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A user-friendly MS-Excel spreadsheet is developed for evaluation of global consumer's and producer's risks in conformity assessment of chemical composition of a multicomponent material or object, when up to four component concentrations are under control. These risks are probabilities of incorrect conformity decisions related to a material batch (lot or similar) randomly drawn from a statistical population of such batches. The probabilities characterize the material quality globally, allowing the prediction of false decisions on conformity of a future batch, based on the future measurement results. The spreadsheet program evaluates risks using Monte Carlo simulations. As input data, the following need to be provided to the software: parameters of normal or lognormal distribution of actual (‘true’) values of the component concentrations (prior distribution); parameters of the distribution of measurements results at the actual value of the component concentration (likelihood function); and correlation matrices for couples of the actual components' concentrations under control and also for corresponding measurement results. The spreadsheet is validated by comparison of the risk estimates with those calculated in R programing environment by numerical integration of the relevant analytical formulae. The developed Excel file and a demonstration videos of its use are available as electronic supplementary material.

The illegal drug 3,4-methylenedioxymethylamphetamine, also known as MDMA, ecstasy or ‘E’, synthesised as the hydrochloride and then made into tablets, has organic impurities arising from manufacture that can be used to profile seized material. Knowing if two samples come from the same batch gives strategic information about the drug manufacturing trade. We report similarity measures (Pearson correlation coefficient, reported as the modified Pearson distance, and its Fisher transform) between impurity content of pairs of samples manufactured using four common reductive amination routes. Powder and tablets are compared using the n th root of GC–MS peak normalised areas of 8 or 31 impurities, ( n = 2, 3, 4, 5, 10). Overall using 31 compounds with 4th root pre-treatment gave the best discrimination. PtO 2 /H 2 , and Al/Hg reductions were completely discriminated among batches while NaBH 4 and NaBH 3 CN routes gave around 4% false assignments. Synthesis parameters were systematically altered to determine what parameters have significant effects on the overall purity of the product and on the impurity profiles. The amount ratio of methylamine and MDP2P, and the temperature control of the reaction mixture were both significant. Comparison of modified Pearson's distances ( r scaled to ∈[0–100]), the Fisher transform of r , and ROC curves are simple ways of providing initial evidence whether seized drugs originate from the same batch.

Matching spectra is necessary for database searches, assessing the source of an unknown sample, structure elucidation, and classification of spectra. A direct method of matching is to compare, point by point, two digitized spectra, the outcome being a parameter that quantifies the degree of similarity or dissimilarity between the spectra. Examples studied here are correlation coefficient squared and Euclidean cosine squared, both applied to the raw spectra and first-difference values of absorbance. It is shown that spectra do not fulfill the requirements for a normal statistical interpretation of the correlation coefficient; in particular, they are not normally distributed variables. It is therefore not correct to use a Student's t-test to calculate the probability of the null hypothesis that two spectra are not correlated on the basis of a correlation coefficient between them. We have investigated the effect on the similarity indices of systematically changing the mean and standard deviation of a single Gaussian peak relative to a reference Gaussian peak, of changing one peak, and of changing many peaks, in a simulated 10-peak spectrum. Squared Euclidean cosine is least sensitive to changes and the first-difference methods are most sensitive to changes in mean and standard deviation of peaks. A shift of the center of a peak has a greater effect on the indices than increases in peak width, but a decrease in peak width does lead to significant changes in the indices. We recommend that if these indices are to be used to match spectra, appropriate windows should be chosen to avoid dilution by regions with no significant change.

We report the use of the Kalman filter to detect the onset of chaos in a non-linear system for which the model is exactly known. The procedure is based on predicting the trajectories of a non-linear dynamical system and testing the innovation sequence for the predicted trajectory using the local overall method tests (LOMT). This is applied to the Rossler–Wegmann model of the Zhabotinskii reaction system. The Rossler–Wegmann model is a three dimensional set of non-linear ordinary differential equations, the solution to which gives the time-evolution of the concentrations of the major species in the Zhabotinskii reaction. With suitable parameters and starting values of concentrations, stable, oscillatory and chaotic solutions may be found. Five thousand points were generated from the model, for each of the three species in the model, by fourth order Runge–Kutta integration. For a complex oscillatory case the LOMT showed no chaos, and when parameters that lead to chaos were used the LOMT quickly revealed the mismatch between predicted and actual trajectories. It is concluded that the Kalman filter with LOMT is a quick and accurate method of diagnosing chaos, which could be used in a monitoring and on-line controlling system for a chemical process.

