Maria de Fátima Brilhante

This case study examines decision‐making processes within a potato chip production line, where controlling the frying oil temperature is vital for maintaining product quality. The process is considered in‐control (InC) when the mean frying oil temperature is 180°C, with a standard deviation of 4°C, and out‐of‐control (OutC) when, in a rising temperature scenario, the mean shifts to 190°C. The factory had employed a likelihood ratio decision rule, classifying temperature readings above 185°C as positive (P), indicating OutC, and those below as negative (N), indicating InC. These P/N labels were further categorized into true positive (TP), false positive (FP), true negative (TN), or false negative (FN). The factory's flagging criterion, which relied on 8‐ary sequences ending with PPP from 2‐min frying cycles, resulted in an increased FP rate and frequent production interruptions. A retrospective analysis, constrained by the lack of preserved raw temperature measurements and reliant solely on categorical labels, identified six methodological weaknesses in the original classification rule. This limitation led to the development of an exploratory scoring framework based on sensitivity and specificity, calculated from the TP/FP/TN/FN composition of each 8‐ary sequence. A consistency analysis revealed that 0‐upcrossings in the moving average of the daily scores preceded 91.9% of recorded production halts, with a median lead time of 12 min, suggesting that the scoring framework holds potential for detecting OutC from categorical process data.

Sir Ronald Fisher, considering it important to consistently obtain significant p-values to support an experimental hypothesis, and thus replicating experiments to yield independent p-values, was one of the first to carry out a meta-analysis of p-values to obtain an overall decision. Suspecting also that Mendel only reported the results that closely agreed with the hereditary laws that Mendel wanted to establish, Fisher denounced the research malpractice, eventually scientific fraud, of researchers replicating experiments with the intent of reporting the best results, in his words “too good to be true”, to support their expectations or claims. On the other hand, publication bias, which largely results from published studies showing evidence of an effect, is a source of temptation to repeat experiments, especially when the first one carried out does not provide a significant p-value that favors its publication. Therefore, if the minimum of two independent “genuine” Uniform(0,1) p-values is reported to increase the chances of publication, it is a “fake” Beta(1,2) p-value, and its use in a meta-analysis changes the distributions of combined tests for genuine p-values. Mendel random variables, useful for modeling mixtures of genuine and fake p-values, are studied in detail, as well as their use in testing independence versus correlation of p-values. In addition, an example shows the usefulness of tables with critical values that consider the existence of a small proportion of fake p-values, to reach an overall informed decision when carrying out a meta-analysis of independent p-values with commonly used combined tests.

Purpose: The healthcare sector is a primary target for cybercriminals, with health data breaches ranking among the most critical threats. Despite stringent penalties imposed by the U.S. Department of Health and Human Services Office for Civil Rights (OCR), vulnerabilities still persist due to slow detection and ineffective data protection measures. On the other hand, as organizations are often reluctant to disclose security breaches for fear of reputational and market share losses, penalties can serve as a useful proxy for quantifying losses and insurance claims. Methods: This study analyzes fines and settlements (2008–2024) using the traditional lognormal, general extreme value (GEV) and other heavy-tailed statistical models, including the geo-max-stable loglogistic law, and also the mixture models hyperexponential and hyperloglogistic. Results: Mixture models, either the hyperexponential or the hyperloglogistic, deliver the best fit for OCR penalties, and for yearly maxima, the best fit is achieved with the GEV distribution. Regarding Attorneys General fines, the hyperexponential model is optimal, with the GEV model excelling again for their yearly maxima. Hence, mixture models effectively capture the dual nature of penalty data, comprising clusters of moderate and extreme values. However, yearly maxima align better with the GEV model. Conclusions: The findings suggest that while Panjer’s theory for aggregate claims suffices for moderate claims, it must be supplemented with strategies to address extreme cybercrime scenarios, ensuring insurers and reinsurers can manage severe losses effectively.