzed in two separate batches and the 

943 laboratory procedure for the reported ethanol concentration is to average the two results. 

944 Repeat measurements of the test specimens provide more information and more 

945 confidence that the reported result is the best estimate of the true value. The measurement 

946 process reproducibility data is based on single measurements of 0.08 g/dL blood matrix QC 

947 sample. Therefore, the %RSD of the mean is calculated by taking the %RSD of the 

948 measurement process and dividing by the square root of the number of measurements 

949 averaged to generate the reported ethanol concentration.

950

951 NOTE: If a single measurement result for the test specimens is selected to be reported (e.g., 

952 the lowest value), then the standard deviation of the mean calculation is not applicable.

953

954 NOTE: If the laboratory makes an equal number of multiple measurements of the quality 

955 control sample as it does of the test specimens and averages the results to evaluate the 

956 acceptability of the quality control sample, then the standard deviation of the mean 

957 calculation is not applicable.

958

959 The %RSD of the reproducibility data in this example is 3.41 %

960

961 The mathematical expression for %RSD of the mean:

962

%RRRRRRmmmmmm = %RRRRRR

√nn

963

964

965 The %RSD of the mean of the reproducibility data in this example is:

966

%RRRRRRmmmmmm = 3.41 %

√2

967 = 2.4101 %

968

969

970

971
 

32

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

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972 Type B Evaluation of uncertainty components

973

974 Interference from the matrix

975

976 The laboratory procedure requires two samples to be taken from the homogenized test 

977 specimens and the ethanol concentration of the two aliquots to be within ±5 % of the 

978 average, or the analysis is repeated. This component is evaluated as a rectangular 

979 distribution:

980

981

982

983 Upper limit = +a

984 Lower limit = -a 

985 Possible range of values = (+a) – (-a) = 2a

986

987 For a rectangular distribution, the standard uncertainty is calculated by:

988

uu uu uu uu = √3

989

990

991 The standard uncertainty for the interference from the matrix in this example is based on an 

992 outside limit of 5 %:

993

uu uu uu uu = 5 %

√3

994 = 2.8868 %

995 

996 Calibrators: Uncertainty in the reference value 

997

998 Based on the certificates from the CRMs used for calibrators in this method, the laboratory 

999 determined in Step 3 that the greatest relative uncertainty for the CRMs is 2.33 %. 

1000

1001 The certificate indicates this expanded uncertainty assumes a normal distribution, a 

1002 coverage factor of k = 2, and a coverage probability of approximately 95 %. The uncertainty 

1003 on the calibration certificate will be divided by the coverage factor to arrive at a relative 

1004 standard uncertainty.

1005

RRRRRR RR RRRR uu uu uu uu = �

2.33 %

2 1006 � = 1.165 %
 

33

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1007

1008 Pipette Diluter 

1009

1010 In Step 3, the laboratory determined that its in-house criteria of ±3 % will be used to 

1011 quantify variability for this uncertainty component. This component is evaluated as a 

1012 rectangular distribution:

1013

1014

1015

1016 Upper limit = +a

1017 Lower limit = -a 

1018 Possible range of values = (+a) – (-a) = 2a

1019

1020 As explained above, for a rectangular distribution, the standard uncertainty is calculated 

1021 by:

1022

uu uu uu uu = √31023

1024

1025 The standard uncertainty for the pipette diluter in this example is based on the outside limit 

1026 of 3 %:

1027

uu uu uu uu = 3 %

√3

1028 = 1.7321 %

1029

1030 Step 5 Calculate the combined standard uncertainty 

1031

1032 The evaluation will assume that the uncertainty components are independent or 

1033 uncorrelated and that the measurement result is the sum of a series of components.

1034

1035 Care shall be taken if the measurement results lie over a range of values. In this scenario, 

1036 the calibration model was determined during method validation and was shown through 

1037 the use of residual plots to have constant variance across the linear range, so a single 

1038 estimation of measurement uncertainty can be calculated for the entire concentration 

1039 range.

1040

1041

1042
 

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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1043

1044

1045

1046

1047 % 

1048

1049 Evaluation of bias 

1050

1051 The laboratory views the monitoring of bias as a component of ensuring the validity of the 

1052 test method and has incorporated three CRMs at a low, medium and high concentration as 

1053 QC samples for the purpose of monitoring bias from unidentified sources on an ongoing 

1054 basis. 

1055

1056 The laboratory procedure requires each measured value for a CRM to be within 5 % of the 

1057 reference value. The largest bias for any of the control levels (low, medium, and high) is 

1058 less than the combined standard uncertainty. Although the bias is viewed as insignificant, 

1059 the laboratory is choosing to include an additional component in the uncertainty 

1060 evaluation that will address the uncertainty in the reference value of the CRM used for the 

1061 evaluation of bias. Steps 3, 4, and 5 must be addressed for this additional uncertainty 

1062 component. 

1063

1064 Step 3 Quantify uncertainty components – bias component

1065

1066 The laboratory reviewed all of the calibration certificates from all CRMs used for the 

1067 evaluation of bias. The greatest uncertainty is 0.0014 % for the 0.3 % CRM. 

1068

RRRRRRRR RR RRRR uu uu uu = �

0.0014 %

0.3 % 1069 � ∗ 100 = 0.4667 %

1070

1071 Step 4 Convert quantities to standard uncertainties – bias component

1072

1073 The certificate indicates this expanded uncertainty assumes a normal distribution, a 

1074 coverage factor of k = 2 and a coverage probability of approximately 95 %. The 

1075 uncertainty on the calibration certificate will be divided by the coverage factor, 2, to 

1076 arrive at a standard uncertainty.

1077

Relative standard uncertainty = �

0.4667 %

2

1078 � = 0.2334 %

1079

1080 Step 5 Calculate combined standard uncertainty – including bias component

1081

1082 The revised RSS calculation:

1083
 

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2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1084

1085

1086

1087

1088

1089

1090 % 

1091

1092 Step 6 Expand the combined standard uncertainty by coverage factor (k) 

1093

1094 The data from the measurement process is assumed to follow a normal distribution. The 

1095 laboratory has 101 measurements of the blood matrix quality control sample. Therefore, 

1096 the laboratory assumes a lower bound on the effective degrees of freedom for the 

1097 combined standard uncertainty of 100.

1098

1099 To expand the uncertainty to a 95.45 % coverage probability for this example, the coverage 

1100 factor k = 2.025, from the Student’s t-distribution table will be used.

1101

1102 UU = 2.025 × 4.3074 = 8.7225 %

1103

1104 NOTE: A laboratory can choose to increase the coverage probability. 

1105

1106 Step 7 Evaluate the expanded uncertainty 

1107

1108 The laboratory determined that the evaluation of uncertainty is fit-for-purpose based on 

1109 the following considerations:

1110

1111 ● Stakeholder interests

1112 Expanded uncertainty (8.7225 %) was below a requirement of 10 %.

1113 ● Legal requirements

1114 There were none.

1115 ● The relationship between the reported test value and the expanded MU

1116 Expanded uncertainty as a percentage across the analytical range ensures a 

1117 consistent relationship.

