## 1 Introduction  
Monitoring and preserving food quality is an increasingly critical aspect of food control that has direct repercussions on human health, also having impact on our economy. The problems of food adulterations make the food items used in daily life unsafe. Adulteration in food items can have a tremendous effect on human health without our knowledge. This effect has been extensively reviewed in reference [1]. On the other hand, the FDA estimates that food fraud affects 1% of the global food industry at a cost of approximately $40 billion per year [2]. The flexibility and adaptability of near infrared (NIR) spectroscopy in the agri-food industry is well known to assess the quality of raw materials and/or the final products. During food quality control using this technology, it is possible to perform the rapid and non-destructive determination of many quality characteristics of different foods and/or the detection of potential counterfeits or adulterations. Technical advances in NIR instruments and the scalation of multivariate chemometric techniques have made this technology one of the most widely used in the analytical agri-food field, specifically in industry. To confirm this, bibliographic research was carried out over the past fifteen years, focusing, firstly, on NIR spectroscopy, secondly, on foods, and finally, on the food matrices of this paper: bibliographic research within \"Article title, Abstract & Keywords\" was carried out in Scopus using, as the keyword search, \"NIR spectroscopy\", having found a total of 31,376 publications. When also adding the word \"foods\", the number decreases to 2269. If focusing on the food matrices of this paper, the number of publications varies according to Figure 1. In those cases, the search was made by separately adding the words \"butter, flour, milk, yogurt, olive oil, and olives\" (which are the food matrices used in this work) to the previous search, having found a total of 357 publications. Among all the publications associated with food and NIR spectroscopy since the year 2010, 16% of them are related to the food matrices of this work; for instance, there are many publications referring to analyses on flour, the majority of them focused on detecting adulterations [3; 4; 5]. Studies on butter are less common but still relevant when quantifying adulterations [6; 7]. Also, in references [8; 9], different procedures based on NIR are presented to study the presence of different agrochemicals in olives. The use of multivariate soft calibration models, such as the ones based on Partial Least Squares (PLS) coupled with NIR spectroscopy signals [10], are quite common in the agri-food industry; in fact, many of the previously cited studies used it. For many years, there have been different International Organization for Standardization (ISO) documents that protocolize how to calibrate using NIR and PLS depending on the analyte and the food matrix [11; 12]. Although the importance of NIR spectroscopy and its advantages have been proven, this technique has some downsides, like its low sensitivity. For that matter, it is imperative to know, with certainty, the minimum discriminable concentration that can be detected with this calibration, that is, the capability of detection of the method or the capability of discrimination (given a target value of interest, whether it is a minimum or a maximum limit). All of this is precisely the main aim of this work, encouraged after having checked that within the latter bibliographic research mentioned, practically none of the publications that were found had used these figures of merit, only 20 (6 for flour [4; 13; 14; 15; 16; 17],  
Figure 1: Number of publications found in Scopus by searching “NIR spectroscopy” and “foods” in each food matrix used in this work. 12 for milk [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29], and 1 for olives and olive oil [30]) out of 357 (the ones schematized in Figure 1) when adding the terms \"capability of detection _or_ detection limit\" to the search.