Preface ................................................... XIII
List of Symbols ........................................... XVII
0. Introduction ................................................. 1
0.1. General Differentiation of Analytical Processes ........ 3
0.2. Quality of Analytical Processes and Results ............ 4
0.3. The System of Analytical Quality Assurance ............. 4
0.4. The Four-Phase Model of Analytical Quality Assurance ... 6
1. Phase I: Establishing a New Analytical Procedure ............. 9
1.1. Introduction ........................................... 9
1.1.1. Objectives of Phase I .......................... 9
1.1.2. When Are Characteristic Data Obtained? ......... 9
1.1.3. The Progression of Phase I .................... 10
1.1.4. Results of Phase I; Statistical Data .......... 14
1.2. Calibration of the Fundamental Analytical Procedure ... 15
1.2.1. Establishment of an Analytical Range .......... 16
1.2.2. Preparation of Standard Samples ............... 16
1.2.3. Determination of the Calibration Function
and Process Data .............................. 17
1.2.3.1. Process Data for the Linear
Calibration Function ................. 18
1.2.3.2. Process Data for the Second-Order
Calibration Function ................. 19
1.2.3.3. Calculating Analytical Results
with the Aid of the Calibration
Function ............................. 21
1.2.4. Verification of the Fundamental Calibration ... 23
1.2.4.1. Verification of Linearity ............ 23
1.2.4.2. Verification of Precision ............ 25
1.3. Analyses at Very Low Concentrations ................... 29
1.3.1. Decision Limit ................................ 32
1.3.2. Determining the Minimum Detectable Value ...... 34
1.3.2.1. Minimum Detectable Value,
Determined Using the Distribution
of Blank Values ...................... 34
1.3.2.2. Minimum Detectable Value, Obtained
Using the Calibration Function ....... 35
1.3.3. Limit of Quantification ....................... 35
1.3.4. Quick Estimation .............................. 36
1.3.5. Estimation of the Decision Limit and Limit
of Quantification Using the S/N Ratio ......... 37
1.4. Validation of Individual Process Steps and
Examination of Matrix Influences ...................... 37
1.4.1. Systematic Errors ............................. 37
1.4.1.1. Constant Systematic Errors,
Additive Deviations .................. 37
1.4.1.2. Proportional Systematic Errors,
Multiplicative Deviations ............ 38
1.4.2. Establishment and Assessment of the Recovery
Function ...................................... 38
1.4.2.1. Prerequisites for the
Interpretation of the
Recovery Function .................... 39
1.4.2.2. Testing for Systematic Errors ........ 40
1.4.3. Application of the Recovery Function .......... 41
1.4.3.1. Checking Individual Process Steps .... 41
1.4.3.2. Determination of the Recovery
Function to Prove the Influence
of a Matrix .......................... 45
1.5. Additional Statistical Methods ........................ 46
1.6. Use of Internal Standards ............................. 46
1.6.1. Definition, Purpose ........................... 46
1.6.2. Conditions and Limitations of the Use of
Internal Standards ............................ 47
1.6.3. Procedure ..................................... 47
1.7. Preparing for Routine Analysis ........................ 49
1.7.1. Examination of the Time Dependency of
Measured Values ............................... 49
1.7.1.1. Comparison of the "Within Batch"
Standard Deviation (sw) with the
"Between Batches" Standard
Deviation (sb) ....................... 49
1.7.1.2. Determining the Need for Daily
Adjustment of Analytical Equipment ... 51
1.7.1.3. The Trend Test ....................... 51
1.8. Summary of the Results of Phase I
(Process Development): Documentation .................. 54
2. Phase II: An Analytical Process Becomes Routine;
Preparative Quality Assurance ............................... 57
2.1. Introduction .......................................... 57
2.1.1. Objectives of Phase II ........................ 57
2.1.2. Execution of Phase II ......................... 57
2.1.3. Progression of Phase II ....................... 57
2.1.4. Results of Phase II ........................... 58
2.2. Selection of the Analytical Procedure ................. 59
2.2.1. Specificity of the Procedure .................. 60
2.2.2. Selectivity of the Analytical Procedure ....... 60
2.2.3. Working Range ................................. 60
2.2.4. Calibration Function, Sensitivity, and
Precision of the Procedure .................... 60
2.2.5. Minimum Detectable Value and Limit of
Quantification ................................ 61
2.2.6. Risk of Systematic Error ...................... 61
2.2.7. Effort, Costs ................................. 61
