Robust collaborative optimization (RCO) is a widely used approach to design multidisciplinary system under uncertainty. In most of the existing RCO frameworks, the mean of the state variable is considered as auxiliary design variable and the implicit uncertainty propagation method is employed for estimating their uncertainties (interval or standard deviation), which are then used to calculate uncertainties in the ending performances. However, as repeated calculation of the global sensitivity equations (GSE) is demanded during the optimization process of the existing approaches, it is typically very cumbersome or even impossible to obtain GSE for many practical engineering problems due to the non-smoothness and discontinuity of the black-box-type analysis models. To address this issue, a new RCO method is proposed in this paper, in which the standard deviation of the state variable is introduced as auxiliary design variable in addition to the mean. Accordingly, interdisciplinary compatibility constraint on the standard deviation of state variable is added to enhance the design compatibility between various disciplines. The effectiveness of the proposed method is demonstrated through two mathematical examples. The results generated by the conventional robust all-in-one (RAIO) approach are used as benchmarks for comparison. Our study shows that the optimal solutions produced by the proposed RCO method are highly close to those of RAIO while exhibiting good interdisciplinary compatibility.