Grey Theory

In the grey theory, before modeling, we usually take a relaxative operator to the original series according to the quditative analysis. It will result to that the disturbance to the series will be weakened, and also result to a desirable effect. 

Liu W.S. 2005. The study of Shanghai stock price index based on Grey Theory and Autiregressive integrated moving average models. Master dissertation. HoHai University, Nan Jing. 

OVERSEAS INVESTMENT RISK ASSESSMENT MODEL FOR MINING ENTERPRISE ON THE BASIS OF THE GREY THEORY SYSTEM... 

Keywords Failure mode and effects analysis, fuzzy set, grey theory, risk ranking. 

To find the degree of relation, the weighting coefficients (fik) of the decision factors must first be decided. For the application of the grey theory to FMEA, yS should be set to suit the intention of the FMEA and comply with Equation (7.4). 

The flowchart in Figure 7.4 illustrates the grey theory method to rank the events, which are identified in the FMEA process (Pillay (2001), Pillay and Wang (2003)). The first step is to set up the membership function of the three categories (probability of occurrence (S/), severity (S)... 

A traditional FMEA using the RPN ranking system is carried out in the first instance. This analysis is summarised in Table 7.9. In Table 7.9,5/represents the probability of occurrence, S the severity, and Sj the detectability. The values for Sf, S and Sd are obtained by using the values detailed in Tables 7.1, 7.2 and 7.3, respectively. The same pool of experts that carried out the analysis for the fuzzy rule based method and grey theory method is used for the traditional FMEA analysis. This ensures the consistency in the opinion of each expert. 

The data from the FMEA in Tables 7.9 and 7.12 is used here to demonstrate the application of the grey theory method. The same data is used for all three methods (traditional I lEA, fuzzy rule base and grey theory), to enable comparisons of the results. The comparative series is generated based on the linguistic terms assigned to each event for the three variables considered and is represented in a matrix linguistically and then converted by defuzzification to express it numerically as seen in the matrix below ... 

Similarly, the degree of relation is calculated for all the events identified in the FMEA to produce a ranking that determines the priority for attention. The complete analysis of the test case using grey theory is tabulated as seen in Table 7.14. 

The effects of the weighting coefficient introduced in the grey theory method can be clearly seen in the results obtained for events 17 and 21, where Sf, S and S are assigned Low, High... 

The described method using grey theory (with the weighting factors of the linguistic variables) would be suitable for use in Step 2 of the FSA (risk estimation phase) as discussed in Chapter... 

The traditional FMEA, the fuzzy rule based method and the grey theory approach may complement each other to produce a risk ranking with confidence. 

Pillay A. and Wang J., (2003) A Risk Ranking Approach Incorporating Fuzzy Set Theory and Grey Theory , Engineering Reliability and System Safety, Vol. 79, No. 1, pp. 61-67. 

Table 7.14 Modified FMEA Using Grey Theory...

ID Component Failure Mode RPN Fuzzy rule base Grey Theory Ranking (RPN) Ranking (Rule base) Ranking (Grey theory)... 

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