this paper presents a new mathematical model for a redundancyallocation problem (rap) withcold-standby redundancy strategy and multiple component choices.the applications of the proposed model arecommon in electrical power, transformation,telecommunication systems,etc.manystudies have concentrated onone type of time-to-failure, butin thispaper, two components of time-to-failures which follow hy...

A new definition of a multivalued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This arises naturally from the cylinder transformation also wellspring exponential scales. will lead to function arbitrary with familiar and useful properties previous definitions in literature lacked.