ISSN 0020-1685, Inorganic Materials, 2009, Vol. 45, No. 14, pp. 1652–1657. © Pleiades Publishing, Ltd., 2009. Original Russian Text ©V.I. Paneva, 2009, published in Zavodskaya Laboratoriya. Diagnostika materialov, 2009, Vol. 45, No. 14, pp. 68–72.

Evaluation of Adequacy of Quantitative Laboratory Chemical Analysis Techniques V. I. Paneva Scientific-Research Institute of Metrology, Yekaterinburg, Russia Received December 27, 2007

Abstract—According to GOST R ISO/IEC 17027, evaluation of adequacy of testing (analysis, measurements) techniques is a constituent element of laboratory technical competence. The stages of the work performed when evaluating adequacy of quantitative chemical analysis techniques, the range of determined metrological characteristics, and the ways of their presentation depending on the applied algorithms of evaluating the precision parameters of analysis techniques are considered. It is shown that, for the majority of the analysis techniques applied in accordance with the requirements of the regulating normative documents (ND), Russian practice of development, certification, and acceptance tolerance for measurement techniques does not necessitate a laboratory procedure of adequacy evaluation. As far as these techniques are concerned, the possibility of correctly using them in laboratory conditions is verified prior to their application for work sample analysis. Algorithms demonstrating the adequacy (experimentally verified compliance) of the analysis performed in laboratory conditions to documented requirements are recommended. DOI: 10.1134/S0020168509140283

Techniques of analysis (metering techniques, methods of measurements) regulating the procedure of analytical control play the key role in the structure of the elements which provide for the quality of analytical control (in a broad meaning of this term specified by GOST [1]) under the stipulation that the concept “anal-

ysis techniques” are interpreted taking into account definitions and such concepts as “metering technique” and “method of measurements” given in Tables 1 and 2. The section “Technical Requirements for Competence of Laboratories” in GOST R ISO/IEC 17025 [4] ascribes testing techniques and evaluation of their ade-

Table 1. List of terms with corresponding definitions Term Technique of substance [material] analysis (object of analytical control)

Technique of quantitative chemical analysis (analysis technique) Metering technique Adequacy evaluation (validation) Evaluation of adequacy of technique of substance [material] analysis (object of analytical control)

Definition

Normative document

Documented totality of procedures and regulations whose implementation ensures obtaining the results of the analysis of substance [material] (object of analytical control) with specified error and uncertainty characteristics; for qualitative analysis techniques, with specified reliability Note: Techniques of quantitative and qualitative analysis of substances [materials] (objects of analytical control) are distinguished. Totality of procedures and regulations whose implementation ensures obtaining the results of quantitative analysis (hereinafter, analysis results) with specified error (uncertainty) characteristics Note: Analysis technique is a form of metering technique). Totality of procedures and regulations whose implementation ensures obtaining the results with specified error (uncertainty) Verification by way of investigating and providing objective proof that actual requirements on specific end use are fulfilled Verification (based on objective evidence) of the fact that technique of analysis of substance [material] (object of analytical control) can be applied for concrete object or group of objects Note: Evaluation of adequacy of the technique of substance or material analysis includes requirement specifications, determination of technique characteristics, verification of the fact that the requirement can be met when applying this technique, and declaration on adequacy.

GOST (State Standard) 52361 [1]

1652

RMG (Interstate Recommendations) 61 [2]

GOST (State Standard) 8.563 [3] GOST (State Standard) R ISO/IEC 17025 [4] GOST (State Standard) 52361 [1]

EVALUATION OF ADEQUACY OF QUANTITATIVE LABORATORY CHEMICAL ANALYSIS

1653

Table 2. List of concepts and their interpretation Concept

Interpretation

References

Measuring procedure (concept used in international standards ISO/IEC 17025 and ISO/IEC 5725 [5])

Includes a totality of procedures and regulations whose implementation ensures obtainment of results with specified precision Note: According to ISO/IEC 17025, the concept of “measuring procedure” is analogous to “metering procedure” in GOST (State Standard) R 8.563. These procedures are intended for estimating the values of the measured magnitudes. The techniques are developed and documented with the goal to yield reliable estimates Estimates of the measured magnitudes Note: The results possess such properties as uncertainty, precision, and traceability.

