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 1 ............................ 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 x-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 .......... 251
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 ................................................. 206
Appendix 1
A1 Sample Calculations ........................................ 219
Al.1 Fundamental Calibration ............................... 219
A1.2 Linearity Tests ....................................... 221
Al.2.1 Visual Linearity Test .......................... 221
Al.2.2 Second-Order Calibration Function .............. 222
Al.2.3 Linearity Test: Goodness-of-Fit Test ........... 224
Al.2.4 Variance Homogeneity Test ...................... 226
Al.2.5 Outlier Tests for Linear Calibration ........... 228
Al.2.6 Securing the Lower Range Limit ................. 230
Al.2.7 Decision Limit, Minimum Detectable Value, and
Limit of Quantification ........................ 231
Al.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
Al.3.1 Blank Value Control Chart ...................... 245
Al.3.2 x-Chart for Standard Solutions ................. 246
Al.3.3 Recovery Rate (RR) Control Chart ............... 247
Al.3.4 Verifying Precision by Means of R-Charts and
s-Charts ....................................... 249
Al.3.5 Testing for Series-Internal Drift .............. 251
Al.3.6 RR-Control Chart by Addition of a Standard ..... 253
Al.3.7 Cusum Chart .................................... 254
Al.3.8 Equivalency .................................... 258
Al.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 Grabbs 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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