Newton-Raphson Versus Fisher Scoring Algorithms in Calculating Maximum Likelihood Estimates

In this work we explore the difficulties and the means by which maximum likelihood estimates can be calculated iteratively when direct solutions do not exist. The NewtonRaphson algorithm can be used to do these calculations. However, this algorithm has certain limitations that will be discussed. An alternative algorithm, Fisher scoring, which is less dependent on specific data values, is a good replacement. The Fisher scoring method converged for data sets available to the authors, that would not converge when using the Newton-Raphson algorithm. An analysis and discussion of both algorithms will be presented. Their real world application on analysis of jet engine part inspection data will also be discussed. This research was initiated with the end goal of improving the safety and reliability of aircraft through understanding the capabilities of current nondestructive inspection techniques. The main emphases in designing “safe” aircraft are to prevent failures and to ensure that the failure of one component will not result in a loss of the aircraft. In the safe-life concept individual aircraft are retired from service when they have flown a specified number of flight hours or a specified number of missions. This predetermined length of time is called the aircraft’s design life. The design life is based