Intermittent power interruptions and blackouts with long outage durations are very common, especially on weak distribution grids such as in developing countries. This paper proposes a hybrid photovoltaic (PV)-battery-system sizing optimization through a genetic algorithm to address the reliability in fragile grids measured by the loss of power supply probability (LPSP) index. Recorded historical outage data from a real stochastic grid in Ethiopia and measured customer load is used. The resulting hybrid-system Pareto solutions give the flexibility for customers/power utilities to choose appropriate sizes based on the required reliability level. To evaluate the sizing solutions’ robustness, this work considers and compares grid outage modeling through two different approaches. The first is a Markov model, developed to be minimally implemented with limited outage data available. The second is a Weibull model, commonly used to describe extreme phenomena and failure analysis. It is more faithful in reproducing the dispersion of outage events. Using these models, the effectiveness and performance of the PV-battery system is verified on a large number of simulated outage scenarios, to estimate the real performance of the optimized design. It leads to a more accurate evaluation of the behavior of a renewable power system to a weak and unreliable electrical grid.