Operational risk assessment is a stochastic approach to power system planning with a lead time of hours to days starting from an observation instant. Operational risk assessment requires component state probabilities as a function of time. The commonly used two-state component outage model does not include protection failures. Two challenges occur when including these: estimating the probability of hidden failure states at the observation instant and estimating time-dependent state probabilities. Both challenges are addressed in this paper. By deploying a Markov model with average transition rates, the probability of the hidden failure states at the observation instant is estimated. From this initial probability and a Markov model with transition rates valid during the lead time, the state probabilities as a function of time are obtained. The Taylor expansion is used to obtain linear, square, or higher-order approximations of the state probabilities as a function of time. The method is illustrated using two case studies: a 4-state component model and a 15-state component model; different levels of adverse weather during the lead time are used.