American Review of Mathematics and Statistics

Optimal Reliability Allocation
Constantin Udriște, Saad Abbas Abed, Ali Sapeeh Rasheed

Abstract
A system (mechanical, electrical, computer hardware and software etc) is generally designed as an assembly of subsystems, each with its own reliability attributes. The cost of the system is the sum of the costs for all the subsystems. This paper examines possible approaches to allocate the reliability values based on minimization of the total cost on the intersection between Tzitzeica semispace and a unit hypercube. The original results include: (i) a critical point is a fixed point of a suitable application, (ii) theorems for restoring Riemannian convex functions; (iii) the first cost with exponential behavior is Euclidean convex; the second cost with exponential behavior is Riemannian convex; our particular posynomial cost is Euclidean convex, (iv) an additively decomposable cost function is convex on a product Riemannian manifold.

Full Text: PDF     DOI: 10.15640/arms.v4n2a9