R. I. Kaiser, P. Jansen, K. Petersen, and K. Roessler, "On line and in situ quantification of gas mixtures by matrix interval algebra assisted quadrupole mass spectrometry", Rev. Scientific Instruments, 1995, Vol. 66, No. 11, p. 5226-5231.

The main objective of a mass spectrometer is to determine the chemical contents of a given gas mixture, i.e., in precise terms, to determine the partial pressures $p_1,p_2,\ldots,$ of different substances. To achieve this objective, the mass spectrometer does the following: it ionizes the gas mixture, sends the resulting ions through an electromagnetic field (thus, separating ions with different ratios $m/z$ of mass $m$ to charge $z$), and measures the currents $I_1,I_2,\ldots,$ caused by ions with different ratios $m/z$.

The main problem with these currents is that different ions have the same value of $m/z$: e.g., the ions C$_2$H$_4^+$, N$_2^+$, and CO$^+$ all contribute to $m/z=28$. Therefore, usually, the gas mixture is first {\it pre-separated} (e.g., by heating), and then mass spectrometer is applied to each of the resulting components. There are two major problems with this approach: first, unlike mass spectrometry itself, this separation requires off-line, {\it ex situ} operations; second, during this pre-separation, chemically reactive and thermally unstable gases decompose, and thus, the measured chemical contents differs from the original one.

These two problems are especially important in space missions to distant planets, because, first, pre-separation means extra payload, and second, reactive gases are an important part of the planetary atmospheres.

Theoretically, it is possible to separate different substances without an artificial pre-separation: Indeed, every substance X leads to different ions (X$^+$, X$^{+2}$, etc.), and the rate of ionization is different for different substances X. As a result, each of the observed currents $I_i$ can be represented as the sum of the components caused by different substances, i.e., as $I_i=\sum_j f_{ij} p_j$ for some coefficients $f_{ij}$ (called {\it calibration factors}). If we knew the coefficients $f_{ij}$ precisely, and if we could measure the currents precisely, then we would be able to determine the desired values $p_j$ by solving a system of linear equations $I_i=\sum f_{ij}p_j$.

In reality, the measurements are not 100\% accurate, and therefore, we only know the {\it intervals} of possible values of $I_i$ and $f_{ij}$. So, to determine the intervals of possible values of $p_j$, we must solve an interval linear system.

If the intervals for $I_i$ and $f_{ij}$ were narrow, then we would be able to use linearized methods. The authors show that in mass spectrometry, linearized methods lead to physically meaningless negative partial pressures $p_j$, and therefore, we must use the true'' interval methods (that lead to guaranteed enclosures). So, the authors arrive at the following on-line, {\it in situ} method of quantification of gas mixtures: measure the currents $I_i$ and determine $p_j$ by solving an interval linear system.

The authors experimentally tested their method and obtained a very good separation of different substances; they recommend this method for the future planetary probes.