This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length ($AR{L}_1$). Tables of $AR{L}_1$ values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of $AR{L}_1$ detecting small and moderate shifts in the process nonconforming rate in-control ($p_0$) compared with MDSRS and DS-np.

This study addresses the quantification of credit risk in solidarity economy entities, proposing a new methodology to redefine the concept of a “default” in the frequent situations of extreme class imbalances. The objective is to develop and evaluate credit scoring models that enhance risk management by incorporating internal and external data to assess default risk. Data mining techniques are applied to address class imbalances, redefining the term “default” to include external credit information and increasing the representation of the minority class. The effectiveness of machine learning and statistical models is evaluated using class-balancing methods such as under-sampling, over-sampling, and the Synthetic Minority Over-sampling Technique (SMOTE). The evaluation is based on the Balanced Accuracy metric and the holding power of the performance, ensuring a consistent predictive power of the model while avoiding overfitting. While machine learning methods can improve credit scoring, logistic regression-based models remain effective, especially when combined with class-balancing techniques. It is concluded that a balanced sample in a class size is essential to improve predictive performance.

The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the $T^2$ multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.

The functional group (FG) approach is used to predict the response of the composition of phytoplankton species to changes in the environmental conditions. We assessed for the first time the dynamics of phytoplankton communities in a High-Rate Algal Pond (HRAP), implemented for the bioremediation of landfill leachate, and using morphology-based functional groups (MBFG), under the American tropics conditions. These groups were later correlated with the physical and chemical variables of the system. Water samples were taken for biological, physical and chemical analysis for seven months. In addition, phytoplankton biovolumes were estimated and a canonical correlation analysis was performed to explain the relation between physical and chemical variables and FGs. Subsequently, the HRAP treated a medium-age leachate characterized by high concentrations of nutrients. Four MBFGs were identified (IV, V, VI and VII). Group V, conformed by phytoflagellates, was found to be dominant during the entire study period. This group proliferate in environments with high concentrations of organic matter, while contributing to the transformation of the contaminants present in the leachate. The largest biovolumes of Groups V and VII occurred during periods of low water levels and dissolved organic carbon. Finally, we show that the MBFG technique may be useful in understanding the dynamics of the phytoplankton community in the HRAP used for the treatment of landfill leachate.