To match intermittent solar energy supply with energy demand, power-to-hydrogen is a viable solution. In this framework, designing a directly coupled photovoltaic-electrolyzer system assuming deterministic parameters (i.e.perfectly known and fixed parameters) is widely studied. However, considering deterministic model parameters in optimization disregards the inherent uncertainty of the system performance during real-life operation (e.g.due to unexpected costs or ineffective maintenance), leading to a fragile, suboptimal direct coupling of the photovoltaic array with the electrolyzer stack. To avoid a suboptimal coupling, we performed a design optimization under parameter uncertainties (i.e.robust design optimization). This paper provides the deterministic designs, robust designs and a global sensitivity analysis on the hydrogen production and levelized cost of hydrogen. The technical robust design provides a 43% reduction in hydrogen production standard deviation compared to the deterministic design, while the robust, cost-efficient design achieves a mean levelized cost of hydrogen of 6.4€/kg and standard deviation of 0.74€/kg. The discount rate and capital expenditure parameters dominate the standard deviation by 52% and 39% respectively. Therefore, bulk manufacturing of these technologies and more demonstration projects are the main actions to improve the robustness. Future works will focus on including accurate probability distributions, a demand load, the grid and batteries to the system.