Abstract
This paper investigates Posbist reliability theory for typical systems with multicomponents. This theory is based on possibility and binary-state assumptions. It works well under situations of insufficient data and epistemic uncertainty. When the lifetime of every component of a typical system is assumed unrelated and a normal, strictly convex fuzzy variable in some possibility space, the Posbist reliability is concretely derived where the exactly value can be obtained at any moment, unlike existing ones only given by a lower and upper bound. We numerically compare the Posbist reliability between typical systems of four types: series, parallel, series-parallel, and parallel-series. Moreover, numerical safety evaluations are given based on possibilistic and probabilistic models.
Highlights
Failures are always inevitable in many industrial systems
The theory was further developed to be three branches: the Posbist reliability theory based on possibility and binary states [11,12,13]; Profust reliability theory based on probability and fuzzy states [14,15,16]; and Posfust reliability theory based on possibility and fuzzy states [17]
Afterwards, a new possibilistic reliability index definition was proposed [18]. e fuzzy reliability theory was extended to structural reliability analysis [19] and reliability analysis of system with fuzzy random variables [20]
Summary
Failures are always inevitable in many industrial systems. To measure the uncertainty of failures, the probabilistic reliability method, defining reliability by probability, is a remarkably successful tool [1,2,3,4,5,6,7]. As for the complex structure in practical engineering, natural language is widely used to express the fuzzy information Another useful theory, the fuzzy reliability theory, was developed. In [26], the authors considered typical systems with n components where distribution functions of the lifetime of the components were assumed to be different. Erefore, for more general cases, a given system has a symmetrical Gaussian fuzzy variable and multiple components with different possibility distribution functions. Obtaining possibility distribution function of the system lifetime and Posbist reliability is a challenging problem. Due to the existence of insufficient and vague data in practical systems, the problem of Posbist reliability modeling and analysis for typical systems with multicomponents is further investigated in this paper via the possibility theory. Numerical examples are provided to illustrate the feasibility of the obtained results
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