The development of a mathematical model is an important step in reliability analysis. However, initial data are often not clearly defined, and some necessary information about the system’s behavior may be missing. Most mathematical models in reliability analysis primarily address aleatory uncertainty. However, recently, many problems in reliability analysis increasingly need to take into consideration epistemic uncertainty. Therefore, methods for developing mathematical models based on uncertain initial data should be refined to account for both aleatory and epistemic uncertainties. This is particularly true for models that represent a system using binary decision diagrams (BDDs). This paper proposes a new method for constructing a system’s mathematical model in the form of a BDD based on incomplete and uncertain data. Machine learning approaches and principles are employed in this method to account for the epistemic uncertainty of the initial data. A fuzzy classifier, specifically a fuzzy decision tree (FDT), is used to build a BDD from epistemically uncertain data. The use of a tree‐based classifier allows simplifying the transformation between FDT and BDD.

The structure function is an often-used mathematical representation of the investigated system in reliability analysis. It is a binary function that models a system state according to the states of its components. The size of the structure function depends on the number of components and can be enormous for systems with many components. Therefore, the system reliability analysis based on the structure function needs special methods to decrease this dimension and to measure the system reliability. The concept of survival signature provides a useful transformation of the structure function to simplify reliability assessment for systems with many components of specified types. The survival signature is a complete probabilistic description of the system. The new methods and algorithms of system reliability analysis based on this mathematical representation should be developed. The Direct Partial Logic Derivative is one of the approaches that are effective in system reliability evaluation based on the structure function. This approach is used to determine different aspects of system failure depending on system components breakdowns. The development of this derivative for survival signature permits to obtain the new method for the reliability analysis of system failure caused by system component breakdown depending on components types.

Electroencephalogram (EEG) signal classification is used in many applications. Typically, this classification is implemented based on methods which consist of two steps. These steps are known as the step of signal preprocessing and the step of the classification. The signal preprocessing step transforms initial signal into classification attributes. According to several studies, this transformation can result in the loss of some useful information and, consequently, the formed classification attributes are uncertain. This information loss can be taken into account if the classification attributes are fuzzy and the fuzzy classifiers are used at the step of classification itself. The transformation of initial EEG signal into fuzzy attributes needs one more procedure at the step of signal preprocessing. This procedure is fuzzification. An approach based on fuzzy classifiers for EEG signal classification is considered in this article. The approach is evaluated based on two classifiers: fuzzy decision tree and fuzzy random Forest. The classification accuracy is 99.5% for fuzzy decision tree and 99.3% for fuzzy random forest. The comparison with similar studies based on non-fuzzy classifiers indicates that fuzzy classifiers are effective tool for EEG signal classification and have best classification accuracy.

The binary information technology reaches its limits set by the atomic size miniaturization, by calculation speed and by the fundamental principle of energy dissipation per bit processing. Employing multiple-valued logic (MVL) cells as computing and memory units reduces energy losses and enables to pack of unprecedented high-density information, but the current silicon-based material technologies have been studied marginally for the material realization of MVL devices. Here, we propose to use the ferroelectrics for the implementation of MVL units using their ability to pin the polarization as a sequence of multistable states. More specifically, the realization of a programmable logic array (PLA) based on MVL units is considered with the application of the ferroelectrics technology in implementation of memory units. The specific of the PLA construction is the use of generalized Reed-Muller expression for the representation of an MVL function. In this article, several possible implementations of such PLAs are considered, and their properties are analyzed from the logic design point of view.

A typical algorithm for signal classification consists of two steps: signal preliminary transformation and classification itself. The procedures of preliminary transformation are used to extract specific features of the initial signal and reduce its dimension for effective classification. The result of this transformation is information loss of initial signal, which implies uncertainty of data used in classification. This uncertainty can be taken into account by the application of fuzzy classifiers. In this paper, a new algorithm with application of fuzzy classifier is proposed for signal classification. A new procedure of fuzzification is added into the preliminary transformation and fuzzy decision tree is used for classification. The efficiency of this algorithm is examined based on the problem of detection of defective blades of an aircraft engine gas turbine. The experiments showed that the accuracy of the classification for the considered example is 0.989. This is the best result in comparison with other classification methods used to solve this problem.

