We propose and study a planning problem called Sequential Fault-Intolerant Process Planning (SFIPP). SFIPP captures a reward structure common in many sequential multi-stage decision problems where the planning is deemed successful only if all stages succeed. Such reward structures differ from classic additive reward ones and arise in important applications such as security, drug/material discovery, and quality-critical product design. We design provably tight online algorithms for settings in which one needs to pick between different actions with unknown success chances at each stage. We do so both for the foundational case in which the behavior of actions is deterministic and for the case of probabilistic action outcomes. In the latter, we effectively balance exploration for learning and exploitation for planning by applying multi-armed bandit algorithms. We further specialize our algorithms exploiting additional information about the structure of the SFIPP instance and empirically demonstrate that they outperform our general algorithm.