Accuracy in Trace Analysis

Most analytical measurements are not absolute but depend on the correlation between physical phenomena and some intrinsic property, e.g., concentration. Therefore, calibration is an indispensable part of analytical chemistry. Unfortunately, calibrations are not free from interference by the environment. This disturbing environment can be the micro-environment, components in the sample that influence the calibration line. As a rule this interference is usually constant, though not always (e.g., separation processes). The macro-environment, however, changes continuously. Temperature, pressure, chemicals, and man are stationary only during a short time. These influences will be seen as random fluctuations or, when autocorrelated, as drift. One approach is to monitor the properties of the calibration system internally by incorporating a calibration system and a measuring system. By monitoring the calibration system, the results of the unknown can be corrected. Kalivas and Kowalski [1] described the solution for the multicomponent situation, using the generalized standard addition method (GSAM). By treating drift as a time dependent component they obtain the equation

Most analytical measurements are not absolute but depend on the correlation between physical phenomena and some intrinsic property, e.g., concentration. Therefore, calibration is an indispensable part of analytical chemistry. Unfortunately, calibrations are not free from interference by the environment. This disturbing environment can be the micro-environment, components in the sample that influence the calibration line. As a rule this interference is usually constant, though not always (e.g., separation processes).
The macro-environment, however, changes continuously. Temperature, pressure, chemicals, and man are stationary only during a short time. These influences will be seen as random fluctuations or, when autocorrelated, as drift. One approach is to monitor the properties of the calibration system internally by incorporating a calibration system and a measuring system. By monitoring the calibration system, the results of the unknown can be corrected. Kalivas and Kowalski [1] described the solution for the multicomponent situation, using the generalized standard addition method (GSAM). By treating drift as a time dependent component they obtain the equation A powerful method which uses all available information is "state estimation" or Kalman filtering.
Information from the past, or when starting the measurement from an educated guess, is used to predict the situation in the present.

Accuracy in Trace Analysis
where c(K)=predicted state (e.g., concentration) at time K, i(K-1)=the estimation of x at K-1, F=the transition function, and w(K)=the variance of noise.
The next step is to do a new measurement z(K).
The estimate x(K) is the best estimate that is possible. The weighting factor

G(K)=P(K)[P(K)+R (K)]-'
depends on the fluctuations in the system, expressed as covariance P(K) and the measuring error R (K).
A Kalman filter enables the on-line estimation of calibration parameters, intercept, sensitivity and drift (of both intercept and sensitivity). The filter requires a model of the system, including system noise and measurement noise. When a good model is available, the filter can predict future values or estimate best values of the changing parameters. These figures may be used to determine when a recalibration is required.
Making a number of assumptions, the usual Kalman filter algorithms can be used resulting in [4,5,6] x

G(K) =P(K)h (K){h'(K)P(K)h (K) + R (K)l'.
The quality performance of the system is controlled on-line by comparison with a predefined criterion. The decision to re-calibrate is followed by optimization of the concentration standards available. The example given treats drift as a deterministic phenomenon. Poulisse [7,8] indicated another approach, considering drift as a stochastic phenomenon. A novel approach aiming at the elimination of the human factor in calibration is the use of expert systems. An expert system allows the objective use of a large knowledge base. This knowledge base consists of facts and rules, the results of long experience. A so-called inference machine searches for the right solution given a set of starting parameters or states the starting parameters when the goal has been stated. Since the computer will not be annoyed when repeatedly asked for the conditions for a good calibration and can deliver calibration correction factors for each situation, it can be expected that this approach will give better calibration results. However, no conclusive results have been reported so far.

Introduction
In clinical laboratories, the major production processes are analytical processes. Quality management strategies must include approaches for optimizing the cost-effectiveness of analytical processes. "Cost-effective QC," in this context, is concerned with selecting or designing a quality control procedure that maximizes both the quality and productivity of an analytical process [1]. There are many factors that need to be considered, including the medically required quality for the analyte being measured, the characteristics of the measurement procedure (type of process or system, precision,