1118 ● Established criteria including control limits for method

1119 The laboratory’s control acceptance limits for the method are 5 % or 0.005 g/dL, 

1120 whichever is larger. Considering the expanded uncertainty, the allowable control 

1121 limits were modified to 8 % or 0.008 whichever is larger to minimize the occurrence 

1122 of excessive QC failures.

1123

1124

1125

1126
36

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1127 Step 8 Report the uncertainty

1128

1129 The laboratory has established a procedure for rounding the expanded uncertainty. 

1130 Following that procedure, the expanded uncertainty was rounded to two significant 

1131 figures:

1132

1133 UU = 8.7 %

1134

1135 For reporting measurement results with the rounded expanded uncertainty to the same 

1136 number of decimal places:

1137

1138 “The concentration of ethanol in Item 1 was found to be 0.090 g/dL ± 0.008 g/dL at a 

1139 coverage probability of 95.45%.”

1140
37

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1141 ANNEX B

1142 (Informative)

1143

1144 Concentration of amphetamine and methamphetamine in a whole blood specimen11

1145

1146 Test Method Information

1147

1148 The laboratory developed and validated a test method for quantitation of amphetamine 

1149 and methamphetamine in whole blood, using liquid chromatography – tandem mass 

1150 spectrometry (LC-MSMS). Multiple analysts were trained and qualified to use the 

1151 laboratory’s procedure. All analysts use the same equipment for this test method. 

1152 Analytical results are normalized to internal standards added during the sample 

1153 preparation process.

1154

1155 The method is calibrated using single replicates of whole blood fortified calibrators at 5 

1156 concentrations from 10 to 1000 ng/mL. The calibrators are prepared from a working stock 

1157 solution that was made by diluting certified reference materials (CRMs). The working stock 

1158 solution is fortified into whole blood with each batch. Method validation determined that 

1159 the proper calibration model was quadratic regression model. Changing variance across 

1160 the concentration range (heteroscedasticity) was observed across the concentration range.

1161

1162 The measurement results from single aliquots of a test specimens are reported.

1163

1164 Calibrators, QC samples, and test specimens are aliquoted at the same time using the same 

1165 equipment.

1166

1167 Measurement Traceability

1168

1169 The traceability for this measurement process is established through the calibrators used 

1170 to generate the calibration curve on the measuring system, as well as through the 

1171 calibration of other equipment used in the measurement process. 

1172

1173 All CRMs have been purchased from a Reference Material Producer that meets the 

1174 ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in Forensic 

1175 Toxicology.

1176

1177 All external calibrations of measuring equipment are performed by calibration laboratories 

1178 that meet the ANSI/ASB Standard 017, Standard Practices for Measurement Traceability in 

1179 Forensic Toxicology. The pipettes and volumetric flasks have been and are routinely 

1180 calibrated. 

11 An evaluation of measurement uncertainty is specific to the measurement traceability that has been 

established for the measurement, the measurement assurance processes that are in place, the laboratory test 

method, the laboratory facility, etc. Therefore, the example that follows shall be evaluated and revised by 

each laboratory to take into consideration the elements that are specific to that laboratory.
38

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1181

1182 Measurement Assurance 

1183

1184 The QC samples at low (30 ng/mL), medium (400 ng/mL), and high (800 ng/mL) 

1185 concentrations are fortified into whole blood from a working stock solution by the 

1186 laboratory with each batch. The working stock solution for the controls are prepared from 

1187 CRMs purchased from a different supplier than the CRMs used as calibrators. The QC 

1188 samples are used to ensure validity of the test method across the concentration range and 

1189 to evaluate the method’s bias on an ongoing basis. 

1190

1191 The laboratory has 15 measurements made of the QC samples during validation for each 

1192 concentration.

1193

1194 Since two analytes are involved in this measurement procedure, two separate uncertainty 

1195 evaluations will be needed.

1196

1197 Step 1 Specify the measurement process

1198

1199 The measurement processes can be described in a written statement:

1200

1201 “The Concentration of Amphetamine in Whole Blood using [the validated laboratory 

1202 procedure]”

1203

1204 “The Concentration of Methamphetamine in Whole Blood using [the validated 

1205 laboratory procedure]”

1206

1207 Step 2 Identify uncertainty components

1208

1209 The following list of possible contributors to uncertainty in this method were identified by 

1210 the laboratory:

1211

1212 Analyst

1213 ● Inter-analyst variation in sample preparation and measurements

1214 ● Training

1215 ● Experience

1216

1217 Calibrators Preparation

1218 ● Components:

1219 ● Methanol – reagent grade

1220 ● Concentration – equipment used to prepare (pipettes, volumetric flask)

1221 ● CRMs – uncertainty in the stated reference value

1222

1223 Quality Controls Preparation

1224 ● Components:

1225 ● Methanol – reagent grade
39

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1226 ● Concentration – equipment used to prepare (pipettes, volumetric flask)

1227 ● CRMs – uncertainty in the stated reference value

1228

1229 Internal Standard Preparation

1230 ● Components:

1231 ● Methanol – reagent grade

1232 ● Stable isotope labeled amphetamine and methamphetamine

1233 ● Impurities in the internal standard (unlabeled drug)

1234 ● Concentration – equipment used to prepare (pipettes, volumetric flask)

1235

1236 Preparation of aliquots of Calibrators, Quality Control Samples and Measurand

1237 ● Homogenization

1238 ● Test Specimens – mixing 

1239

1240 ● Temperature

1241 ● All calibrators, quality control samples and the test specimens are brought to room 

1242 temperature

1243 ● Variation in the time allowed to reach room temperature

1244 ● Variation in room temperature at different times of year

1245

1246 ● Pipettes

1247 ● Volume of sample, calibrators, controls and internal standard 

1248 ● Calibration uncertainty or laboratory specification to verify calibration status 

1249

1250 Analysis

1251 ● Instrument parameter settings (e.g., gradient, flow rate, aging of chromatographic 

1252 column, autosampler syringe, autosampler precision, etc.)

1253 ● Interference from the matrix

1254 ● Interference from reagents

1255 ● Interference from other compounds

1256 ● Stability of sample(s) from preparation through analysis

1257 ● Instrument precision

1258 ● Systematic instrumental variation within an analytical batch

1259 ● Matrix effect (ionization suppression/enhancement)

1260

1261 Data Processing

1262 ● Calibration model

1263 ● Integration parameters 

1264 ● Processing algorithms

1265

1266 NOTE: This list of uncertainty components to be considered could also be compiled into a 

1267 fishbone diagram or into any other format of the laboratory’s choosing.

