Maintenance and Replacement Models under a Fuzzy Framework

Abstract

Uncertainty is present in virtually all replacement decisions due to unknown future events, such as revenue streams, maintenance costs, and inflation. Fuzzy sets provide a mathematical framework for explicitly incorporating imprecision into the decision-making model, especially when the system involves human subjectivity. This chapter illustrates the use of fuzzy sets and possibility theory to explicitly model uncertainty in replacement decisions via fuzzy variables and fuzzy numbers. In particular, a fuzzy set approach to economic life of an asset calculation as well as a finite horizon single asset replacement problem with multiple challengers is discussed. Because the use of triangular fuzzy numbers provides a compromise between computational efficiency and realistic modeling of the uncertainty, this discussion emphasizes fuzzy numbers. The algorithms used to determine the optimal replacement policy incorporate fuzzy arithmetic, dynamic programming with fuzzy rewards, the vertex method, and various ranking methods for fuzzy numbers. A brief history of replacement analysis, current conventional techniques, the basic concepts of fuzzy sets and possibility theory, and the advantages of the fuzzy generalization are also discussed.KeywordsCash FlowFuzzy NumberTriangular Fuzzy NumberEconomic LifePossibility TheoryThese 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.