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.

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.