Analytical Solution to the Consistency Problem for the Littlewood Model inSoftware Reliability

摘要

Two different approaches to construct estimators for the model parameters of theLittlewood model are considered and whether they are consistent or not is investigated. Littlewood's parametric software reliability model is presented. The maximum likelihood estimation method for counting processes is discussed. It is shown that for the software reliability model of Littlewood, the likelihood equations can have more than one solution. It is also shown how an initial estimator, that is square root of n-consistent, can be found. An algorithm that produces an asymptotically efficient estimator is described. A second, more analytical approach to the problem, exploiting the mathematical properties of the log-likelihood function of the Littlewood model is described. The results of the two methods are compared.