and 



e|^ is the value of the k^'^ figure of merit 



aj is the probability that the system is in state i 



djj is the probability that the effective state of the system 

 is j, given that the mission was begun in state i 



Cji^ is the value of the k^'^ figure of merit, given that the 

 effective state of the mission is j 



The effectiveness vector E = e|^ can be considered to be composed 

 of three components; 



1. The availability vector A = aj 



2. The dependability matrix [D] = dj: 



3. The capability matrix [C] = Cj|^ 

 Therefore 



E = e. = I X Z ^i dij Cjk = A [D] [C] 



i = 1 j = 



Availability Vector 



The availability vector is a row vector 



A = [a| . . . aj . . . a^] 



The term aj is the probability the system is in the i^'^ state at the time the 

 mission begins. 



33 