2.3. The "Training" Phase of the Process ................... 62
2.4. Establishment of Quality Objectives to be Adhered to
in Routine Usage ...................................... 64
2.4.1. External Quality Requirements ................. 65
2.4.2. Internal Quality Requirements ................. 66
2.5. Control Samples for Internal Quality Assurance ........ 66
2.5.1. Requirements of Control Samples ............... 66
2.5.2. Types of Control Samples ...................... 67
2.5.2.1. Standard Solutions ................... 67
2.5.2.2. Blank Samples ........................ 67
2.5.2.3. Natural Samples ...................... 67
2.5.2.4. Spiked Natural Samples ............... 68
2.5.2.5. Synthetic Samples .................... 68
2.5.2.6. Certified Reference Materials
(CRMs) ............................... 68
2.5.3. Requirements for Producers of Control
Materials ..................................... 69
2.5.4. Applicability of Control Sample Types ......... 69
2.6. The Control Chart System .............................. 70
2.6.1. Introduction: History of the Control Chart .... 70
2.6.2. Principle of a Control Chart .................. 72
2.6.3. Average Run Length (ARL) and Evaluation of
Control Charts ................................ 73
2.6.4. Derivation of the Average Run Length (ARL) .... 74
2.6.4.1. Examples of Theoretical
Calculations ......................... 75
2.6.4.2. Analytical Example ................... 76
2.6.5. Concept for the Preparation of Routine
Quality Control ............................... 78
2.6.6. Evaluation of the Preliminary Period .......... 80
2.6.6.1. Variance Analysis .................... 80
2.6.6.2. Adherence to Required Quality
Objectives .................................... 80
2.6.7. Types of Control Charts and Their
Applications .................................. 80
2.6.7.1. Shewhart Charts ...................... 81
2.6.7.2. R-Chart (Range Control Chart) ........ 89
2.6.7.3. Difference Chart ..................... 96
2.6.7.4. Standard Deviation Chart (s-Chart) ... 98
2.6.7.5. Target Value Charts .................. 99
2.6.7.6. Cusum Chart ......................... 100
2.6.8. Summary of the Characterization of Control
Charts ....................................... 112
3. Phase III: Routine Quality Assurance ....................... 115
3.1. Introduction ......................................... 115
3.1.1. Setting the Objectives of Phase III .......... 115
3.1.2. Execution of Phase III ....................... 115
3.1.3. Progression of Phase III ..................... 115
3.2. Fundamental Measures of Internal Quality Assurance ... 118
3.2.1. The Laboratory and Laboratory Management ..... 118
3.2.2. Personnel .................................... 119
3.2.3. Outfitting and Equipment ..................... 119
3.2.3.1. Performance Monitoring,
Calibration and Adjustment
of Measuring Equipment .............. 119
3.2.3.2. Maintenance of Equipment ............ 120
3.2.4. Materials .................................... 121
3.2.4.1. Certifying Sample Quality ........... 121
3.2.4.2. Analysis-Related Materials .......... 121
3.2.4.3. Control Samples for Routine
Quality Control ..................... 122
3.2.5. Instituted Analytical Processes .............. 122
3.2.6. Testing the Equivalency of Analytical
Results ...................................... 122
3.2.6.1. Testing the Equivalency for a
Single Matrix ....................... 123
3.2.6.2. Testing the Equivalency in
Different Matrices .................. 126
3.2.7. Uncertainty of Measurements .................. 130
3.2.7.1. New Terms According to the
EURACHEM Guide ...................... 131
3.2.7.2. Overview of Common Procedures for
the Determination of Measurement
Uncertainty ........................ 133
3.2.7.3. Indication of Measurement
Uncertainty in Test Reports ......... 142
3.2.7.4. Interpretation of Measurement
Uncertainty in the Context of
Limit Value Monitoring .............. 143
3.2.7.5. Summary ............................. 144
3.2.8. Reporting Analytical Results ................. 145
3.3. Routine Quality Control .............................. 145
3.3.1. Trueness Control ............................. 146
3.3.1.1. General ............................. 146
3.3.1.2. Blank Value Monitoring .............. 146
3.3.1.3. χ-Chart .............................. 148
3.3.1.4. Recovery Rate Control Chart ......... 148
3.3.2. Precision Control ............................ 148
3.3.2.1. General ............................. 148
3.3.2.2. Precision Control Using an
R-Chart ............................. 149
3.3.2.3. Securing Precision Using a
Standard Deviation Control Chart .... 149
3.3.3. Revision of Quality Control Charts ........... 150
3.3.4. Quality Assurance in the Case of Time-
Consuming or Infrequent Analyses ............. 150
