Transformation from availability expression to failure frequency expression

The problem of computing the system´s Failure Frequency is reduced to the problem of computing its Availability. This is performed by a transformation operator. However, the existing transformation operator is not practical because its transformation time increases exponentially with system size. To overcome this difficulty, this paper proposes a new method of transforming the Availability expression of a system into the corresponding Failure Frequency expression of the system. This method is based on a matrix approach using a 2 × 2 matrix consisting of 0, Availability, and Failure Frequency in an appropriate manner. This transformation also enables algorithms for computing the Availability of a system to be transformed into algorithms for computing its Failure Frequency by replacing parameters and operations with matrix parameters and operations. The computation time after transformation is linear with respect to the original Availability algorithm. This implies that the problems of computing other well-known reliability measures including, Availability, Unavailability, MTBF, MTTR, MCT, Failure Rate, Failure Rate, and Failure Frequency, are reduced to only the Availability computation problem.