Importance of Components and Power of Players

Abstract

We confine our analysis to the case where the components and hence the system cannot be repaired. In attempting to achieve high reliability of a system, a basic problem is that of evaluating the relative importance of various components comprising the system. Quantifying the relative importance of components enables one to determine the components which merit the most additional research and development effort to improve the over all system reliability at minimum cost or effort. We consider only the time independent measures of relative importance. In literature these are referred to as measures of structural importance. The same problem is encountered in game theory also. How much influence a player has on the outcome of a simple game? In this context, it will be useful to visualize a simple game as a conceptual model of a voting situation. A group of individuals (that is, the set of players) have collectively to decide whether to accept or reject a proposal. Each individual votes either ‘yes’ or ‘no’. The winning (blocking) coalitions of a simple game constitute all coalitions that can ensure acceptance (rejection) by voting yes (no). We note the close analogy between reliability systems and simple games. The functioning (failure) of a component is equivalent to a yes (no) vote of a player. The functioning (failure) of a system is equivalent to the acceptance (rejection) of the proposal. Intuitively, the power of a player is his ability to change the outcome of the game by changing his vote. There are two possible approaches for the quantification of relative importance (power) of components (players) — the axiomatic and probabilistic approaches.KeywordsJoint Probability DistributionSimple GameReliability FunctionVote GameSeries StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.