3.4. Special Quality Problems in Routine Analysis ......... 151
3.4.1. Matrix Effects ............................... 151
3.5. Corrective Measures .................................. 154
3.5.1. Sources of Error in Analytical
Laboratories ................................. 154
3.5.2. Systematic Troubleshooting ................... 155
3.5.2.1. Analytical Errors That Can Be
Detected Using Statistical Quality
Control Methods ..................... 161
3.5.2.2. Plausibility Checks ................. 162
3.6. Documentation and Archiving .......................... 166
4. Phase IV: External Analytical Quality Assurance ............ 169
4.1. Introduction ......................................... 169
4.2. Audits ............................................... 169
4.3. Interlaboratory (or Round Robin) Tests ............... 170
4.3.1. Interlaboratory Tests for Process
Standardization .............................. 171
4.3.2. Interlaboratory Tests as Proof of
Laboratory Performance ....................... 171
4.3.3. Other Interlaboratory Tests .................. 172
4.3.4. Planning and Execution of Interlaboratory
(or Round Robin) Tests ....................... 173
4.3.4.1. Quality Management System of the
Provider of an Interlaboratory
Test ................................ 173
4.3.4.2. Planning the Interlaboratory Test ... 174
4.3.4.3. Interlaboratory Test Samples ........ 175
4.3.5. Procedures for the Execution and Evaluation
of Interlaboratory Tests ..................... 176
4.3.5.1. Interlaboratory Test Programs
According to ISO 5725-2 ............. 177
4.3.5.2. The Youden Method of
Interlaboratory Tests ............... 179
4.3.5.3. Interlaboratory Tests According
to ISO Guide 43 ..................... 188
4.4. Effects of Internal Quality Assurance on the
Results of Interlaboratory Tests ..................... 191
4.5. Conclusion ........................................... 194
5. Definitions ................................................ 195
5.1. Quality and Quality Management ....................... 195
5.2. Analytical Terms ..................................... 197
5.3. Analytical Results ................................... 201
5.4. Deviation, Uncertainty ............................... 202
5.5. Materials, Samples ................................... 205
5.6. Statistical Tests .................................... 206
6. References
Appendix 1
A1 Sample Calculations ..................................... 219
A1.1 Fundamental Calibration ............................ 219
A1.2 Linearity Tests .................................... 222
A1.2.1 Visual Linearity Test ...................... 221
A1.2.2 Second-Order Calibration Function .......... 222
A1.2.3 Linearity Test: Goodness-of-Fit Test ....... 224
A1.2.4 Variance Homogeneity Test .................. 226
A1.2.5 Outlier Tests for Linear Calibration ....... 228
A1.2.6 Securing the Lower Range Limit ............. 230
A1.2.7 Decision Limit, Minimum Detectable Value,
and Limit of Quantification ................ 231
A1.2.8 Recovery Function .......................... 236
A1.2.9 Testing Analytical Results for Temporal
Stability .................................. 239
A1.2.10 Trend Test ................................. 242
A1.2.11 Practice Phase: Checking the Analysis
Quality Achieved Based on the Process
Standard Deviation ......................... 243
A1.3 Phases II and III: Control Charts .................. 244
A1.3.1 Blank Value Control Chart .................. 245
A1.3.2 χ-Chart for Standard Solutions ............. 246
A1.3.3 Recovery Rate (RR) Control Chart ........... 247
A1.3.4 Verifying Precision by Means of R-Charts
and s-Charts ............................... 249
A1.3.5 Testing for Series-Internal Drift .......... 251
A1.3.6 RR-Control Chart by Addition of a
Standard ................................... 253
A1.3.7 Cusum Chart ................................ 254
A1.3.8 Equivalency ................................ 258
A1.3.9 Standard Addition ........................... 261
Appendix 2
A2 Statistical Tables ...................................... 263
A2.1 t-Table ........................................... 263
A2.2 F-Table(95%) ...................................... 264
A2.2 F-Table (99%) ..................................... 265
A2.3 Grubbs Table ...................................... 267
A2.4 χ2-Table .......................................... 268
Appendix 3
A3 Contents of the CD ...................................... 269
A3.1 Checklists ........................................ 269
A3.2 Instructions for Using the Calculation Examples ... 269
A3.3 Statistical Table Values .......................... 270
Subject Index ................................................. 271
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