## 3 Methodology
### Sentiment Analysis  
The proposed method begins with an attribute-level sentiment analysis to determine the sentiment expressed in each review regarding individual product attributes. Notably, the method presupposes that the corpus of product reviews is accessible and provided at the outset, assuming that access to the review database or the web crawling of online reviews is permitted. The sentiment analysis deals with typical online reviews that include a time stamp, target product, and textual review. In addition, it is assumed that a predefined lexicon of attribute words is given at the beginning. This attribute lexicon comprises a list of nouns that represent the product attributes of interest and importance to the decision maker. However, the construction of the lexicon, or attribute extraction, is beyond the scope of this article. Various natural language processing (NLP) methods are available for developing the lexicon, including those based on domain-expert knowledge, term frequency, TF-IDF, and topic modelling techniques, such as LDA, LSA, and BERT, among others. Further details on the techniques for attribute extraction can be found in the literature [16; 36; 37; 38; 39; 40; 41; 42]. Using the predefined attribute lexicon, the sentiment analysis identifies product attributes in each review and classifies sentiments toward individual attributes. The effectiveness of the review-based control charts significantly depends on the performance of the sentiment analysis. Therefore, it is crucial to choose an appropriate method and optimize its performance for the proposed method's success. However, it should be noted that this article's primary focus and contribution are on combining the results of the attribute-level sentiment analysis with BLCCs and DIPA, rather than advancing sentiment analysis techniques. Several techniques for sentiment analysis exist, such as deep learning-based, machine learning-based, and sentiment lexicon-based approaches. Any of these techniques can be employed within the proposed method's framework, provided that the output form meets the requirements. Hence, this article concentrates on elaborating the necessary output of the sentiment analysis, rather than explaining the techniques themselves. Additional details on the available techniques for sentiment analysis can be found elsewhere [8; 15; 43; 44; 45; 46]. Figure 3 depicts the procedure of sentiment analysis required for the proposed method. With respect to an individual attribute, \(i\) (\(i\in\{1\cdots\}\)), the sentiment analysis examines each review, \(j\) (\(j\in\{1\cdots\}\)), that is collected at a given time, \(t_{j}\) (\(t_{j}\in\{1\cdots T\}\)), and identifies two values, \(x_{i,j}\) and \(y_{i,j}\), which indicate the appearance and negativeness of attribute \(i\), respectively, as expressed in Equations (1) and (2). \[x_{i,j}= \begin{cases}1&\text{attribute $i$ is mentioned in review $j$}\\ 0&\text{attribute $i$ is not mentioned in review $j$}\end{cases}  \tag{1}\]  
\[y_{i,j}= \begin{cases}1&\text{attribute $i$ is ever mentioned negatively in review $j$}\\ 0&\text{otherwise}\end{cases}  \tag{2}\]  
Figure 2: Overview of the proposed method for review-based complaint analysis. Here, the appearance, \(x_{i,j}\), reflects the relative importance of attribute \(i\) to the customer of review \(j\). Online reviews primarily aim to share opinions and experiences with the public, as well as assist others in making purchase decisions. Therefore, customers typically review only the attributes they consider significant in their purchase decision-making. In this regard, the appearance of an attribute in a group of reviews can be a measure of the attribute's importance in the group; an attribute that appears more frequently is more important in the group. The negativeness, \(y_{i,j}\), indicates whether attribute \(i\) is negatively mentioned in review \(j\) (=1) or not (=0). In other words, it indicates whether the review contains a complaint with respect to attribute \(i\).