1268

1269 NOTE: A laboratory may identify different uncertainty components when an evaluation of 

1270 their specific measurement process is performed.
40

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1271

1272 Step 3 Quantify uncertainty components

1273

1274 The laboratory has validation data from the measurement process:

1275

1276 ● The calibration model was determined during method validation and was shown 

1277 through the use of residual plots to have some heteroscedasticity (the variance was not 

1278 constant across the linear range). Therefore, the laboratory is going to evaluate the 

1279 measurement uncertainty using data from the control with the largest variance and 

1280 apply it to the entire reportable concentration range.

1281

1282 ● The QC samples at low (30 ng/mL), medium (400 ng/mL), and high (800 ng/mL) 

1283 concentrations are fortified into whole blood from a working stock solution by the 

1284 laboratory with each batch. All analysts have contributed to the 15 replicate 

1285 measurements of the quality control samples at each concentration. 

1286

1287 Table 2 shows the individual uncertainty components and how they will be evaluated:

1288

1289 Table 2: Method of Evaluation of Uncertainty Components (Example 2)

Uncertainty Component Method of Evaluation

Analysts

Inter-analyst variation Adequately represented by the Type A Evaluation

of process reproducibility data

Training Adequately represented by the Type A Evaluation

of process reproducibility data 

Experience Adequately represented by the Type A Evaluation

of process reproducibility data

Calibrators Preparation

Components:

Methanol – reagent grade

Adequately represented by the Type A Evaluation

of process reproducibility data

Concentration

CRM – uncertainty in the 

stated reference value

Equipment used to prepare 

(pipettes, volumetric flask)

Type B Evaluation

Quality Control Samples Preparation

Components:

Methanol – reagent grade

Adequately represented by the Type A Evaluation

of process reproducibility data

Concentration

CRM – uncertainty in the 

stated reference value

Equipment used to prepare 

(pipettes, volumetric flask)

Type B Evaluation (if necessary for bias)

Internal Standard Preparation
41

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

Components:

 Methanol – reagent grade Adequately represented by the Type A Evaluation

of process reproducibility data

Stable isotope labeled 

amphetamine and 

methamphetamine

Impurities in the internal 

standard (unlabeled drug)

No influence

Certificate of analysis from material provider 

indicates no impurity

The measurement result will only be impacted by 

the volume of the internal standard added to each 

sample

Concentration- equipment used 

to prepare (pipettes,

volumetric flask)

No influence

Procedural requirement to use the same lot of 

Internal Standard for all samples in an analytical 

batch

Preparation of aliquots of Calibrators, Quality Control Samples and Test 

Specimens

Homogenization – mixing Demonstrated during method validation to be 

insignificant.

Temperature – all calibrators, 

quality controls and the 

measurand are brought to room 

temperature

Variation in the time allowed to 

reach room temperature

Variation in room 

temperature at different times 

of year

Adequately represented by the Type A Evaluation

of process reproducibility data

Pipettes:

Volume of sample, calibrators, 

quality controls , and internal 

standard 

Calibration uncertainty or 

laboratory specification to verify 

calibration status

Volume of internal standard adequately 

represented by the Type A Evaluation of process 

reproducibility data

Type B Evaluation for volume of sample and 

calibrators (for controls only if necessary for bias)

Analysis

Instrument parameter settings 

(e.g., gradient, flow rate, aging of 

chromatographic column, 

autosampler syringe, autosampler 

precision, etc.)

Adequately represented by the Type A Evaluation

of process reproducibility data

Interference from the matrix

Matrix interference was evaluated during method 

validation and found to be insignificant for the 

matrix type allowed in this method. 

Interference from reagents

This component is not an uncertainty component 

but is a quality control concern. The laboratory 

analyzes a matrix blank that contains no analyte 

that does evaluate all reagents used in the 

analytical method. The laboratory procedure 

specifies acceptable criteria for this quality control 

sample.

Interference from other 

compounds

Demonstrated lack of interference from other 

compounds during method validation. This 

component is not considered an uncertainty 

component.
42

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

Stability of sample(s) from 

preparation through analysis

Adequately represented by the Type A Evaluation

of process reproducibility data

Instrument precision Adequately represented by the Type A Evaluation

of process reproducibility data

Systematic instrumental variation 

within an analytical batch

The positive controls are reinjected at the end of 

the batch and must meet predefined criteria

Data Processing

Calibration model Adequately represented by the Type A Evaluation

of process reproducibility data

Integration parameters Adequately represented by the Type A Evaluation

of process reproducibility data

Processing algorithms Adequately represented by the Type A Evaluation

of process reproducibility data

1290

1291 Type A Evaluation of uncertainty components

1292

1293 Measurement Process Reproducibility 

1294

1295 The number of observations of each QC sample is 15. The statistic that will be calculated is the 

1296 percent relative standard deviation.

1297

1298 Through validation, it was determined that the variance was not consistent across the calibration 

1299 range. Therefore the reproducibility data from the multiple QC sample levels for either target 

1300 compound may not be combined. The 400 ng/mL QC sample had the greatest variance and will be 

1301 used for this evaluation.

1302

1303 To begin, the mean (average) and standard deviation of the control data will be calculated.

1304

1305 ● The mean of the reproducibility data in this example is 404 ng/mL for amphetamine and 416 

1306 ng/mL for methamphetamine.

1307

1308 ● The standard deviation of the reproducibility data in this example is 15.90 ng/mL for 

1309 amphetamine and 12.01 ng/mL for methamphetamine.

1310

1311 The %RSD of the reproducibility data in this example is 3.936 % for amphetamine and 2.888 % 

1312 for methamphetamine.

1313

1314 Type B Evaluation of uncertainty components

1315

1316 Calibrators Preparation

1317

1318 Uncertainty in the reference value 

1319

1320 The laboratory reviewed the calibration certificates from all CRMs used for the preparation of the 

1321 calibration working stock solutions. The largest uncertainty was 0.005 mg/mL for the 1.000 mg/mL 

1322 amphetamine CRM and 0.006 mg/mL for the 1.000 mg/mL methamphetamine CRM.

1323
43

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

RRRRRR RR RRRR uu uu uu uu oooo AAAAAAh CC CC = �

0.005 /

1.000 / 1324 � ∗ 100 = 0.5 %

1325

RRRRRR RR RRRR uu uu uu uu oooo h h CC CC = �

0.006 /

1.000 / 1326 � ∗ 100 = 0.6 %

1327

1328 Uncertainty in pipettes

1329

1330 The laboratory reviewed the calibration certificates of all pipettes that may be used for preparation 

1331 of the calibration working stock solution. The largest uncertainty was 0.74 μL for a 100μL pipette.

