A Note on Kabak's “Some Aspects of Optimal Design”

Abstract

Abstract Kabak in (1) considers a system's steady-state availability with mean uptime of U and mean downtime of D. He then formulates a model of total system cost of: as an approximation to the actual model which may be written as: The approximation is used because it is assumed that D << U. In the above formulas K 1 U a is the cost of equipment that has a mean uptime of U; and K 2 D −b is the cost of equipment that has a mean downtime of D. The downtime costs are assumed to be proportional to the downtime and are therefore given by the last term in the above equations. Kabak solves the first equation, (the approximation), with geometric programming because, he points out that the exact model “does not lend itself to solution by geometric programming.” However, this author asserts that the “necessary” conditions for the solution of any geometric program can show that the exact model's geometric programming solution is tightly bounded and gives considerable information as to the effect of approximating the...