Introduction to national standard GOST R ISO/IEC 17025 [4]

Measurement techniques Measurement results

quacy to the factors which determine correctness and reliability of testing performed in the laboratory. According to the standard requirements, the techniques developed or accepted by the laboratory can be utilized if their adequacy is evaluated; when standard methods are used (within their scope), the correctness of their application in this very laboratory should be verified. It seems reasonable to consider interpretation of such a term as “adequacy evaluation” (validation), which is given in Instruction Manual of EUROCHEM/SITAK [6], with an aim to clearly specify the meaning of the definitions fixed in GOST R ISO/IEC 17025 [4] and GOST R 52361 [1] (see Table 1). According to [6], development of the analysis techniques is reduced to development of a procedure ensuring reasonable estimation of the magnitude to be measured. This procedure involves an equation which shows how the measurement results can be obtained based on the other measured magnitudes and determines the conditions under which this equation is assumed to be valid. Evaluation of technique adequacy (validation) confirms that this equation and the aforementioned totality of conditions are sufficient for the measurements to achieve their goal. The stages of the work performed when estimating technique adequacy are shown in the figure and a range of determined quantitative analysis characteristics (validation parameters according to [7] and general efficiency indicators according to [8]) is given below: Range —of measurements (of the determined parameter) —of variations of level allowable by metering technique (MT): sample influencing factors, MT —of detectability threshold Specific characteristics —selectivity, sensitivity, extraction, linearity, resolution, resistance to external effects, etc. Quality factors of the technique —interval values (preferable) Precision —repetition limit INORGANIC MATERIALS

Vol. 45

No. 14

2009

EUROCHEM/SITAK Instruction Manual [6] EUROCHEM/SITAK Instruction Manual [6]

—limit of intralaboratory precision —reproducibility limit Correctness —shift (systematic error boundaries) Uncertainty (accuracy) —extended uncertainty (assigned error characteristics—total error limits). Validation parameters are evaluated by the developer of the technique or its user when the conditions under which the technique is utilized are different from those specified in ND which regulate this technique. The equation relating the measured magnitude to the influencing parameters allows selecting an algorithm of uncertainty evaluation. The following approaches are recommended according to the manuals [6, 8]: —identification of the main sources of uncertainly with their subsequent analysis using “cause-and-effect” diagrams to determine both concatenation and the effect of the end result on the uncertainty (for analytical procedures subject to the effect of a totality of factors)—method I;

Technique developer

User of standardized techniques in conditions of – application beyond the target distribution range – extension and modification

Specification of requirements Determination of technique characteristics

Verification of possibility to meet the requirements using this technique Confirmation of adequacy (MT attestation certificate)

Work stages implemented when evaluating adequacy of the analysis

1654

PANEVA

– utilization of the elements of total efficiency of the technique (a shift with respect to the accepted reference point: certified reference sample with an appropriate matrix, the known value of addition to the sample, etc., and the precision data which characterize the analytical process as a whole) for evaluation of extended uncertainty—method II. For the required data to be obtained using method II (depending on the planned application of the technique), the staging of special experiments is foreseen; they are aimed at determining precision and shift under conditions of convergence (during development and subsequent application of the technique in one laboratory only) or reproducibility (for the techniques to be standardized), thus implementing the requirements of the interlaboratory evaluation experiment recommended by GOST R ISO 5725-1 [5]. A statistical model (for the analysis of the integrated data)1 and the equations for calculating total standard uncertainty (when data on precision and shift are available) can be presented in the form l

y = μ' + δ r +

∑ c x' + e , i i

(1)

r

i=1 l

2 2 u c ( y ) = u ( δˆ ) r +

∑ i=1

2

S 2 2 c i u ( x i ) + -----r , n

(2)

when the experiment is staged under repetition conditions and m

y = μ' + δ R + B +

∑ c x' + e ; i i

(3)