1332

RRRRRR RR RRRR uu uu uu uu oooo PP PP CC WW WW = �

0.74 μLL

100 μLL

1333 � ∗ 100 = 0.74 %

1334

1335 Uncertainty in volumetric flasks

1336

1337 The laboratory reviewed the calibration certificates of all volumetric flasks that may be used for 

1338 preparation of the calibration working stock solution. The largest uncertainty was 0.0086 mL for a 

1339 25mL volumetric flask.

1340

RRRRRR RR RRRR uu uu uu uu oooo VV FF PP CC WW WW = �

0.0086

25 1341 � ∗ 100 = 0.0344 %

1342

1343 Preparation of aliquots of Calibrators and Test Specimens

1344

1345 Uncertainty in pipettes

1346

1347 The laboratory reviewed the calibration certificates of all pipettes that may be used to fortify the 

1348 calibrators from the working stock solution into whole blood. The method requires the same 

1349 pipette to be used to add the internal standard to calibrators, controls, and test specimens. The 

1350 largest uncertainty was 0.74 μL for a 100-μL pipette.

1351

RRRRRR RR RRRR uu uu uu uu oooo PP FF CC = �

0.74 μ

100 μ

1352 � ∗ 100 = 0.754 %

1353

RRRRRR RR RRRR uu uu uu uu oooo PP II = �

0.74 μ

100 μ

1354 � ∗ 100 = 0.74 %

1355

1356 The laboratory reviewed the calibration certificates of all pipettes that may be used to aliquot the 

1357 test item. The largest uncertainty was 6.9 μL for a 1000-μL pipette.

1358

RRRRRR RR RRRR uu uu uu uu oooo PP AA AA TT = � 6.9 μ

1000 μ

1359 � ∗ 100 = 0.69 %

1360

1361 Step 4 Convert quantities to standard uncertainties

1362

1363 The measurement unit

1364

1365 In this example the estimated relative uncertainty is expressed as a percentage. 
44

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1366

1367 Type A Evaluation of uncertainty components

1368

1369 Measurement Process Reproducibility data 

1370

1371 The % RSD (sr) of the reproducibility data in this example is 3.936 % for amphetamine and 2.888 % 

1372 for methamphetamine.

1373

1374 Type B Evaluation of uncertainty components

1375

1376 Calibrators Preparation

1377

1378 Uncertainty in the reference value 

1379

1380 Based on the certificates from the CRMs used to prepare the calibrator working stock solutions in 

1381 this method, the laboratory determined in Step 3 that the relative uncertainty is 0.5 % and 0.6 % for 

1382 amphetamine and methamphetamine, respectively.

1383

1384 The certificates indicate the expanded uncertainties assume a normal distribution, a coverage 

1385 factor of k = 2, and a coverage probability of approximately 95 %. The relative uncertainties will be 

1386 divided by the coverage factor to arrive at relative standard uncertainties.

1387

RRRRRR RR RRRR uu uu uu uu oooo AAAAAAh CC CC = �

0.5 %

2 1388 � = 0.25 % = uuCCCCCC

1389

RRRRRR RR RRRR uu uu uu uu oooo h h CC CC = �

0.6 %

2 1390 � = 0.30 % = uuCCCCCC

1391

1392 Uncertainty in pipettes

1393

1394 In Step 3, the laboratory determined that among the pipettes used to prepare the working stock 

1395 solutions, the largest relative uncertainty was 0.74 % for a 100-μL pipette.

1396

1397 The pipette’s calibration certificate indicates this expanded uncertainty assumes a normal 

1398 distribution, a coverage factor of k = 2.87, and a coverage probability of approximately 95 %. The 

1399 relative uncertainty derived from the calibration certificate will be divided by the coverage factor, 

1400 2.87, to arrive at a relative standard uncertainty.

1401

RRRRRR RR RRRR uu uu uu uu oooo PP PP CC WW WW = �

0.74 %

2.87 1402 � = 0.258 % = uuCCCCCCCC

1403

1404 Uncertainty in volumetric flasks

1405

1406 In Step 3, the laboratory determined that among the volumetric flasks used to prepare the working 

1407 stock solutions, the largest relative uncertainty was 0.0344 % for a 25mL flask.

1408

1409 The volumetric flask’s calibration certificate indicates this expanded uncertainty assumes a normal 

1410 distribution, a coverage factor of k = 2, and a coverage probability of approximately 95 %. The 

1411 relative uncertainty derived from the calibration certificate will be divided by the coverage factor, 

1412 2, to arrive at a relative standard uncertainty.
45

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1413

RRRRRR RR RRRR uu uu uu uu oooo VV FF PP CC WW WW = �

0.0344 %

2 1414 � = 0.172 % = uuCCCCCCCC

1415

1416 Preparation of aliquots of Calibrators and Test Specimens

1417

1418 Uncertainty in pipettes

1419

1420 In Step 3, the laboratory determined that among the pipettes used to fortify the calibrators from the 

1421 working stock solution into whole blood, the largest relative uncertainty was 0.74 % for a 100μL 

1422 pipette. The same pipette is used to fortify all samples with the internal standards.

1423

1424 The pipette’s calibration certificate indicates this expanded uncertainty assumes a normal 

1425 distribution, a coverage factor of k = 2.87 and a coverage probability of approximately 95 %. The 

1426 uncertainty derived from the calibration certificate will be divided by the coverage factor to arrive 

1427 at a relative standard uncertainty.

1428

RRRRRR RR RRRR uu uu uu uu oooo PP FF CC = �

0.74 %

2.87 1429 � = 0.258 % = uuCCCC CC

1430

RRRRRR RR RRRR uu uu uu uu oooo PP II = �

0.74 %

2.87 1431 � = 0.258 % = uuIIII

1432

1433

1434 The laboratory also determined in Step 3 that among the pipettes used to aliquot test specimens, 

1435 the largest relative uncertainty was 0.69 % for a 1000-μL pipette.

1436

1437 The pipette’s calibration certificate indicates this expanded uncertainty assumes a normal 

1438 distribution, a coverage factor of k = 2.87, and a coverage probability of approximately 95 %. The 

1439 uncertainty on the calibration certificate will be divided by the coverage factor, 2.87, to arrive at a 

1440 relative standard uncertainty.

1441

RRRRRR RR RRRR uu uu uu uu oo PP AA AA TT = �

0.69 %

2.87 1442 � = 0.24 % = uuIIIIII

1443

1444 Step 5 Calculate the combined standard uncertainty

1445

1446 The evaluation will assume that the uncertainty components are independent or uncorrelated and 

1447 that the measurement result is the sum of a series of components.

