lambda_{DU1} and lambda_{DU2} are rates (cf. e.g., transitions 3->5 and 1->5), thus sqrt(lambda_{DU1} * lambda_{DU2}) is the geometric mean, and a rate, too. Beta is probably some weight, and it is without unit.
Thanks for your attention. As you know, when the failure of a system or a component obey from exponential distribution we use lambda as failure rate of a system. Unfortunately, in this model, I cannot understand why author use the sqrt (lambda_{DU1} * lambda_{DU2}) and which behavior of a system can be described by this rate?
Above-mentioned figure achieved from the paper entitled: "Calculating the Probability of Failure on Demand (PFD) of complex structures by means of Markov Models".