Method for analyzing intact capsules and tablets by near-infrared reflectance spectrometry

Claim 2

An analytical method for detecting adulterants in samples using a Near Infrared Reflectance Analysis (NIRS) instrument comprising the steps of: (a) obtaining spectra at an appropriate number of wavelengths for a training set of an appropriate number of unadulterated samples; (b) performing a transformation of each spectrum by representing such spectrum as a single point in hyperspace, and thus yielding a cluster of points in n-dimensional hyperspace, where n is the number of wavelengths utilized; (c) creating a large set of training set sample replicates, each replicate being the same size as the training set, by randomly selecting samples from the training set, with replacement from the training set, and thus creating a bootstrap replicate distribution; (d) calculating the center of the bootstrap replicate distribution; (e) obtaining a spectrum for an adulterated sample; (f) transforming this spectrum into a point in hyperspace; (g) forming a hyperline in hyperspace between the point in hyperspace yielded from the spectrum of the adulterated sample and the center point of the bootstrap replicate distribution; (h) forming a hypercylinder around the hyperline containing points of the training set sample replicates; (i) projecting the multivariate points of the training set sample replicates onto the hyperline to form a univariate distribution of points; (j) using this univariate distribution of points to construct confidence limits; (k) identifying as abnormal the adulterated sample, the point of which falls three central 68% quantiles outside of the cluster of points yielded by the replicate spectra obtained from the training set sample replicates of the training set.

Claim 3

An analytical method for detecting inhomogeneous samples using a Near Infrared Reflectance Analysis (NIRS) instrument comprising the steps of: (a) obtaining spectra at an appropriate number of wavelengths for a training set of an appropriate number of homogeneous samples; (b) performing a transformation of each spectrum by representing such spectrum as a single point in hyperspace, and thus yielding a cluster of points in n-dimensional hyperspace, where n is the number of wavelengths utilized; (c) creating a large set of training set sample replicates, each replicate being the same size as the training set, by randomly selecting samples from the training set, with replacement from the training set, and thus creating a bootstrap replicate distribution; (d) calculating the center of the bootstrap replicate distribution; (e) obtaining a spectrum for an inhomogeneous sample; (f) transforming this spectrum into a point in hyperspace; (g) forming a hyperline in hyperspace between the point in hyperspace yielded from the spectrum of the inhomogeneous sample and the center point of the bootstrap replicate distribution; (h) forming a hypercylinder around the hyperline containing points of the training set sample replicates; (i) projecting the multivariate points of the training set sample replicates onto the hyperline to form a univariate distribution of points; (j) using this univariate distribution of points to construct confidence limits; (k) identifying as abnormal the inhomogeneous sample, the point of which falls three central 68% quantiles outside of the cluster of points yielded by the replicate spectra obtained from the training set sample replicates of the training set.

Claim 4

An analytical method for detecting inhomogeneous samples using a Near Infrared Reflectance Analysis (NIRS) instrument comprising the steps of: (a) obtaining spectra at an appropriate number of wavelengths for a training set of an appropriate number of homogeneous samples; (b) performing a transformation of each spectrum by representing such spectrum as a single point in hyperspace, and thus yielding a cluster of points in n-dimensional hyperspace, where n is the number of wavelengths utilized; (c) creating a large set of training set sample replicates, each replicate being the same size as the training set, by randomly selecting samples from the training set, with replacement from the training set, and thus creating a bootstrap replicate distribution; (d) calculating the center of the bootstrap replicate distribution; (e) obtaining a spectrum for an inhomogeneous sample; (f) transforming this spectrum into a point in hyperspace; (g) forming a hyperline in hyperspace between the point in hyperspace yielded from the spectrum of the inhomogeneous sample and the center point of the bootstrap replicate distribution; (h) forming a hypercylinder around the hyperline containing points of the training set sample replicates; (i) projecting the multivariate points of the training set sample replicates onto the hyperline to form a univariate distribution of points; (j) using this univariate distribution of points to construct confidence limits; (k) identifying as abnormal the inhomogeneous sample, the point of which falls three central 68% quantiles outside of the cluster of points yielded by the replicate spectra obtained from the training set sample replicates of the training set.

Claim 5

An analytical method for detecting adulterants using a Near Infrared Reflectance Analysis (NIRS) instrument comprising the steps of: (a) obtaining spectra at an appropriate number of wavelengths for a training set of an appropriate number of adulterated samples; (b) performing a transformation of each spectrum by representing such spectrum as a single point in hyperspace, and thus yielding a cluster of points in n-dimensional hyperspace, where n is the number of wavelengths utilized; (c) creating a large set of training set sample replicates using a Monte Carlo integration, each replicate being the same size as the training set, by randomly selecting samples from the training set, with replacement from the training set, and thus creating a bootstrap replicate distribution; (d) calculating the center of the bootstrap replicate distribution; (e) obtaining a spectrum for an adulterated sample; (f) transforming this spectrum into a point in hyperspace; (g) forming a hyperline in hyperspace between the point in hyperspace yielded from the spectrum of the adulterated sample and the center point of the bootstrap replicate distribution; (h) forming a hypercylinder, the radius of which is 2 orders of magnitude greater than the length, around the hyperline containing points of the training set sample replicates; (i) projecting the multivariate points of the training set sample replicates by triangulation onto the hyperline to form a univariate distribution of points; (j) using this univariate distribution of points to construct confidence limits; (k) identifying as abnormal the adulterated sample, the point of which falls three central 68% quantiles outside of the cluster of points yielded by the replicate spectra obtained from the training set sample replicates of the training set.

Claim 6

An analytical method for detecting adulterants using a Near Infrared Reflectance Analysis (NIRS) instrument comprising the steps of: (a) obtaining spectra at an appropriate number of wavelengths for a training set of an appropriate number of adulterated samples; (b) performing a transformation of each spectrum by representing such spectrum as a single point in hyperspace, and thus yielding a cluster of points in n-dimensional hyperspace, where n is the number of wavelengths utilized; (c) creating a large set of training set sample replicates using a Monte Carlo integration, each replicate being the same size as the training set, by randomly selecting samples from the training set, with replacement from the training set, and thus creating a bootstrap replicate distribution; (d) calculating the center of the bootstrap replicate distribution; (e) obtaining a spectrum for an adulterated sample; (f) transforming this spectrum into a point in hyperspace; (g) forming a hyperline in hyperspace between the point in hyperspace yielded from the spectrum of the adulterated sample and the center point of the bootstrap replicate distribution; (h) forming a hypercylinder, the radius of which is 2 orders of magnitude greater than the length, around the hyperline containing points of the training set sample replicates; (i) projecting the multivariate points of the training set sample replicates by triangulation onto the hyperline to form a univariate distribution of points; (j) using this univariate distribution of points to construct confidence limits; (k) identifying as abnormal the adulterated sample, the point of which falls three central 68% quantiles outside of the cluster of points yielded by the replicate spectra obtained from the training set sample replicates of the training set.