1448

1449 For Amphetamine:

1450

uucc( ) = �3.936rr

2 + 0.25CCCCCC

2 + 0.258CCCCCCCC2 + 0.0172CCCCCCCC2 + 0.258CCCC CC2 + 0.258IIII2 + 0.24IIIIII

2 1451

1452

uucc 1453 ( ) = √15.8122

1454

uucc 1455 ( ) = 3.9765 %

1456

1457
46

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1458 For Methamphetamine:

1459

uucc( ) = �2.888rr

2 + 0.30CCCCCC

2 + 0.258CCCCCCCC2 + 0.0172CCCCCCCC2 + 0.258CCCC CC2 + 0.258IIII2 + 0.24IIIIII

2 1460

1461

uucc 1462 ( ) = √8.6881

1463

uucc 1464 ( ) = 2.9476 %

1465

1466 Evaluation of bias

1467

1468 The laboratory in this example views the monitoring of bias as a component of ensuring the validity 

1469 of the test method and has incorporated three controls prepared from CRMs at a low, medium and 

1470 high concentration as QC samples for the purpose of monitoring bias from unidentified sources on 

1471 an ongoing basis.

1472

1473 The largest average bias for any of the control levels (low, medium and high) during validation was 

1474 -2.4 % for amphetamine and 4.0 % for methamphetamine. 

1475

1476 The bias for amphetamine is less than the combined standard uncertainty (3.9765 %) and is 

1477 therefore insignificant. No additional component for the uncertainty of the CRM used to evaluate 

1478 bias will be added.

1479

1480 The bias for methamphetamine is greater than the combined standard uncertainty (2.9476 %) and 

1481 is therefore significant. Steps 3, 4, and 5 must be addressed for the methamphetamine bias 

1482 component.

1483

1484 Step 3 Quantify uncertainty components – bias component 

1485

1486 During validation the largest bias for methamphetamine was quantified to be 4.0 %.

1487

1488

1489 Step 4 Convert quantities to standard uncertainties – bias component

1490

1491 The laboratory has chosen option 4.2.6.1.1.1 (c) to address the bias for methamphetamine 

1492 that was determined to be significant. Following the guidance in section 3.2.5.5 of NIST SOP 

1493 29, the bias is treated as an uncorrected systematic error and the following equation 

1494 applying a rectangular distribution is used to address the uncertainty of the difference 

1495 component (uudd) in the MU evaluation:

1496

uudd = bbbbbbbb

√3 = 4.0√3

1497 = 2.3094

1498

1499

1500

1501

1502

1503
47

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1504 Step 5 Calculate combined standard uncertainty – including bias component

1505

1506 For Methamphetamine the updated root sum of the squares:

1507

uucc( ) = �2.888rr

2 + 0.30CCCCCC

2 + 0.37CCCCCCCC2 + 0.0172CCCCCCCC2 + 0.258CCCC CC 2 + 0.258IIII2 + 0.24IIIIII2 + 2.3094dd

2 1508

1509

uucc 1510 ( ) = √14.0918

1511

uucc 1512 ( ) = 3.7539 %

1513

1514 Step 6 Expand the combined standard uncertainty by coverage factor (k)

1515

1516 The data from the measurement process is assumed to follow a normal distribution. The laboratory 

1517 has 15 measurements of the 400 ng/mL QC control. Therefore, the laboratory assumes that the 

1518 effective degrees of freedom for the combined standard uncertainty cannot be lower than 14.

1519

1520 Refer to the Student’s t-distribution table to determine the k factor.

1521

1522 To expand the uncertainty to a 95.45 % coverage probability for this example the coverage factor k

1523 = 2.20 will be used.

1524

1525 For Amphetamine:

1526

1527 UU = 2.20 × 3.9765 = 8.4079 %

1528

1529 For Methamphetamine:

1530

1531 UU = 2.20 × 3.7539 = 8.2586 %

1532

1533 Step 7 Evaluate the expanded uncertainty

1534

1535 The laboratory determined that the evaluation of uncertainty is fit-for-purpose based on the 

1536 following considerations:

1537

1538 ● Stakeholder interests

1539 There were none.

1540 ● Legal requirements

1541 There were none.

1542 ● The relationship between the reported test value and the expanded MU

1543 Expanded uncertainty as a percentage across the analytical range ensures a consistent 

1544 relationship.

1545 ● Established criteria including control limits for method

1546 The laboratory’s control limits for the method are 20 %. The allowable control limits were 

1547 modified to 10 % for amphetamine and for methamphetamine to reflect the expanded 

1548 uncertainty.

1549

1550

1551
48

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1552 Step 8 Report the uncertainty

1553

1554 The laboratory has established a procedure for the process of rounding the expanded uncertainty. 

1555 Following that procedure, the expanded uncertainty rounded to two significant figures:

1556

1557 For Amphetamine:

1558

1559 U = 8.4%

1560

1561 For Methamphetamine:

1562

1563 U = 8.3 %

1564

1565 For reporting measurement results with the rounded expanded uncertainties to the same number 

1566 of decimal places: 

1567

1568 “The concentration of amphetamine in Item 1 was found to be 90 ± 8 ng/mL at a coverage 

1569 probability of 95.45%. The concentration of methamphetamine in Item 1 was found to be 143 

1570 ± 12 ng/mL at a coverage probability of 95.45%.”

1571

1572

1573
49

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1574 ANNEX C

1575 (Informative)

1576

1577 Calibration of breath alcohol measuring instrumentation using long-term calibration 

data from a single instrument 1578 12

1579

1580 Calibration Method Information

1581 The calibration of an individual breath alcohol instrument uses dry gas measurement 

1582 standard data from the current calibration as well as historical calibration data for this 

1583 single instrument over time. The calibration method uses measurement standards at 

1584 multiple concentrations. 

1585

1586 The calibration method does require each concentration of the dry gas measurement 

1587 standards to be evaluated in triplicate. The method requires each of the triplicate 

1588 measurements to be within 3 % or 0.003 g of ethanol/210 L of breath (g/210 L), whichever 

1589 is greater, of the certified reference value of the measurement standard. Furthermore, the 

1590 method requires that there shall be no greater than 0.003 g/210 L difference in all three 

1591 measurements at each concentration. 

