Random Fuzzy Unrepairable Warm Standby Systems
Usually, the lifetimes of components in operation and in warm standby are assumed to be random variables. The probability distributions of the random variables have crisp parameters. In many practical situations, the parameters are difficult to determine
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Abstract Usually, the lifetimes of components in operation and in warm standby are assumed to be random variables. The probability distributions of the random variables have crisp parameters. In many practical situations, the parameters are difficult to determine due to uncertainties and imprecision of data. So it is appropriate to assume the parameters to be fuzzy variables. In this paper, the lifetimes of components in operation and in warm standby are assumed to have random fuzzy exponential distributions, then reliability and mean time to failure (MTTF) of the warm standby systems are given. Finally, a numerical example is presented. Keywords Reliability · Mean time to failure · Random fuzzy variable · Random fuzzy exponential distribution · Warm standby system.
1 Introduction Warm standby is a technique widely used to improve system reliability and availability. Warm standby means that the inactive component can fail at the standby state. Warm standby systems have been investigated extensively in the past. In classical reliability theory, the lifetimes of the components in operation or warm standby are considered as random variables. For example, Dhillon and Yang [1], Li et al. [2], Mokaddis et al. [10], Naidu and Gopalan [11], She and Pecht [12], Tan [13], Uematsu and Nishida [14], Vanderperre [15], Wang and Ke [16], Yuan and Meng [17] and so on. In practice, the probability distribution is known except for the values of parameters. For example, the lifetime of a component is exponentially distributed variable Y. Liu (B) · L. Wang · X. Li Department of Computer Sciences, Tianjin University of Science and Technology, Tianjin 300222, China e-mail: [email protected]
B.-Y. Cao and H. Nasseri (eds.), Fuzzy Information & Engineering and Operations Research & Management, Advances in Intelligent Systems and Computing 211, DOI: 10.1007/978-3-642-38667-1_49, © Springer-Verlag Berlin Heidelberg 2014
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with parameter λ, in which λ is obtained by history data. But sometimes there is a lack of sufficient data. So it is more suitable to consider λ as fuzzy variable. Random fuzzy theory introduced by Liu [3] is one of the powerful tools to deal with this kind of phenomena. But just some researchers have paid attention to the reliability problems by using this theory. Zhao et al. [19] used random fuzzy theory into renewal process, which was a very useful tool to deal with repairable systems. Zhao and Liu [18] provided three types of system performances, in which the lifetimes of redundant systems were treated as random fuzzy variables. The lifetimes and repair times of components were assumed to have random fuzzy exponential distributions in Liu et al. [8], then the limiting availability, steady state failure frequency, mean time between failures, mean time to repair of the repairable series system were proposed. Liu et al. [9] considered a random fuzzy shock model and a random fuzzy fatal shock model, then bivariate random fuzzy exponential distribution was derived from the random fuzzy fatal shock m
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