The paper is devoted to classification of MMPI (Minnesota Multiphasic Personality Inventory) profiles using fuzzy decision trees generated by means of the algorithm that uses cumulative information estimations of the initial data proposed by V. Levashenko et al.All of the stages of the classification process (i.e., fuzzification of the input data, generation of the classifier, testing the classifier) are presented and the results are discussed.A special attention is focused on determination of the center points on the MMPI scales for the fuzzification process.

Reliability is one of the principal characteristics in the design of many systems. Logic circuits are one of them. These systems are very interesting objects from the reliability point of view, because they have some characteristics that are not very common in classical approaches used in reliability engineering. First, their activity depends not only on the operability of its components (logic gates), but also on other influences, which are represented by values of the circuit input signals. Second, logic circuits are typical instances of noncoherent systems. We propose a new method of computing circuit availability (unavailability) and several measures for investigation of topological properties of a logic circuit. These measures allow us to detect components (logic gates) with the greatest influence on the circuit operability. The method is based on using the methodology of Boolean differential calculus. All the approaches presented in this paper are illustrated using the example of reliability analysis of a one-bit full adder.

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Structure function is one of the possible mathematical models of the real systems under study in reliability engineering. The structure function represents the correlation the system performance level and components states. The system performance level is defined from the states of all its components. It means that all possible components states and performance levels must be indicated and reflected in the structure function. Initial data for the analysis of real system is uncertain. New methods to construct a structure function based on initial uncertain data is proposed. Fuzzy decision trees (FDTs) are used in this method to transform initial uncertain data about a real system into an exact-defined a system structure function. The proposed method includes three principal steps for the structure function construction: 1) collection of data in the repository; 2) representation of the system model in the form of an FDT; and 3) construction of the structure function based on the FDT.

Data mining (DM) is a collection of algorithms that are used to find some novel, useful and interesting knowledge in databases.DM algorithms are based on applied fields of mathematics and informatics, such as mathematical statistics, probability theory, information theory, neural networks.Some methods of these fields can be used to find hidden relation between data, what can be used to create models that predict some behavior or describe some common properties of analyzed objects.In this paper, we combine methods of DM with tools of reliability analysis to investigate importance of individual database attributes.Results of such investigation can be used in database optimization because it allows identifying attributes that are not important for purposes for which the database is used.Our approach is based on some coincidence between the key terms of DM and reliability analysis.

Reliability is a very important characteristic of many systems. However, there are some problems how to represent a complex system that contains a lot of different components. The problem of component variability can be solved by using Multi-State Systems (MSSs), which consists of components with different number of performance levels. The problem of large system dimension can be solved by using decision diagrams for system representation. However, new algorithms have to be developed for reliability analysis of MSSs represented by decision diagrams. A possible way is the extension of existing tools of reliability analysis on this representation of a MSS. Direct Partial Logic Derivatives (Direct Partial Logic Derivatives) are one of the tools that have been expanded on decision diagrams. Direct Partial Logic Derivatives can be used in reliability analysis to model the consequence of the component performance change on the system performance. Therefore, they can be used to find components that have the most influence on the system reliability. In some papers, there have been proposed algorithms that can be used to compute Direct Partial Logic Derivatives from decision diagrams. However, their computational complexity has not been yet studied. In this paper, we summarize these algorithms and analyze their time complexity using some benchmarks that are often used to compare the complexity of algorithms designed for logic synthesis.

The principal goal of application of information technologies in medicine is improvement of medical care. Modern healthcare systems have to guarantee perfect care of patient. Therefore, the healthcare has to be characterized by high reliability first of all and reliability analysis of such system is an important problem. Most of the reliability analysis methods suppose the investigation of the structure of a system. But the healthcare system consists of heterogeneous components, such as software, hardware, human factor and etc. The structure definition for such system is a complex problem. We propose original approach for the construction of a healthcare system structure based on the monitoring of the system behavior. The monitoring examples are interpreted as Direct Partial Logic Derivatives of the structure function of the healthcare system. The structure function defines the correlation between system components states and system performance level unambiguously.

This paper presents a pedagogical model of online student collaboration and discusses results of collaboration of students from UK, Netherlands, Germany and Australia, participated in peer-evaluation of multimedia presentations. Analysis of the post-collaboration survey revealed that, while students, irrespective of their role in the collaboration, responded positively to perceived academic benefits of engaging in discussion, they had more critical attitudes toward specific parameters of the collaboration - timing of the activity and its general planning, allocation of projects between evaluators and shortage of social, off-topic interaction.