1592

1593 Step 1 Specify the measurement process 

1594

1595 Calibration of breath alcohol measuring instrumentation using long-term calibration data 

1596 from a single instrument

1597

1598 Step 2 Identify uncertainty components 

1599

1600 The following list of possible contributors to uncertainty in the calibration method were 

1601 identified: 

1602

1603 Analyst

1604 ● Inter-analyst variation in performing calibration 

1605 ● Training 

1606 ● Experience 

1607

1608 Breath Alcohol Measuring Instrument Being Calibrated

1609 ● Variability of instrument over time 

1610

1611 Measurement Standards

12 An evaluation of measurement uncertainty is specific to the measurement traceability that has been 

established for the measurement, the measurement assurance processes that are in place, the laboratory 

calibration method, the laboratory facility, etc. Therefore, the example that follows shall be evaluated and 

revised by each laboratory to take into consideration the elements that are specific to that laboratory.
50

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1612 ● Dry Gas Certified Reference Materials - uncertainty in the stated reference value 

1613

1614 Environmental Conditions 

1615 ● Barometric pressure 

1616 ● Humidity 

1617 ● Temperature 

1618

1619 Varying Facilities/Location Change

1620 ● Instrument transport 

1621 ● Power fluctuation

1622

1623 Data Processing 

1624 ● Processing algorithms 

1625

1626 Step 3 Quantify uncertainty components 

1627

1628 Measurement standard data has been collected from use of this calibration method over 

1629 time. All analysts have participated in acquiring the measurement standard data for this 

1630 single breath alcohol measuring instrument. The laboratory has 51 measurements made 

1631 using each measurement standard. The instrument has demonstrated constant variance 

1632 across the concentration range of the measurement standards used in the calibration 

1633 method. Because the 0.100 g/210 L measurement standard has the greatest observed 

1634 variance of the measurement standards, it will be used to represent the process 

1635 reproducibility data. 

1636

1637 Table 1 shows the individual uncertainty components and how they will be evaluated:

1638

1639 Table 1: Method of Evaluation of Uncertainty Components (Example 3)

1640

Uncertainty Component Method of Evaluation

Analysts

Inter-analyst variation

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard 

Training

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Experience

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Breath Alcohol Measuring Instrument Being Calibrated

Variability of instrument over 

time

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Measurement Standards 
51

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

CRM –uncertainty in the stated 

reference value Type B Evaluation

Environmental Conditions

Barometric pressure 

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Humidity 

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Temperature 

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

Varying Facilities/Locations

Instrument transport Not Applicable

Power fluctuations

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard.

Data Processing 

Processing algorithms

Adequately represented by Type A Evaluation of 

process reproducibility data – measurement 

standard

1641

1642 Type A Evaluation of uncertainty components

1643

1644 Measurement Standard Reproducibility – 0.100 g/210 L Measurement Standard

1645

1646 The number of observations in this example is 51. The statistic that will be calculated is the 

1647 standard deviation.

1648

1649 To begin, the mean (average) and standard deviation of the measurement data will be 

calculated. 1650 13

1651

1652 The mean is calculated as: 

1653

1654

1655

1656

13 For the readability of the example, the display of digits used in all calculations was abbreviated. Best 

practice is to include and carry all digits through all calculations and only round the reported value and its 

uncertainty to the proper number of significant figures.

1

1 n

i

i

x x

n =

= ∑

1 2 3 ( ... ) n xxx x

x

n

+++ =
52

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1657

1658 The mean of the reproducibility data in this example = 0.0994 g/210 L

1659 The standard deviation is calculated as:

1660

1661 The standard deviation of the reproducibility data in this example = 0.0012 g/210 L

1662 Type B Evaluation of uncertainty components

1663

1664 Certified Reference Materials 

1665

1666 Based on the certificates from the CRMs, the laboratory determined in Step 3 that the 

1667 greatest relative uncertainty for the CRM was 0.0018 g/210 L for the 0.100 g/210 L CRM.

1668 The certificate indicates this expanded uncertainty assumes a normal distribution, a 

1669 coverage factor of k = 2 and a coverage probability of approximately 95 %. The uncertainty 

1670 on the calibration certificate will be divided by the coverage factor to arrive at a relative 

1671 standard uncertainty.

1672

RRRRRR RR RRRR uu uu uu uu = �

0.0018 gg /210

2 � = 0.0009 gg

210 1673

1674

1675 Step 4 Convert quantities to standard uncertainties 

1676

1677 The measurement unit: g of ethanol/210 L of breath (g/210 L) 

1678

1679 Type A Evaluation of uncertainty components

1680

1681 Measurement Standard Reproducibility – 0.100 g/210 L Measurement Standard

1682

1683 The standard deviation of the reproducibility data in this example is 0.0012 g/210 L.

1684

1685 ● No additional conversion is necessary to reach a standard uncertainty. 

1686

1687 Type B Evaluation of uncertainty components:

1688

1689 Certified Reference Materials

1690

1691 The CRM certificate indicates that the stated expanded uncertainty assumes a normal 

1692 distribution, a coverage factor of k = 2 and a coverage probability of approximately 95 %.
53

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1693 ● The uncertainty is stated to be 0.0018 g/210 L for the 0.100 g/210 L CRM. 

1694 ● The uncertainty on the calibration certificate will be divided by the coverage factor, 

1695 2, to arrive at a standard uncertainty. 

1696 ● 0.0018 g/210 L /2 = 0.0009 g/210 L for the standard uncertainty

1697

1698 Step 5 Calculate combined standard uncertainty 

1699

1700 The evaluation will assume that the uncertainty components are independent or 

1701 uncorrelated and that the measurement result is the sum of a series of components. The 

1702 combined standard uncertainty was calculated.

uucc( ) = � rr rrrr rr rr rr rrrr

2 + uuCCCCCC

2 1703

1704

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 1705

1706

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 1707

1708

uucc( ) = �2.25xx10−6 1709

1710

uucc 1711 ( ) = 0.0015 gg/210

1712

1713 Evaluation of Bias

1714

1715 In this example, bias is evaluated as part of instrument calibration. 

1716 The data for the 0.100 g/210 L measurement standard shows a difference of the average to 

1717 reference value of 0.001 g/210 L. This value is less than the combined standard uncertainty 

1718 and therefore, is insignificant. No additional component will be added to the measurement 

1719 uncertainty evaluation.

1720 Step 6 Expand the combined standard uncertainty by coverage factor (k) 

1721

1722 The laboratory has 51 measurements of the measurement standard. Therefore, the 

1723 laboratory assumes a lower bound on the effective degrees of freedom for the combined 

1724 standard uncertainty of 50. 

1725

1726 The data from the measurement process is assumed to follow a normal distribution; 

1727 therefore, refer to the Student’s t-distribution table to determine the k factor.

1728 To expand the uncertainty to a 95.45 % coverage probability for this example the coverage 

1729 factor k = 2.05 (n=50) will be used.
54

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1730 A laboratory can choose to increase the coverage probability.

1731 = 2.05

1732 UU = 2.05 × 0.0015 = 0.00308 gg/210

1733 Step 7 Evaluate the expanded uncertainty 

1734

1735 The calibration laboratory determined that the evaluation of uncertainty is fit-for-purpose.

1736

1737 The laboratory identified that the current method allows for a variance of 0.005 g/ 210L or 

1738 5%, whichever is greater, from a measurement standard known reference value. However, 

1739 this is greater than the expanded uncertainty at 95.45 %. Left unchanged, a calibration 

1740 could be reported that would have a bias that is significant. Therefore, the laboratory 

1741 revised the method so that the variability allowed in any calibration must be equal to or 

1742 less than the 0.003 g/ 210L or 3% whichever is greater.

