Abstract
Fuzzy multi-state systems (FMSSs) exist widely in practical engineering. It is usually difficult to evaluate the reliability of FMSSs because the reliability data is usually fuzzy due to the inaccuracy or imperfection of information, and there is often correlation between the main components and others which constitute the FMSSs. Although many research works with respect to the independent failure of components have been carried out, the master-slave relationship between the main components and others of the FMSSs is often ignored, thus unrealistic results are often obtained with this treatment. Based on fuzzy universal generating function (FUGF), an effective reliability analysis method of FMSSs considering the correlation and fuzziness is proposed in this paper. In the novel method, the fuzziness of reliability data and the master-slave relationship between the main and other components are taken into consideration, and the performance levels and corresponding probabilities of the non-main components are considered as conditional probability distributions. A case study with respect to the reliability analysis of hydraulic system is presented to illustrate the application of the proposed method.
Highlights
Due to abrasion, fatigue, deformation and so on, the degradation of the performance level is inevitable in a mechanical system
The conventional MSS models regard the observed reliability data of all components as crisp values, but some unrealistic results are often obtained with this treatment because of the inaccuracy or fluctuation of information, fuzzy multi-state systems (FMSSs) are proposed to overcome the deficiencies of conventional MSS models [1], [2]
I=1 where represents the structure function of the FMSS, ̃ is the composition operator, Us (z) is the z-transformation of performance level for the entire FMSS, M is the number of the possible fuzzy performance levels, gi and pi are the performance level and corresponding probability, respectively
Summary
Fatigue, deformation and so on, the degradation of the performance level is inevitable in a mechanical system. The conventional MSS models regard the observed reliability data of all components as crisp values, but some unrealistic results are often obtained with this treatment because of the inaccuracy or fluctuation of information, fuzzy multi-state systems (FMSSs) are proposed to overcome the deficiencies of conventional MSS models [1], [2]. A novel reliability assessment method for FMSSs which can take the fuzziness of reliability data caused by the inaccuracy and insufficiency of information, and the master-slave relationship between the main and other components into account is proposed in this paper. The probability of component j associated with different states at any time instant t can be expressed as pj (t) = pj (t) , pj (t) , · · · , pjkj (t). J=1 where pi (t) represents the probability of the whole system performance staying in state i at time instant t, pjij (t) is the corresponding probability of component j
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