A computerized method for quantitative analysis of measurements derived from signals or samples of signals measured in respect with an apparatus, the method comprising the steps of, performed with one or more processors: for a set of the measurements where noise appears as a single vector with a length and a direction, producing a signature estimated from a characteristic sequence repeatable from one measurement to another corresponding to an operating condition of the apparatus; computing multidimensional statistics on the measurements in a multidimensional space with respect to the estimated signature where a value in each dimension is in correspondence to each element of the characteristic sequence, the computation of the multidimensional statistics comprising at least computation of an average distance, with respect to the estimated signature, of a center of a shell corresponding to a distribution of the measurements enveloping a signature manifold to produce a shell manifold in the multidimensional space, and computation of a thickness of the shell corresponding to an average standard deviation of the measurements with respect to a center of the shell and defining a density probability function of a measurement in the multidimensional space, the signature manifold corresponds to (i) a point of the multidimensional space when the estimated signature is computed for a given operating condition measured in the measurements, in which case the shell manifold resembles a hypersphere shell, and (ii) a domain of the multidimensional space when the estimated signature changes with respect to two or more conditions measured in the measurements, in which case the shell manifold resembles a structure enveloping the domain; and quantifying matching likelihoods of the measurements based on distances of the measurements with respect to the shell manifold in order to monitor the apparatus, wherein the thickness of the shell manifold is smaller than an average distance of a center of the shell manifold with respect to the signature manifold, thereby increasing a likelihood of detecting an anomaly exhibiting a measurement having a deviation with respect to the center of the shell manifold and reducing a computational time of said one or more processors to detect an anomaly. for a set of the measurements where noise appears as a single vector with a length and a direction, producing a signature estimated from a characteristic sequence repeatable from one measurement to another corresponding to an operating condition of the apparatus; computing multidimensional statistics on the measurements in a multidimensional space with respect to the estimated signature where a value in each dimension is in correspondence to each element of the characteristic sequence, the computation of the multidimensional statistics comprising at least computation of an average distance, with respect to the estimated signature, of a center of a shell corresponding to a distribution of the measurements enveloping a signature manifold to produce a shell manifold in the multidimensional space, and computation of a thickness of the shell corresponding to an average standard deviation of the measurements with respect to a center of the shell and defining a density probability function of a measurement in the multidimensional space, the signature manifold corresponds to (i) a point of the multidimensional space when the estimated signature is computed for a given operating condition measured in the measurements, in which case the shell manifold resembles a hypersphere shell, and (ii) a domain of the multidimensional space when the estimated signature changes with respect to two or more conditions measured in the measurements, in which case the shell manifold resembles a structure enveloping the domain; and quantifying matching likelihoods of the measurements based on distances of the measurements with respect to the shell manifold in order to monitor the apparatus, wherein the thickness of the shell manifold is smaller than an average distance of a center of the shell manifold with respect to the signature manifold, thereby increasing a likelihood of detecting an anomaly exhibiting a measurement having a deviation with respect to the center of the shell manifold and reducing a computational time of said one or more processors to detect an anomaly.