Grey Theory Method

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 ... 

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. 

On the basis of grey system theory and fuzzy comprehensive assessment method, an overseas investment risk assessment model that is suitable for Chinese mining enterprises is to be established by adopting the AHP index weighing. The contents... 

In this paper, based on the grey system theory, a fuzzy comprehensive assessment model is established for overseas investment risk of mining enterprises, which provides a quantitative method of the assessment and study for the overseas investment risk of mining enterprises. This model can deal with the greyness and fuzziness properly in the assessment process and reduce the impact of human factors on the assessment results. At the same time, from the applied analysis on risks of Potash project in Canada invested by Yankuang... 

The marine industry is recognising the need for powerful techniques that can be used to perform risk analysis of marine systems. One technique that has been applied in both national and international marine regulations and operations is Failure Mode and Effects Analysis (FMEA). This risk analysis tool assumes that a failure mode occurs in a system/component through some failure mechanism. The effect of this failure is then evaluated. A risk ranking is produced in order to prioritise the attention for each of the failure modes identified. The traditional method utilises the Risk Priority Number (RPN) ranking system. This method determines the RPN by finding the multiplication of factor scores. The three factors considered are probability of failure, severity and detectability. Traditional FMEA has been criticised to have several weaknesses. These weaknesses are addressed in this Chapter. A new approach, which utilises the fuzzy rules base and grey relation theory, is presented. 

Junjiang H., (1986) On the Applications of Grey System Theory and Methods to History Studies , Journal of Social Sciences, Vol. 10, pp. 64-6S. 

Wu J.R. and Ouhyoung M., (1994) Reducing the Latency in Head-mounted Display by a Novel Prediction Method Using Grey System Theory , Computer Grrqihics Forum, Vol. 13, No. 3, pp. 503-512. 

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