In this paper, a statistical distribution is presented that possesses the ability to describe failure rates exhibiting both monotonic and non-monotonic behaviors, and the bathtub curve, which represents the performance of a device in reliability engineering. The proposed distribution is based on the sum of the hazard functions of the Chen distribution and the Perks distribution, thus presenting the Chen–Perks distribution (CPD). Statistical properties of the CPD focused on reliability engineering are presented to make the model attractive to practitioners of the discipline. The parameters of the CPD were calculated via the maximum likelihood estimator. On the other hand, a comparative analysis was conducted in three study cases to determine the behavior of the CPD relative to other distributions that can describe failure times with the shape of a bathtub curve. The results show that the CPD can offer competitive results, which practitioners can consider when conducting reliability analysis.

The Ant Colony Optimization (ACO) algorithms have been well-studied by the Operations Research community for solving combinatorial optimization problems. A handful of researchers in the Data Science community have successfully implemented various ACO methodologies for rule-based classification. This family of ACO algorithms is referred to as AntMiner algorithms. Due to the flexibility of the framework, and the availability of alternative strategies at the modular level, a systematic review on the AntMiner algorithms can benefit the broader community of researchers and practitioners interested in highly interpretable classification techniques. In this paper, we provided a comprehensive review of each module of the AntMiner algorithms. Our motivation is to provide insight into the current practices and future research scope in the context of the rule-based classification. Our discussions address ACO methodologies, rule construction strategies, candidate selection metrics, rule quality evaluation functions, rule pruning strategies, methods to address continuous attributes, parameter selection, and experimental settings. This review also reports a summary of real-life implementations of the rule-based classifiers in diverse domains including medical, genetics, portfolio analysis, geographic information system (GIS), human-machine interaction (HMI), autonomous driving, ICT, quality, and reliability engineering. These implementations demonstrate the potential application domains that can be benefitted from the methodological contributions to the rule-based classification technique.