r

i=1 2

S 2 2 u c ( y ) = u ( δˆ ) R + S L + -----r + n 2

m

∑ c u( x ) ; 2 i

2

i

(4)

i=1

m

2 2 u c ( y ) = u ( δˆ ) R + S R + 2

∑ c u( x ) , 2 i

2

i

(5)

i=1

m < l, when an interlaboratory evaluation experiment is carried out. The accepted notation used here is as follows: y is the analysis result; uc(y) is the total standard uncertainly of measurements; μ' is the reference value; δr(δR) is the shift inherent to the analysis technique and determined under repetition (reproducibility) conditions; u( δˆ r )[u( δˆ R )] is the standard uncertainty stipulated by the experiment of evaluation of the shift under repetition (reproducibility) conditions, taking into account standard uncertainty of reference value determination;

Sr(SR) is the standard deviation of the analysis results under repetition (reproducibility) conditions; n is the number of concurrent determination results; B is the 2 interlaboratory variation; S L is the estimate of B dispersion; er is the residual error (at the repetition level); x 'i is the deviation from the rated value of xi; ci is the coefficient of [dy/dxi] sensitivity; m(l) is the number of influencing magnitudes whose values varied in the experiments performed under reproducibility (convergence) conditions.2 Depending on the accepted approaches to description of precision of analysis techniques (according to GOST R 8.563 [3], PMG 43 [9], GOST R ISO/IEC 17025 [4]), which were evaluated during their development and verified during certification in the process of their validation, the precision factors can be represented as an assigned error characteristic, a characteristic of error or extended uncertainty components, and extended uncertainty components (Tables 3 and 4). As far as standardized analysis techniques are concerned, the requirements of the RF law On Ensuring Uniformity of Measurements specify that only the techniques certified according to GOST R 8.563 [3] are considered allowed for application; thus, the introduced mechanism of certification (it being the final stage of technique validation at the state level) allows authentication as follows: – An optimized procedure of admissible evaluation of the measured magnitude, comprising the equations and a totality of measurement conditions, is documented, thus making it possible to clearly determine the range of MT application (range of the measured magnitudes and MT-allowable variations in the levels of influencing factors for the sample and MT). —When implemented, the optimized procedure ensures obtaining the analysis results characterized by the precision factor, namely, extended uncertainty (assigned error characteristic), which is specified for the evaluated technique. Hence, when a certified analysis technique is used in an actual laboratory, it is possible to ascribe its precision factors to the analysis results if the adequacy (validation) of the analysis procedure implemented in the laboratory is demonstrated to correspond to the requirements of ND, regulating this very technique. The procedures evaluating adequacy of this technique for laboratory application are not necessary since all the responsibility for the precision factor values specified in ND is borne by the organization which has attested this technique and which is accredited for such activity in statute-established order. 2 Interactions

1 According

to GOST R ISO 5725-2-2002 [10] and GOST R ISO 5725-4-2002 [11], for interlaboratory evaluation experiment.

of influencing magnitudes should be taken into account (in the case of their significance) when determining a precision factor of the technique (extended uncertainty.) INORGANIC MATERIALS

Vol. 45

No. 14

2009

EVALUATION OF ADEQUACY OF QUANTITATIVE LABORATORY CHEMICAL ANALYSIS

1655

Table 3. Comparative analysis of two approaches to presentation of quality indices of analysis technique (method I of evaluating analysis technique precision) Assigned error characteristic, characteristics of error components

Extended uncertainty, components of extended uncertainty

Δp – confidence boundary of erro σΣ – error MSD (mean-square deviation) (σΣ ≈ SΣ) σr – MSD of random error component (σr ≈ Sr) Θi – confidence boundaries of the systematic error of the ith influencing factor Kp – superimposed fractile for confidence probability p = 0.95 X – results of analysis X ± Δp, p – form of presentation of analysis results,

k(p) – coverage ratio y – results of analysis y ± U, k(p) – form of presentation of analysis results,

