# Failure Analysis for Hydraulic System of Heavy-Duty Machine Tool with Incomplete Failure Data
## 4 Conclusions  
The hydraulic system of HCMT is a complex system with a high failure rate. For its fault tree quantitative analysis, failure data contains a lot of information about reliability and is useful for measuring the probability of BEs. However, conventional FTA approaches just using failure data have some limitations in quantitative analysis.  
In this study, the proposed approach, which incorporates the experts' opinions and the conventional FTA technique, is demonstrated as a viable method for the estimation of the occurrence probability when encountered with data uncertainty and incompleteness. Through a case study, the fault tree of a hydraulic system of HCMT is constructed, and the result shows that there are 27 basic events that cause hydraulic failure in an HCMT, where oil pollution is the most critical basic event.  
The function of experts' opinions is embodied from two aspects: (1) Experts' opinions are utilized for correcting failure data with uncertainty, so that the data can be used for quantitative analysis; (2) Experts' opinions are used as supplementary information for BEs with no observed data. The purpose is to integrate the subjective information with the objective information to improve the accuracy of quantitative analysis results. Therefore, based on the above idea, the proposed approach is also applicable to the fault tree quantitative analysis of other products with incomplete failure data.  
Finally, although expert opinion was introduced for uncertainty and incompleteness of failure data, it more or less brought subjectivity. One solution is to detect the fault  
Figure 11: Comparison results of importance analysis in different cases: (**a**) Comparison between C0 and C1; (**b**) Comparison between C0 and C2; (**c**) Comparison between C0 and C3.  
accurately through analyzing condition signals of hydraulic such as vibration, flow, leakage, oil pollution, and so on, without relying on the experience of experts. Due to the complexity and ambiguity of hydraulic failure mechanism, an intelligent diagnosis approach may be needed to learn fault features from fault data. In addition, considering there is no single intelligent diagnosis approach that can be suitable for all fault diagnosis tasks, ensemble methods, such as bagging, boosting, and other rules, are also needed to combine multiple base intelligent fault diagnosis approaches to become a strong learning mode. This put forward demands on the condition monitoring technique of a hydraulic system and related algorithms, which cannot be implemented in this article, because only fault event data were obtained. Nonetheless, it provides a direction for future FTA works.  
Conceptualization: H.T. and Z.Y.; Methodology: S.L. ([PERSON]) and H.T.; Data curation: C.C. and H.T.; Software: S.L. ([PERSON]); Formal analysis and investigation: S.L. ([PERSON]) and H.T.; Writing--original draft preparation: S.L. ([PERSON]); Writing--review and editing: Y.Z. and C.C.; Funding acquii-sition: Z.Y., F.D., and C.C.; Resources: F.D. and S.L. ([PERSON]); Supervision: Z.Y. and Y.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China [Grant No. 51675227, 62073274, 62075168]; National Major Science and Technology Projects of China [Grant No. 2018 ZX04014001, 2014 ZX04015031]; Jilin Province Science and Technology Development Funds [Grant No. 20180201007 GX, 20190302017 GX]; Special Plan of Provincial School Building [SXG]SF2017-2]; Technology Development and Research of Jilin Province [Grant No. 2019C037-01]; Changchun Science and Technology Planning Project [Grant No. 198S011]; Special projects in key fields of Guangdong Provincial Department of Education of China [Grant No. 2019 KZDZX1025]; Key R & D projects in Guangdong Province [Grant No. 2019B040403003]; Shenzhen Peacock Plan of Shenzhen Science and Technology Program (Grant No. KQTD201611301047034).  
The authors declare no conflict of interest.