Lumen depreciation, the condition that the light output falls below a fraction of its peak output, is known to be the main failure mode in light emitting diodes (LEDs). In lighting systems comprising multiple LEDs, lumen depreciation leads to reduced average illuminance and a distorted illumination rendering. Diagnosing lumen depreciation in LED lighting systems is thus an important problem. We propose an estimation approach to diagnosing individual LED failures using a photosensor system. We specifically study the impact of perturbations in the photosensor positions on diagnosability by analyzing the sensor output matrix-the matrix relating the luminous flux values of the multiple LEDs to the measurements at the photosensor system. The conditions on diagnosability are first derived in terms of bounds on the smallest singular value of the sensor output matrix. Subsequently, sufficient conditions are derived on the photosensor positions to ensure that individual LED lumen depreciations are diagnosable. Numerical results are provided to validate our analytical results.