Element availability importance in generalized k-out-of-r-from-n systems

An algorithm for evaluating the overall system availability and the availability importance of elements in a generalized consecutive k-out-of-r-from-n:F system is presented. This system consists of n linearly ordered nonidentical elements with different reliability characteristics and performance rates. Each element can have two states: (i) complete failure with a performance rate of zero; and (ii) perfect functioning with a nominal performance rate. The system fails if the sum of the performance rates of any r consecutive elements is lower than a demand W. The suggested algorithm, based on an extended universal moment generating function, is convenient for numerical implementation. Analytical and numerical examples of evaluating availability importance indices are presented.