Background of Grey Theory

Grey system theory was proposed and developed by Deng in 1982 (Deng (1982, 1989)). In grey systems, the information, such as operation, mechanism, structure and behaviour, are neither deterministic nor totally unknown, but are partially known. It explores system behaviour using relation analysis and model construction. It also deals with making decisions characterised by incomplete information (Shih et al. (1996), Wu et al. (1984)). 

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)  

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 degree of relation in FMEA denotes the relationship between the potential causes and the optimal value of the decision factors. The higher the value obtained from Equation (7.5), the smaller the effect of the identified events. 

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