1743

1744 Step 8 Report the uncertainty 

1745

1746 The laboratory has established a procedure for the process of rounding the expanded 

1747 uncertainty. Following that procedure, the expanded uncertainty is rounded to the third 

1748 decimal place to equal the number of decimal places reported in the breath alcohol 

1749 instrument display. The expanded uncertainty will be 0.003 g/210 L. 

1750

1751 The certificate of calibration shall contain: 

1752 ● 0.003 g/210 L, the combined expanded uncertainty, rounded to the third 

1753 decimal place.

1754 ● k = 2.05, the coverage factor based on the student’s t distribution.

1755 ● 95.45 %, the coverage probability 

1756

1757 For reporting calibration results use the rounded expanded uncertainty to the same level of

1758 significance

1759

1760 0.100 g/210 L ± 0.003 g/210 L at a coverage probability of 95.45 % (k=2.05).”
55

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1761 ANNEX D

1762 (Informative)

1763

1764 Calibration of breath alcohol measuring instruments using control data from the 

1765 calibration method14

1766

1767 Calibration Method Information

1768 A population of breath alcohol measuring instruments is calibrated using the same 

1769 calibration method. The calibration method includes multiple measurement standards of 

1770 varying concentrations and a control. The control data obtained is from a population of 100 

1771 breath alcohol measuring instruments that have all demonstrated constant variance across 

1772 the measurement standard concentration levels. Three measurements of the 0.100 g of 

1773 ethanol/210 L of breath (g/210 L) control is made during each instrument calibration. The 

1774 current calibration as well as historical control data for the population of instruments over 

1775 time was used in the calculation. 

1776

1777 Step 1 Specify the measurement process 

1778 Calibration of breath alcohol measuring instruments using control data from the 

1779 calibration method

1780

1781 Step 2 Identify uncertainty components 

1782

1783 The following list of possible contributors to uncertainty in the calibration method were 

1784 identified: 

1785

1786 Analyst

1787 ● Inter-analyst variation in performing calibration 

1788 ● Training 

1789 ● Experience 

1790

1791 Breath Alcohol Measuring Instrument Being Calibrated

1792 ● Population of 100 breath alcohol measuring instruments 

1793 ● Variability of instrument over time 

1794

1795 Measurement Standards

1796 ● Dry Gas Certified Reference Materials - uncertainty in the stated reference value 

1797

1798 Calibration Method Control

14 An evaluation of measurement uncertainty is specific to the measurement traceability that has been 

established for the measurement, the measurement assurance processes that are in place, the laboratory 

calibration method, the laboratory facility, etc. Therefore, the example that follows shall be evaluated and 

revised by each laboratory to take into consideration the elements that are specific to that laboratory.
56

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1799 ● Dry Gas Certified Reference Material from a different manufacturer than that of the 

1800 Measurement Standards - uncertainty in the stated reference value 

1801

1802 Environmental Conditions 

1803 ● Barometric pressure 

1804 ● Humidity 

1805 ● Temperature 

1806

1807 Varying Facilities/Location Change

1808 ● Instrument transport 

1809 ● Power fluctuations

1810

1811 Data Processing 

1812 ● Processing algorithms 

1813

1814

1815 Step 3 Quantify uncertainty components 

1816

1817 The calibration laboratory has existing data from the calibration method. Each instrument 

1818 is evaluated, in triplicate, using a 0.100 g/210 L dry gas cylinder with measurement 

1819 traceability as a calibration control. The calibration method requires the control to be 

1820 within 3 % or 0.003 g/210 L (whichever is greater) of the certified reference value. 

1821 Furthermore, there shall be no greater than 0.003 g/210 L difference in all three 

1822 calibration control values. 

1823

1824 Control data is collected on an on-going basis with all analysts contributing to the control 

1825 data for the population of instruments. 

1826

1827 Table 1 shows the individual uncertainty components and how they will be evaluated:

1828

1829 Table 1: Method of Evaluation of Uncertainty Components (Example 4)

Uncertainty Component Method of Evaluation

Analysts

Inter-analyst variation Adequately represented by Type A Evaluation of 

process reproducibility data – control

Training Adequately represented by Type A Evaluation of 

process reproducibility data – control

Experience Adequately represented by Type A Evaluation of 

process reproducibility data – control

Breath Alcohol Measuring Instrument Being Calibrated

Population of 100 breath 

alcohol measuring 

instruments

Adequately represented by Type A Evaluation of 

process reproducibility data – control
57

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

Variability of instrument over 

time

Adequately represented by Type A Evaluation of 

process reproducibility data – control

Measurement Standards 

CRM –uncertainty in the stated 

reference value Type B Evaluation

Calibration Method Control 

CRM –uncertainty in the stated 

reference value Type B Evaluation

Environmental Conditions

Barometric pressure Adequately represented by Type A Evaluation of 

process reproducibility data – control

Humidity Adequately represented by Type A Evaluation of 

process reproducibility data – control

Temperature Adequately represented by Type A Evaluation of 

process reproducibility data – control

Varying Facilities/Locations

Instrument transport Not Applicable 

Power fluctuations Adequately represented by Type A Evaluation of 

process reproducibility data – control.

Data Processing 

Processing algorithms Adequately represented by Type A Evaluation of 

process reproducibility data – control

1830

1831 Type A Evaluation of uncertainty components

1832

1833 Calibration Control Reproducibility – 0.100 g/210 L Calibration Control

1834

1835 The number of measurements of the control in this example is greater than 300. 

1836

1837 The statistic that will be calculated is the standard deviation. 

1838

1839 To begin, the mean (average) and standard deviation of the measurement data will be 

calculated. 1840 15

1841

1842 Mean 

1843

1844

15 For the readability of the example, the display of digits used in all calculations was abbreviated. Best practice 

is to include and carry all digits through all calculations and only round the reported value and its uncertainty 

to the proper number of significant figures.

1

1 n

i

i

x x

n =

= ∑
58

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1845

1846

1847 The mean of the reproducibility data in this example = 0.0996 g/210 L

1848 Standard Deviation 

1849

1850 The standard deviation of the reproducibility data in this example = 0.0012 g/210 L

1851

1852 Type B Evaluation of uncertainty components

1853

1854 Certified Reference Materials 

1855

1856 The calibration laboratory reviewed the certificates of analysis from all dry gas cylinders. 

1857 The greatest uncertainty is 0.0018 g/210 L for the 0.100 g/210 L CRM.

1858

1859 Step 4 Convert quantities to standard uncertainties 

1860

1861 The measurement unit: g of ethanol/210 L of breath (g/210 L)

1862

1863 Type A Evaluation of uncertainty components

1864

1865 Calibration Control Reproducibility – 0.100 g/210 L Calibration Control

1866

1867 The standard deviation of the reproducibility data in this example is 0.0012 g/210 L. 

1868 ● No additional conversion is necessary to reach a standard uncertainty. 

