# Application of probability principles to ecodesign function

1.2 Probability approach

To illustrate the model-set probability, let us consider the sample space Q that contains all the possible subsets (events) defined by Equation (1) and illustrated in Figure 3. Since the three key sets Q, H and E are composed of several variable elements associated to the different stages involved in the design process where each key set is assumed to fulfil a specific function; it can therefore be written that (Attaf, 2007):

Q = { x1, X2 , X3 , ….. , Xm}

H = { yi, У2, уз,……….. , yn } (2)

E = { zi, Z2, Z3,……. , Zp } probabilistic measure. Figure 4 illustrates the different branches representing the possible events (Attaf, 2009).

1st proposition    2nd proposition

3rd proposition иПНПЕ) QnHnE ОПНПЕ ОПНПЕ ОПНПЕ ОПНПЕ ОПНПЕ ОПНПЕ

Events

Fig. 4. Probability tree diagram and possible events

The probability theory will be applied to investigate the behaviour of the subset F, identified by the encircled area in Figure 4. As a result, the corresponding event and its associated probability can respectively be written as (Attaf, 2007 & 2009)

 F = QnHnE (3) P(F ) = P(QnHnE) (4)