An explanation of the quantum measurement process must do more than produce the Born Rule.Conventional quantum mechanics makes other specific predictions about intermediate states,which develop before the completion of a measurement. This paper’s measurement model addressesthat more general problem. For a detector with efficiency less than one, the model predictsthe conventional quantum results almost exactly: an initial superposed state develops into awell-defined mixture of eigenstate and altered superposition. The minor departures of the modelfrom conventional quantum mechanics could be revealed, in principle, in an optical interferenceexperiment that is also described here. The measurement model assumes that the conversion intoan eigenstate is not instantaneous but results from a random sequence of unitary perturbationsarising from conventional quantum interactions with the microscopic components of the measuringdevice. A random walk model describes how wave functions change. And the model’s successrelies on small biases in transition probabilities which, however, could be expected of a devicedesigned to measure a specific observable. The biases help to define a generalized Ornstein-Uhlenbeck equation for the distribution of quantum states, and it admits solutions that substantiallyreplicate those of conventional quantum mechanics.