Estimating the number of errors in a system using a martingale approach

A new, efficient procedure estimates the number of errors in a system. A known number of seeded errors are inserted into a system. The failure intensities of the seeded and real errors are allowed to be different and time dependent. When an error is detected during the test, it is removed from the system. The testing process is observed for a fixed amount of time τ. Martingale theory is used to derive a class of estimators for the number of seeded errors in a continuous time setting. Some of the estimators and their associated standard deviations have explicit expressions. An optimal estimator among the class of estimators is obtained. A simulation study assesses the performance of the proposed estimators