Grey Relation Coefficient

The standard series is an objective series that reflects the ideal or desired level of all the decision factors and can be expressed asxo = Ml) X(t(2)... xe(K)]. This could be assumed to be the lowest level of the linguistic terms describing the decision factors. The difference between the two series (comparative and standard series) is calculated. The grey relation coefficient is obtained using Equation (7.3) ... 

The grey relation coefficient, y xo(k),x,ik) k= 1,2, 3), is calculated using Equation (7.3) for each of the failure events identiEed in the FMEA. In the example used in Table 7.5, the grey relation coefficient can be calculated as shown here, assuming that = 0.5 ... 

The grey relation coefficients for events B and C are calculated in the same way. The results of these calculations are summarised as seen in Table 7.6. 

Consider the first event where Sf, S and Sd are assigned Remote, High and High for the probability of occurrence, severity and detectability, respectively. The grey relation coefficients y/, y and yd are calculated as shown below ... 

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). 

Hong G., (1986) Identification Coefficient of Relational Grade of Grey Systems , Fuzzy Mathematics, Vol. 2, pp. 55-58. 

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