ON REDUNDANCY ALLOCATIONS IN SYSTEMS

Allocation of a redundant component in a system in order to optimize, in some sense, the lifetime of the system is an important problem in r eliability theory, having practical applications. Consider a series sy stem consisting of two components (say C-1, and C-2), having independe nt random lifetimes X(1) and X(2), and suppose a component C having ra ndom lifetime X (independent of X(1) and X(2)) is available for active redundancy with one of the components. Let U-1 = min(max(X(1), X), X( 2)) and U-2 = min(X(1), max(X(2), X)), so that U-1 (U-2) denote the li fetime of a system obtained by allocating C to C-1 (C-2). We consider the criterion where C-1 is preferred to C-2 for redundancy allocation if P(U-1 > U-2) greater than or equal to P(U-2 > U-1). Here we investi gate the problem of allocating C to C-1, or C-2, with respect to the a bove criterion. We also consider the standby redundancy for series and parallel systems with respect to the above criterion. The problem of allocating an active redundant component in order that the resulting s ystem has the smallest failure rate function is also considered and it is observed that unlike stochastic optimization, here the lifetime di stribution of the redundant component also plays a role, making the pr oblem of even active redundancy allocation more complex.