Grey Theory Application

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 difference between the comparative series and standard series is then calculated and expressed as a matrix. Since all entries for the matrix representing the standard series was determined to be 0, the difference between the comparative and standard series would be equal to the comparative series (considering that A, (k) =11 x ik)- x, (k) II). 

Using the values obtained from the difference of the standard and comparative series, the grey relation coefficient, y xo(k),xi(k)], is calculated using Equation (7.3) for each variable of the events identified in the P MEA. Take [x/(]) x/(2) xj(3)] = [Rem High High] as an example. Equation (7.3) can be simplified and is represented by Equation (7.10) (Pillay (2001), Pillay and Wang (2003))  

One of the objectives of applying an FMEA study to fishing vessels is to identify areas where safety features are lacking in the system. These include interlocks, alarms, auto cut-off/shut- 

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  

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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 advantages of the described fuzzy rule based method and grey theory method for application to FMEA of ships can be summarised as follows (Pillay (2001), Pillay and Wang... 

Shire, SJ Hanania, GIH Gurd, FRN, Electrostatic Effects in Myoglobin. Application of the Modified Tanford-Kirkwood Theory to Myoglobins from Elorse, California Grey Whale, Harbor Seal, and California Sea Lion, Biochemistry 14, 1352, 1975. 

In the application of Grey System Theory to forecast the emission volume of gas from coal mine, we usually select a grey system theoretical differential equation model called GM(1, 1) which includes a first-order variable. The forecasting process can be split to three steps grey generation, parameter calculation and precision test. 

Si Feng, et al. 1999. The grey system theory and its application. BeijingThe Science Press (in Chinese). 

Wu Aiyou, et al. 2005. Application of the grey system theory for predicting amout of mine gas emission in coal mine, Journal of china coal society, 30(5) 589-592 (in Chinese). 

Hu Jinhang. 2007. The application of grey system theory in mathematical modeling. Science and Technology Consulting Herald (8) 94-95... 

Liu S, Lin Y, Forrest JYL (2010) Grey systems theory and applications. Springer, Berlin (Vol 68)... 

It is the task of corrosion experts to predict what will happen, to highlight possible limitations in lifetime or in acceptable stress for the material under consideration, to the extent allowed by theory and experience. Many grey and uncertain areas still exist. These will incite corrosion experts to adopt a cautious attitude, but also promote a certain boldness, because in many cases, predictions can be made based on experience with existing applications, without taking an inconsiderate risk. 

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

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