A risk evaluation method to prioritize failure modes based on failure data and a combination of fuzzy sets theory and grey theory☆
Introduction
The reliability analysis of CNC (Computer Numerical Control) lathes is the key to ensure their normal operations (Zhang, 2010, Keller et al., 1982, Zhang and Sun, 2014). A CNC lathe with high reliability has low failure rate, short maintenance time, and high processing efficiency. So that it is a particularly important task to improve reliability of CNC lathes. As an important part of the reliability analysis of CNC lathe, FMECA (Failure Mode, Effects and Criticality Analysis) can identify potential failure modes and their influences, and make sure the criticality degrees of each failure mode (Liu et al., 2013, Du et al., 2017). RPN analysis, which is a part of quantitative analysis in FMECA, can evaluate risk of failure modes through calculation RPN value and ranking. In addition, it can prevent failure from occurring and make improvement measures according to the analysis results in order to improve reliability of the system (Chen et al., 2010).
Scholars at home and abroad have proposed many methods and made improvements aiming at drawbacks of traditional RPN analysis. Zadeh established fuzzy theory in 1965 (Zadeh, 1965), which provided mathematical basis for its application in the scientific research field. Bowles discussed the traditional RPN analysis and made assessment to its application. At the same time, he also gave some recommendations to improve the method, suggesting that the RPN approach should be dropped and an alternative prioritization technique may be developed (Bowles, 2003). Bowles also introduced fuzzy logic theory into reliability engineering, and conducted fault tree analysis and criticality assessment based on severity and occurrence assessment (Bowles and Pelaez, 1995). Rachieru et al. evaluated risks of failure modes of CNC lathes using fuzzy logic toolbox in Matlab, and made comparisons with the results of traditional RPN method (Rachieru et al., 2015). Liu et al. applied fuzzy sets theory and MULTIMOORA (Multiple Objective Optimization by Ratio Analysis plus Full Multiplicative Form) method to help establish assessment model of risk priority number (Liu et al., 2014). Abdelgawad et al. discussed risk management problem in construction industry using combined fuzzy FMEA and fuzzy AHP (Analytic Hierarchy Process) method, in which cost, time and quality factors were taken into consideration. The method explores the concept of fuzzy expert systems to map the relationship between impact, probability of occurrence, and detection/control, and the level of criticality of risk events (Abdelgawad and Fayek, 2010). Chin et al. proposed a fuzzy knowledge-based evaluation system for product development at the conceptual design stage. Based on the proposed approach and methodologies, a prototype system named EPDS (Expert Product Development System)-1 was developed to help to optimize product quality and reliability and costs and to reduce the iterations of redesign so as to shorten the development lead time (Chin et al., 2008).
Grey theory is also widely used in improved RPN analysis, which is popular in decision making field. Deng first proposed grey system theory in 1982 and made great improvements (Deng, 1982, Deng, 1989, Deng, 2005). Yin gave a specific bibliometric study on publication and citation patterns of grey system theory published from 1996 to 2010 through using the ISI web-based databases (Yin, 2013). Wang et al. applied grey theory to risk analysing for steam turbine system in power plant to eliminate deviation in traditional RPN analysis caused by excessive classified levels (Wang et al., 2009b). Pillay et al. improved traditional FMEA and introduced fuzzy rule base approach, and grey theory was also applied to make analysis. The advantages of the improved method were illustrated through an example of fishing vessel (Pillay and Wang, 2003). Zhou et al. determined the rankings of the failure modes by FRPNs (Fuzzy Risk Priority Numbers) from fuzzy set theory and grey theory in failure prediction of oil tanker equipment (Zhou and Thai, 2016). Liu et al. proposed a modified FMEA (Failure Mode and Effects Analysis) method based on fuzzy evidential reasoning approach and grey theory, which can prioritize failure modes under different types of uncertainties (Liu et al., 2011).
With the literature review stated above, it can be seen that fuzzy sets theory is practicable in risk assessment and management due to its too many advantages over the traditional RPN method. Grey theory could be used independently in risk analysis, also it can be used as verification of fuzzy sets theory. Furthermore, grey theory could be used combined with fuzzy sets theory to get analytical results of risk rankings of failure modes. By applying fuzzy and grey theories, the results are more realistic and there will be a flexible reflection of the real situation (Zhou and Thai, 2016).
Above all, a modified risk prioritization method is proposed in this paper by using failure data and a combination of fuzzy sets theory and grey theory. O, S, and D in traditional RPN analysis are treated as linguistic variables, and maintenance time T is introduced as the fourth variable. The importance weights of the four variables are fully taken into account. Moreover, Failure data is used in the analytical process to make expert rating more objective and easier, which improves the feasibility and practicability of the entire analysis. Fuzzy sets theory is applied to calculate FRPN value, and grey theory is adopted to make result comparisons. The proposed method is applied to a real case of risk analysis of the spindle system in a CNC lathe. Results show that the proposed method is applicable and effective. It can be concluded that the method can identify failure modes which are more risky with known failure data and makes risk assessment more objective, thus, it can provide designers with theoretical support and practical guidance.
Section snippets
Traditional RPN technology
RPN analysis is a commonly used method in FMECA, which can identify risk degree of potential failure modes, prioritize and evaluate risk. Traditionally, calculation method of RPN is (Chen, 2007, Xiao et al., 2011) where, O, S and D are occurrence, severity and detection values respectively. All of the three variables are divided into 10 levels. Obviously, RPN values range from 1 to 1000. The larger RPN value is, the more risky of failure mode will be, thus the potential problems will
Failure data of CNC lathes
For CNC lathes, failure data normally contains failure modes, stopping time, maintenance time and so on. Maintenance time means here the only maintenance time T for failure location without unnecessary waste of time. Through data processing, failure number and maintenance time of each failure mode can be obtained.
For each failure mode, occurrence O, severity S, detection D and maintenance time T are the four variables, among which, S and D are obtained by expert rating, O is obtained by
Example applying the proposed method
This section presents a real case of risk analysis of a CNC lathe applying the proposed method. Spindle system of ETC series CNC lathes in a certain company is taken as the research object, as is shown in Fig. 4. Double row cylindrical roller bearings are used at both front and rear ends of the spindle as radial supports, which own high rigidity. Torque reaches 170 Nm, which makes the spindle performs well in heavy cutting conditions. Imported V belt drive is adopted, and the motor directly
Conclusions
RPN analysis plays an important role in risk control and maintenance plan making. In this paper, a risk assessment method based on failure data and fuzzy sets theory is proposed. Through steps such as failure data processing, expert rating, model programming solution and defuzzification and so on, priority ranking of failure modes is realized. At the same time, grey theory is applied to make comparisons and verification. The proposed method is applied into a case of risk evaluation of a CNC
Funding
This work was supported by the National Natural Science Foundation of China (grant numbers 51135003, U1234208), the National Basic Research Program of China (grant number 2014CB046303), the High-class CNC Machine Tools and Basic Manufacturing Equipment of Important National Science and Technology Specific Projects, China (grant number 2013ZX04011-011), National Key Laboratory of Mechanical System and Vibration Project, China (grant number MSV201402), Scientific Research Business Fund of Central
Conflict of interest
The authors declare that there is no conflict of interest in this paper.
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No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.engappai.2019.03.023.