1869

1870 Type B Evaluation of uncertainty components

1871

1872 Certified Reference Materials

1873

1874 The certificates of analysis state that the expanded uncertainty assumes a normal 

1875 distribution, a coverage factor of k = 2 and a coverage probability of approximately 95 %.

1876 ● The greatest uncertainty is 0.0018 g/210 L. 

1877 ● The uncertainty on the calibration certificate will be divided by the coverage factor, 

1878 2, to arrive at a standard uncertainty. 

1879 ● 0.0018 g/210 L /2 = 0.0009 g/210 L for the standard uncertainty.

1880

1881

1 2 3 ( ... ) n xxx x

x

n

+++ =
59

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1882 Step 5 Calculate combined standard uncertainty 

1883

1884 The evaluation will assume that the uncertainty components are independent or 

1885 uncorrelated and that the measurement result is the sum of a series of components. The 

1886 combined standard uncertainty was calculated.

uucc( ) = � rr rrrr rr rr rr rrrr

2 + uuCCCCCC

2 1887

1888

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 1889

1890

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 1891

1892

uucc( ) = �2.25xx10−6 1893

1894

uucc 1895 ( ) = 0.0015 gg/210

1896

1897 Evaluation of Bias

1898

1899 In this example, bias is evaluated as part of the instrument calibration. The calibration 

1900 method requires the control to be within 3 % or 0.003 g/210 L (whichever is greater) of 

1901 the certified reference value. Furthermore, there shall be no greater than 0.003 g/210 L 

1902 difference in all three calibration control values. 

1903 The data for the 0.100 g/210 L calibration control shows a difference between the average 

1904 and the reference value of 0.001 g/210 L. This value is less than the combined standard 

1905 uncertainty and therefore, is insignificant. Although the bias is viewed as insignificant, the 

1906 laboratory is choosing to include an additional component in the uncertainty evaluation. An 

1907 uncertainty contributor equal to the uncertainty of the reference value of the calibration 

1908 control used for the bias evaluation was added to the evaluation of measurement 

1909 uncertainty. 

1910 Step 3 Quantify uncertainty components – bias component

1911

1912 The laboratory noted the difference of the average data for the 0.100 g/210 L 

1913 calibration to be 0.001 g/210 L. 

1914

1915 Step 4 Convert quantities to standard uncertainties – bias component

1916

1917 The standard uncertainty for the bias was 0.001 g/210 L. 

1918

1919 Step 5 Calculate combined standard uncertainty – including bias component
60

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1920

1921 The updated RSS calculation:

1922

uucc( ) = � rr rrrr rr rr rr rrrr

2 + uuCCCCCC

2 + uu bb 2 1923

1924

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 + 0.001 bb 2 1925

1926

uucc( ) = �0.0012rr rrrr rr rr rr rrrr

2 + 0.0009CCCCCC

2 + 0.001 bb 2 1927

1928

uucc 1929 ( ) = 0.0018 gg/210

1930

1931 Step 6 Expand the combined standard uncertainty by coverage factor (k) 

1932

1933 The data from the measurement process is assumed to follow a normal distribution. 

1934 The laboratory has 300 measurements of the calibration control. Refer to the Student’s t1935 distribution table to determine the k factor.

1936

1937 To expand the uncertainty to a 95.45 % coverage probability for this example the coverage 

1938 factor k = 2.0 will be used.

1939 A laboratory can choose to increase the coverage probability. 

1940 = 2.0

1941 UU = 2.0 × 0.0018 = 0.0036 gg/210

1942 Step 7 Evaluate the expanded uncertainty 

1943

1944 The calibration laboratory determined that the evaluation of uncertainty is fit-for-purpose.

1945

1946 Step 8 Report the uncertainty 

1947

1948 The laboratory has established a procedure for the process of rounding the expanded 

1949 uncertainty. Following that procedure, the expanded uncertainty rounded to the third 

1950 decimal place. The expanded uncertainty will be 0.004 g/210 L. 

1951

1952 The certificate of calibration shall contain: 

1953 ● 0.004 g/210L, the combined expanded uncertainty, rounded to the third 

1954 decimal place.

1955 ● k = 2.0, the coverage factor based on the student’s t distribution.

1956 ● 95.45 %, the coverage probability 

1957
61

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1958 For reporting calibration results use the rounded expanded uncertainty to the same level of 

1959 significance

1960

1961 0.100 g/210 L ± 0.004 g/210 L at a coverage probability of 95.45 % (k=2.0).”

1962
62

2021-S-0004 Standard Practices for Evaluating Measurement Uncertainty of 

Quantitative Measurements in Forensic Toxicology 

1963 ANNEX E

1964 (informative)

1965 Bibliography

1966

1967 1. ASCLD/LAB Policy on Measurement Uncertainty

1968 Note: Document can be obtained from anab@anab.org

1969

1970 2. ASCLD/LAB Guidance on the Estimation of Measurement Uncertainty –

1971 Overview

1972 Note: Document can be obtained from anab@anab.org

1973

1974 3. ASCLD/LAB Guidance on the Estimation of Measurement Uncertainty – Annex 

1975 A Details on the NIST 8-Step Process

1976 Note: Document can be obtained from anab@anab.org

1977

1978 4. ASTM International E542-01 Standard Practice for Calibration of Laboratory 

1979 Volumetric Apparatus available at www.astm.org

1980

1981 5. Eurachem Terminology in Analytical Measurement – Introduction to VIM 3 

1982 available at www.eurachem.org

1983

1984 6. The National Institute of Standards and Technology (NIST) definition of 

1985 “internal measurement assurance program” available at 

1986 www.nist.gov/traceability/index.cfm

1987

1988 7. Internal Organization for Standardization (ISO). ISO/IEC 9000:2015 Quality 

1989 Management Systems-Fundamentals and Vocabulary (Geneva, Switzerland: 

1990 ISO, 2000)

1991

1992 8. Internal Organization for Standardization (ISO). ISO/IEC 17000:2004 

1993 Conformity Assessment – Vocabulary and General Principles (Geneva, 

1994 Switzerland: ISO, 2014)

1995

1996 9. ANSI/ASB Standard 036, Standard Practices for Method Validation in Forensic 

1997 Toxicology. Available for download at XXX.

1998

1999 10. ANSI/ASB Standard 054, Standard for a Quality Control Program in Forensic 

2000 Toxicology Laboratories. Available for download at XXX.

2001

2002 11. ANSI/ASB Standard 053, Standard for Report Content in Forensic Toxicology. 

2003 Available for download at XXX.

2004

2005 12. ISO/IEC 17025:2017 General requirements for the competence of testing and 

2006 calibration laboratories. Available for purchase at https://webstore.ansi.org/.

2007