Parameter Estimation of Jelinski-Moranda Model Based on Weighted Nonlinear Least Squares and Heteroscedasticity

Abstract

Parameter estimation method of Jelinski-Moranda (JM) model based on weighted nonlinear least squares (WNLS) is proposed. The formulae of resolving the parameter WNLS estimation (WNLSE) are derived, and the empirical weight function and heteroscedasticity problem are discussed. The effects of optimization parameter estimation selection based on maximum likelihood estimation (MLE) method, least squares estimation (LSE) method and weighted nonlinear least squares estimation (WNLSE) method are also investigated. Two strategies of heteroscedasticity decision and weighting methods embedded in JM model prediction process are also investigated. The experimental results on standard software reliability analysis database-Naval Tactical Data System (NTDS) and three datasets used by J.D. Musa demonstrate that WNLSE method can be superior to LSE and MLE under the relative error (RE) criterion.