Active-redundancy allocation in systems

An effective way of improving the reliability of a system is the allocation of active redundancies. Let X/sub 1/, X/sub 2/ be s-independent lifetimes of the components C/sub 1/ and C/sub 2/, respectively, which form a series system. Let us denote U/sub 1/ = min(max(X/sub 1/,X),X/sub 2/) and U/sub 2/ = min(X/sub 1/, max(X/sub 2/, X)), where X is the lifetime of a redundancy (say R) s-independent of X/sub 1/ and X/sub 2/. That is, U/sub 1/(U/sub 2/) denote the lifetime of a system obtained by allocating R to C/sub 1/(C/sub 2/) as an active redundancy. Singh and Misra (1994) considered the criterion where C/sub 1/ is preferred to C/sub 2/ for the allocation of R as active redundancy if P(U/sub 1/ > U/sub 2/) /spl ges/ P(U/sub 2/ > U/sub 1/). In this paper, we use the same criterion of Singh and Misra (1994). We investigate the allocation of one active redundancy when it differs depending on the component with which it is to be allocated. We also compare the allocation of two active redundancies (say R/sub 1/ and R/sub 2/) in two different ways; that is, R/sub 1/ with C/sub 1/ & R/sub 2/ with C/sub 2/, and viceversa. For this case, the hazard rate order plays an important role. We furthermore consider the allocation of active redundancy to k-out-of-n: G systems.