1 2 2 where Δp = KpσΣ = Kp σ r + --- ∑ Θ i 3

where U = k(p)us = k(p) ( ∑ u y ) A + ( ∑ u y ) B 2

When a technique is used within the scope its application range, the task of the laboratory is to confirm that the analysis procedure corresponds to the requirements specified in ND, which envisages the following: —verification of availability of all required analysis conditions; —control over compliance of operations and regulations, implemented in the laboratory during analysis, with ND requirements; — experimental verification of the possibilities that the results of the analysis to be performed in the laboratory will have the precision meeting ND requirements for this very technique. The choice of methods of experimental verification depends, in turn, on the ways of evaluating the obtained precision factor for this analysis technique. As far as the techniques with stage-by-stage evaluated extended uncertainty are concerned (method I of evaluating the precision factor for the technique), it is admissible to demonstrate the adequacy of the analysis in the laboratory by experimental verification of the factors whose standard uncertainties calculated using type A significantly contribute to total uncertainty. The experimental procedure can correspond to that used for technique certification. For the procedures of verification and subsequent stability control over the analysis results, obtained using the techniques belonging to this group, to be effective, it is relevant to specify the sources of uncertainty contributing to its budget and requiring verification and subsequent control in the technology attestation certificate. For the techniques with the values of extended uncertainty specified based on the data on shifts and precision evaluated using the results of interlaboratory experiments (method II of evaluating precision factor for the technique), the adequacy of the laboratory analysis to the technology requirements can be demonstrated using one of the following methods: INORGANIC MATERIALS

Vol. 45

U – extended uncertainty us – total standard uncertainty (uy)A – standard uncertainties estimated by type A (uy)B – standard uncertainties estimated by type B

No. 14

2009

2

(1) evaluation of the quality of the analysis results and verification of their compliance with the quality index for this technique during a special laboratory experiment (this experiment and evaluation algorithms can be implemented in accordance with Appendices B and C of interstate recommendations RMG 76 [12]; (2) evaluation of the compliance of repetition of the analysis results and laboratory shift (evaluation of the difference between the result which is the average from those obtained during a single analysis under repetition conditions and reference values) with ND requirements during laboratory technique implementation (the algorithms used according to R 50.1.060 [13]). When specifying the norms of internal control, the quality factors of the analysis (in the first case) and the quality factors of the technique (in the second case) are used as a base when verifying the adequacy of the analysis. Managers on quality (no matter how such position in the laboratory is called) are responsible for the procedures of compliance verification. Work procedures and registration of the obtained results should be specified in the Quality Manual. Positive conclusions on the results, obtained when verifying adequacy of the analysis and the specified requirements, form the base for using the technique in the laboratory and for organizing subsequent intralaboratory control aimed at ensuring the required precision of current analysis results and guaranteeing stability, thus providing for the control over the analytical process in the laboratory. When evaluating the laboratory competence, the task of experts of SAAL (System of Accreditation of Analytical Laboratories) is to substantiate the validity of algorithms of laboratory procedures from the point of view of their compliance with the requirements of GOST R ISO/IEC 17025 [4] on the technique taking into account the existing Russian practice of implementation of norms, regulations, and GSI provisions. In

1656

PANEVA

Table 4. Comparative analysis of two approaches to presentation of quality indices of analysis technique (method II of evaluating analysis technique precision) Assigned error characteristic, characteristics of error components

Extended uncertainty, components of extended uncertainty

Precision factor of technique Δ – assigned error characteristic (interval estimate)* U – extended uncertainty (interval estimate) σ(Δ) – MSD (mean-square deviation) of the assigned error us – total standard uncertainty (point estimate)* characteristic (point estimate)** Δ = Zσ(Δ), where Z is distribution fractile [σ(Δ) ≈ S(Δ)] U = k(p)us, where k(p) is coverage ratio X ± Δ, P – form of presentation of analysis results y ± U, k(p) – form of presentation of analysis results X – results of analysis y – analysis results Technique reproducibility index σR – MSD (mean-square deviation) of technique reproducibil- SR – estimate of standard reproducibility deviation stanity (σR ≈ SR) dard uncertainty (under reproducibility conditions) Technique repetition index σr – MSD (mean-square deviation) of technique repetition (σr Sr – estimate of standard repetition deviation standard ± Sr) uncertainty (under repetition conditions) Technique validity index Θ – estimate of mathematical expectation of the systematic δˆ – estimated shift (correction to analysis results) error (correction to analysis results) Δs – estimate of the systematic error of the technique Δs = ZΔs