Principal components regression (PCR) and linear discriminant analysis (LDA) have been applied to the classification of ion chromatographic detectors using information about the sample and other IC method conditions (19 attributes in total), a training set of 12 693 cases and a randomly-chosen test set of 1410 cases. Missing data was entered as a separate `unknown' code. When the value of each attribute was coded in a simple cardinal series (e.g., column=1, 2, 3, etc.), PCR correctly predicted the detector in 27% of the training set and 28% of the test set. By creating a variable (taking a value between 0 (absent) and 1 (present)) for each value of each attribute, the PCR prediction for both sets increased to 60%. LDA was more successful, predicting 69% of the detectors of each set, using a prior probability of the frequency of a given detector in the database, but this included zero hits for detectors that were poorly represented in the database. If equal prior probabilities were chosen the overall success rate dropped to 33% but now the classification of less frequently used detectors was improved. The ability of these numerically-oriented methods to classify discrete, non-numerical data, is surprisingly good and compares with induction methods, neural networks and expert systems reported previously.

Gas chromatograms (GCs) of oil extracted from Eucalyptus species have been compared using principal components analysis (PCA), linear discriminant analysis (LDA), and the Tanimoto distance in which the number of similar peaks between two species are determined. Two systems were studied, a number of examples of E. camaldulensis Dehnh. (River Red Gum) and clones of that species, and samples from two trees E. woodwardii Maiden and E. torquata Luehm. and a number of their hybrids (E. torwoodii). The PCA revealed natural groupings of E. camaldulensis clones and showed, via loading plots, that eight intensities of the 180 times studied were sufficient to explain most of the variance and characterise each tree. The chemical species were identified by GC-mass spectrometry as a-pinene, 1,8-cineole, p-cymene, terpinen-4-ol/aromadendrene, cryptone, borneol, spathulenol, and torquatone. Each hybrid (E. torwood) of the trees E. woodwardii and E. torquata has a distribution of oils that lies between those of the parents. LDA was able to define two distinct groups and performed better than the Tanimoto distance in classifying the trees.

Hibbert, D.B., 1993. Generation and display of chemical structures by genetic algorithms. Chemometrics and Intelligent Laboratory Systems , 20: 35–43. A genetic algorithm (GA) is described for generating isomeric structures of a molecule given a molecular formula and information about allowed bonding of atoms. Bonds are represented by tuples of the bonded atoms. These are manipulated as the genes by a greedy procedure that attempts to maintain valid molecules. GAs that draw a molecule in two dimensions given bonding information are also demonstrated. The function to be minimised is optimum when bonded atoms are at one bond length distance from each other, and non-bonded atoms are as far apart as possible. The chromosome may be x, y coordinates or a series of angles that each atom makes with two previous atoms in a bonding list. The potential for use of GAs in three-dimensional structure determination is discussed.

Genetic algorithms (GAs) are described to optimise the rate coefficients for the hydrolysis of adenosine 5′-triphosphate by fitting a kinetic model to concentration versus time data. A simple GA is compared with one in which the genes are real variables, and to one that operates with the so-called incest prevention algorithm of Eshelman and Schaffer. The fastest convergence to a good optimum is achieved by a hybrid GA in which a steepest descent, pseudo-Newton procedure is iterated with an incest-preventing GA, each providing a starting point for the other. The best optimum was one of the results of using a pseudo-Newton routine on each of the converged population of a GA (not necessarily the best from the GA). This approach gives good results for problems having a multimodal response surface when there is no good initial guess for a traditional optimisation algorithm. After a small number of generations a GA gives good starting points for steepest ascent optimisers.

Genetic algorithms (GAs), a set of optimisation techniques, are so called after their similarity to evolutionary processes in nature. The algorithm's equivalents of genes and chromosomes are the unknown parameters of the problem and these may be mated and mutated to give better solutions. The major strengths of GAs, namely the ability to search a large parameter space with no initial guesses per se, no derivatives of the objective function and to cope with local minima, make it a candidate method for several areas of chemistry. Chemical problems that have been tackled by GAs are described and suggestions for new applications are made. Subroutines in object-oriented Pascal are given to set up a simple GA.

The concept of a fractal as a self-similar geometrical object with non-integer dimension is introduced. The measurement of fractal dimension by the box counting method is described and a program in Pascal is given. Diffusion limited aggregation (DLA), kinetics on fractals and chromatography in fractal media are used as chemical examples. A program to simulate a random DLA fractal is described.

Hibbert, D.B., 1989. A Prolog program for the calculation of isotope distributions in mass spectrometry. Chemometrics and Intelligent Laboratory Systems , 6: 203–212. The isotopic distribution of the mass spectrum of a molecule is calculated by the expansion of the equivalent polynomial in abundances and masses of the isotopes of each element. In Prolog the expansion is done symbolically more efficiently than by procedural languages. Binomial coefficients are calculated from the logarithms of factorials, themselves obtained from the Gamma function. A pruning algorithm is applied to avoid continued expansion of the polynomial when the coefficients are below a predetermined fraction of the most intense peak. The spectrum may be displayed to any mass accuracy — limited by the precision and the memory of the computer. Running on an IBM-AT clone the mass spectrum of the molecular ion bovine insulin (C 254 H 377 N 65 O 75 S 6 ) was calculated in 35 s and polystyrene n = 1000 (C 8004 H 8010 ) in 2.1 s.