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In multiple criteria secretary problem selection of a unit is based on two independent characteristics. The units, appeared before an observer are known (say N). N is considered as best rank of a unit. A unit is selected, if it is better with respect to either first or second or both the characteristics. In this paper, joint probability distributions along with marginal distributions (of real ranks of both the characteristics and the position at which the selection is made) are derived systematically using simple and explicable method. Further these marginal distributions are used to derive expected cost of inspection and expected value of real rank of selected unit. A new criterion for selecting the best unit based on expected real rank is developed.

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