You choose a certain amount of radioactive material, so you have the information that, given its half-life, there is a 0.5 probability of a decay event occurring in a known time interval. This knowledge in fact corresponds to a measurement because you have some classical information. It also tells you that after 1/10 of the time interval the probability of decay is 0.05; in fact you know the probability of decay over the entire interval of time. This measurement is usually called preparation of a quantum state. When the decay event occurs (or doesn't), the cat 'measures' the quantum state; actually the cat is measuring the state over the whole interval. When the box is opened at the end of the allotted time, a human observer sees the result of this measurement.