U( δˆ ) – extended uncertainty of the shift estimate, U( δˆ ) = k(p)u( δˆ )

σs – MSD of the nonexcluded systematic error (σs ≈ Ss)

u( δˆ ) – standard uncertainty of shift estimate

Notes: * Δ = |Δlow| + Δup , where [Δlow + Δup] are the boundaries of 2 Sr the interval where the error of any of the analysis results * u = u ( δˆ ) 2 + S 2 , where S 2 = S 2 + ----, s R R L from the totality obtained using the technique is found n tainty of interlaboratory variation. with accepted probability.

2

S L – is standard uncer-

2

2 2 2 2 σr ** σ(Δ) = σ s + σ R , where σ R = σ L + ------ , n – the number n of the results of parallel determination, specified for the technique in ND; σL – MSD of interlaboratory variations (ΔL ≈ SL).

turn, with the goal to harmonize the Russian regulatory base with international documentation and to create conditions for mutual recognition of the results, it is necessary to liven up the efforts in the field of transition to the uncertainty concept in normative documentation; to revise fundamental standards and, first of all, GOST R 8.563 [3] and PMG 61 [2], which harmonize with ISO; to implement different recommended approaches to evaluation of uncertainty of analytical measurements [8, 10, 11]; and to ensure traceability of their results. REFERENCES 1. GOST (State Standard) R 52361: Analytical object control, 2005. 2. RMG(Interstate Recommendations) 61 GSI: Indicators of accuracy, correctness and precision of quantitative chemical analysis techniques, 2003. 3. GOST (State Standard) 8.563 GSI: Metering techniques, 1996.

4. GOST (State Standard) R ISO/IEC 17025: General requirements to competence of testing and calibrating laboratories, 2006. 5. GOST (State Standard) R ISO 5725-1: Accuracy (correctness and precision) of methods and results of measurements, 2002. 6. Rukovodstvo EUROCHEM/SITAK. Proslezhivaemost’ v khimicheskikh izmereniyakh. Rukovodstvo po dostizheniyu sopostavimykh rezul’tatov khimicheskogo analiza. Per. s angl. (Tracability in chemical measurements. Manual on obtaining comparable results of chemical analysis., St. Petersburg: VNIIM im. Mendeleeva, 2005, 52 P. 7. Vaganova, O.A., Kasatkin, I.A., and Skobelev, D.O., Validation of analytical techniques, Metody Otsenki Sootvetstviya, 2007, no. 8, pp. 12-14. 8. Rukovodstvo EUROCHEM/SITAK. Kolichestvennoe opisanie neopredelennosti v analiticheskikh izmereniyakh. Per. s angl. (Quantitative description of uncertainty in analytical measurements), St. Petersburg: VNIIM im. Mendeleeva, 2002, 139 P. INORGANIC MATERIALS

Vol. 45

No. 14

2009

EVALUATION OF ADEQUACY OF QUANTITATIVE LABORATORY CHEMICAL ANALYSIS 9. RMG(Interstate Recommendations) 43 GSI: Application of “Manual on expressing uncertainties of measurments”, 2001. 10. GOST (State Standard) R ISO 5725-2: Accuracy (correctness and precision) of methods and measurement results. Part 2. The main method of determining repetition and reproducibility of a standard method of measurements, 2002. 11. GOST (State Standard) R ISO 5725-4: : Accuracy (correctness and precision) of methods and measurement

INORGANIC MATERIALS

Vol. 45

No. 14

2009

1657

results. Part 4. The main methods of determining correctness of a standard method of measurements, 2002. 12. RMG (Interstate Recommendations) 76: State system of ensuring unity of measurements. Internal quality control over results of quantitative chemical analysis, 2004. 13. R 50.1.060: Statistical methods. Manual on application estimates of repetition, reproducibility and correctness when evaluation uncertainty of measurements, 2006.