Generalized integrated importance measure for system performance evaluation: application to a propeller plane system

The integrated importance measure (IIM) evaluates the rate of system performance change due to a component changing from one state to another. The IIM simply considers the scenarios where the transition rate of a component from one state to another is constant. This may contradict the assumption of the degradation, based on which system performance is degrading and therefore the transition rate may be increasing over time. The Weibull distribution describes the life of a component, which has been used in many different engineering applications to model complex data sets. This paper extends the IIM to a new importance measure that considers the scenarios where the transition rate of a component degrading from one state to another is a time-dependent function under the Weibull distribution. It considers the conditional probability distribution of a component sojourning at a state is the Weibull distribution, given the next state that component will jump to. The research on the new importance measure can identify the most important component during three different time periods of the system lifetime, which is corresponding to the characteristics of Weibull distributions. For illustration, the paper then derives some probabilistic properties and applies the extended importance measure to a real-world example (i.e., a propeller plane system)

Switching-Algebraic Calculation of Banzhaf Voting Indices

This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation, and (b) computation of the weight (the number of true vectors or minterms) of a switching function. Both operations can be considerably simplified and facilitated if the pertinent switching function is symmetric or it is expressed in a disjoint sum-of-products form. We provide a tutorial exposition on how to implement these two operations, with a stress on situations in which partial symmetry is observed among certain subsets of a set of arguments. We introduce novel Boolean-based symmetry-aware techniques for computing the Banzhaf index by way of two prominent voting systems. These are scalar systems involving six variables and nine variables, respectively. The paper is a part of our ongoing effort for transforming the methodologies and concepts of voting systems to the switching-algebraic domain, and subsequently utilizing switching-algebraic tools in the calculation of pertinent quantities in voting theory

Reliability Optimization and Importance Analysis of Circular-Consecutive k

The circular-consecutive k-out-of-n:F(G) system (Cir/Con/k/n:F(G) system) usually consists of n components arranged in a circle where the system fails (works) if consecutive k components fail (work). The optimization of the Cir/Con/k/n system is a typical case in the component assignment problem. In this paper, the Birnbaum importance-based genetic algorithm (BIGA), which takes the advantages of genetic algorithm and Birnbaum importance, is introduced to deal with the reliability optimization for Cir/Con/k/n system. The detailed process and property of BIGA are put forward at first. Then, some numerical experiments are implemented, whose results are compared with two classic Birnbaum importance-based search algorithms, to evaluate the effectiveness and efficiency of BIGA in Cir/Con/k/n system. Finally, three typical cases of Cir/Con/k/n systems are introduced to demonstrate the relationships among the component reliability, optimal permutation, and component importance

Determining the set of the most important components for system reliability

Mere značajnosti (Importance measures) predstavlјaju načine merenja, tj. brojčanog iskazivanja značajnosti pojedinih komponenata u sistemu sa aspekta ukupne pouzdanosti sistema. Merama značajnosti je moguće odrediti (izdvojiti) komponente najznačajnije za pouzdanost sistema. Od šezdesetih godina, kada je koncept mera značajnosti prvi put uveden, do danas postoji neprekidno interesovanje za ovu oblast, tako da se, pored primene tradicionalnih mera značajnosti, neprestano uvode i definišu nove mere radi njihove primene na specifične sisteme. Opšti nedostatak mera značajnosti, nezavisno od kategorije kojoj pripadaju, je taj što se one utvrđuju za svaku pojedinačnu komponentu, a tek nakon toga se može izdvojiti skup najznačajnijih komponenata zadate kardinalnosti...Importance measures are numerical representations of the importance of each system’s component considering total system reliability. Using importance measures, the most important components for system reliability can be determined. Since the sixties, when the concept of importance measures was first introduced, there is a constant interest in this area, so that, in addition to the traditional importance measures, new measures for specific systems observed are continually introduced and defined. The general weak point of importance measures, irrespective of the category they belong to, is that they are determined for each individual component, and only afterwards a certain number of most important components can be set aside..