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(sic)/kg and standard deviation of 0.74(sic)/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.