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An array of passive silicon-on-insulator optical devices is laid out in repeating patterns on four foundry-fabricated wafers. The physical and optical characterization of these microrings, racetrack resonators, and directional couplers are found to exhibit significant variation in optical response. A device-heating experiment carried out on a number of different devices demonstrates that thermal effects are independent of the device's location on the wafer. An analysis of the variation of the optical responses of the room-temperature devices is used to determine the process variation. We find that if we form successive arrays of the values of a quantity of interest (the peak wavelength of a transfer function) at a single device at some point on the wafer, and then increase the size of the array by including the values of the devices at ever greater distances from the original, then the variance of the values of the successive arrays increases linearly with the linear extent of the sample. That is, the process variation exhibits "random walk" pattern with spatial extent. We express the process variation in units of variance per length and find that our measured values agree with others in the literature; that is, the process variation is approximately 1 nm2/cm.