## 1 Introduction  
Orange juice is undoubtedly one of the most commonly consumed products daily worldwide, and thus, it is one of the most commonly exported and imported food products [1]. The pioneer in orange juice production is Brazil, followed by the US, Mexico, and Europe [2]. Moreover, the consumption of orange juice is accompanied by numerous health benefits, including the fact that it is a rich source of vitamin C (ascorbic acid) and a source of many bioactive compounds like carotenoids, flavonoids, folate, and potassium [3]. Despite its many nutritional benefits, orange juice is also a very popular beverage because of its distinguished aroma, flavor, and freshness [4]. However, there is a great necessity to increase the lifetime of the products produced--as they may have to travel a long distance and be stored for a long time to reach their destination--without jeopardizing their safety or their physicochemical and sensory qualities. The most common process through which the safety of the distributed orange juices is guaranteed is thermal pasteurization, which mainly focuses on the inactivation of spoilage and pathogenic microbes and thermally resistant endogenous enzymes, like peroxidase, polyphenol oxidase, and polymethylesterase, which can lead to enzymatic browning [5, 6]. However, the thermal processing of orange juice is also correlated with a series of negative sensory attributes, such as color and ascorbic acid retention [6]. Normally, pasteurized orange juice is considered a microbiologically stable product, but several sporoforming bacteria of the genus _Alicyclobacillus_ and _Bacillus_, and more specifically _Alicyclobacillus aciodeterstris, Bacillus coagulans_, and _Bacillus cereus_, can survive pasteurization and germinate in a beneficial environment, thus leading to the deterioration of the product [7]. Nevertheless, apart from the safety point of view, it is also very important to maintain the physicochemical and sensory attributes of the product because they determine consumer acceptability. Among these, the color of orange juice is a significant attribute that is correlated with the freshness and acceptability of the product; so, the handling of the browning reactions that occur during storage before the expiration date is of high importance [8]. The main browning reactions that happen during the storage of pasteurized orange juice are enzymatic and non-enzymatic browning reactions, including the degradation of ascorbic acid, acid-catalyzed degradation of sugars, and Maillard reactions [9]. The kinetics of non-enzymatic browning reactions, which are more difficult to handle, depend on both the physicochemical attributes of products and storage conditions, such as temperature and pH, and more specifically, a higher temperature and higher pH, which intensify these reactions [10]. Under normal conditions, the mean temperature of production and distribution of pasteurized orange juice does not exceed 7 \({}^{\circ}\)C, but temperature fluctuations during storage are the main problem that affects the product's acceptability [11]. So, it is very challenging when estimating the shelf life of products to be able to incorporate these unwanted deviations of conditions. Moreover, the shelf life and expiration date estimation are based on microbiological safety and not sensorial and physicochemical characteristics or \"sensory shelf life\", which poses the risk that the product is considered safe for consumption but its sensory characteristics have been compromised, which has a negative impact on consumer acceptability [12]. A significant innovation in the field of the prediction of food shelf life is accelerated shelf life testing (ASLT), which provides the possibility of predicting the shelf life of products based on both microbial and sensory characteristics during different stressing conditions, like temperature, without extensive amounts of testing and time using different statistical models [13].