Computing the elements of the availability vector requires that the 

 n states be defined. Also, account must be taken of the failure and repair 

 time distributions, checkout procedures, and similar factors to determine 

 the probability that a system is in the i state. The total number of states 

 which must be explicitly represented in the analysis depends on the system 

 and the degree of importance associated with its availability. 



Dependability iVIatrix 



The dependability matrix permits representation of the system during 

 a mission based on its condition at the beginning of the mission. It is a square 

 array of numbers 



[D] = 



dii . . . d 



'nl 



In 



where 



n 



J = 1 



djj = 1; i = 1, 



and djj is the probability that the system is in state j, given that the mission 

 was begun in state i. 



Formulation of the dependability matrix is dependent upon the effect 

 of failures during a mission and whether repair is possible during the mission. 

 In an ICBM, for instance, no repair is possible during a mission and the state 

 of the system is important only at the end of a mission. For most of the 

 heavy-lift systems discussed earlier, limited repair is possible during a mission 

 yet the fraction of the time out of commission is a mission criterion as is the 

 time at which the failure occurs. 



Capability Matrix 



.th 



The element Cj|^ of the capability matrix is the k^'' figure of merit 

 associated with the effectiveness of the system in state j. 



34 



