The application of the measurement uncertainty concept to in-process control in pharmaceutical development

 Any analytical data is used to provide information about a sample. The "possible error" of the measurement can be of extreme importance in order to have complete information. The measurement uncertainty concept is a way to achieve quantitative information about this "possible error" using an estimation procedure. On the basis of the analytical result, the chemist makes a decision on the next step of the development process. If the uncertainty is unknown, the information is not complete; therefore this decision might be impossible. The major problem for the in-process control (IPC) procedure is that not only the repeatability but also the intermediate precision (which expresses the variations within laboratories related to different days, different analysts, different equipment, etc.) has to be good enough to make a decision. Unfortunately, the statistical information achieved from one single analytical run only gives information about the repeatability. This paper shows that the estimation of the measurement uncertainty for IPC is a way to solve the problem and gives the necessary information about the quality of the procedure. An example demonstrates that an estimate of uncertainty based on the standard deviations of an analytical method gives a value similar to one based on the standard deviations obtained from a control chart. Therefore, the estimation is both a very useful and also a very cost-effective tool. Though measurement uncertainty cannot replace validation in general, it is a viable alternative to validation for all methods that will never be used routinely. Received: 24 May 1996 Accepted: 10 August 1996     

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.¹ Received: 11 August 2001 Accepted: 22 February 2002     

Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the -optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.This research was supported in part by ARPA Grant N00174-91-C-0116 and NSF Grant NCR-92-04419.     

Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties

A spreadsheet method allowing rapid calculation of combined standard uncertainties is described. The model used allows explicitly for correlation effects, and requires a user to enter only the parameters, the calculation used to obtain the final result (including relevant influence factors), the individual standard uncertainties for the parameters, and estimates of correlation coefficients where necessary. The estimation of correlation coefficients in common cases is discussed, and it is shown that correlation is likely to be practically significant only when the correlated contribution to individual standard uncertainties is significantly over about 30% of the relevant standard uncertainty, leading to correlation coefficients |r| greater than 0.1. The implementation includes a more robust differentiation algorithm than previously reported for spreadsheet use, and initial preparation of the spreadsheets has been automated. The principle is illustrated with a simple example. Electronic Supplementary Material  Supplementary material is available in the online version of this article at and is accessible for authorized users.

A way of establishing quality of measurements in gas analysis—national and international aspects

Standardising quality of measurements at both the national and international level results in a unity in measurement that may be regarded a synonym of traceability. In gas analysis, the key issue in achieving this aim is production of gaseous reference materials. Establishing a network of secondary measurement standards at gaseous CRM producers’ sites in Ukraine might be interesting for those involved in gas analysis activities. Inevitably, problems concerning the recognition of measuring capabilities of both national metrological institutes and local CRM producers are now an international issue. Thus, the problems of national adoption of international standards, as well as harmonisation between different international documents are currently relevant, and Ukrainian experience may be useful to others in this field. Presented at the 3rd International Conference on Metrology, November 2006, Tel Aviv, Israel.     

Robust estimates of the theoretical standard deviation to be used in interlaboratory precision experiments

Interlaboratory experiments often contain results that strongly deviate from other results obtained in the same laboratory under repeatability conditions, or laboratory means that strongly deviate from other laboratory means. In ISO 5725-2 [1] and IUPAC [2], the basic standards for the organisation and analysis of interlaboratory experiments for the determination of precision of a measurement method, outlier tests are performed in order to detect such situations and to finally decide whether these values are retained in the analysis or discarded as outliers. This outlier treatment, which always has a subjective aspect, becomes unnecessary by using robust estimates of the repeatability and reproducibility standard deviation. This paper proposes to use Rousseeuw’s Q _n as an extremely robust and efficient estimate of the standard deviation. Two examples show the performance of the new method.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

Measurement uncertainty and the use of reference materials

The use of (certified) reference materials and quality control materials can form a suitable basis for evaluating measurement uncertainty of routine measurements. In particular when these materials are used for quality control purposes, it is not always evident how the quality control data can be used in the uncertainty budget of a routine measurement. Current guidance documents on the evaluation of measurement uncertainty and the use of reference materials treat this subject only in part, or in very generic terms. ISO/REMCO has established a new working group that will provide practical guidance and examples on how to use quality control data in the evaluation of measurement uncertainty. A short introduction to the subject is given.

Towards a new edition of the “Guide to the expression of uncertainty in measurement”

The “Guide to the expression of uncertainty in measurement” (GUM) is an extremely important document. It unifies methods for calculating measurement uncertainty and enables the consistent interpretation and comparison of measurement results, regardless of who obtained these measurements and where they were obtained. Since the document was published in 1995, it has been realised that its recommendations do not properly address an important class of measurements, namely, non-linear indirect measurements. This drawback prompted the initiation of the revision of the GUM in the Working Group 1 of the Joint Committee for Guides in Metrology, which commenced in October 2006. The upcoming revision of the GUM provides the metrological community with an opportunity to improve this important document, in particular, to reflect developments in metrology that have occurred since the first GUM publication in 1995. Thus, a discussion of the directions for this revision is important and timely. By identifying several shortcomings of the GUM and proposing directions for its improvement, we hope this article will contribute to this discussion. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.